JBIS Journal of the British Interplanetary Society
VOL. 70 No. 2/3/4 FEBRUARY/MARCH/APRIL 2017
Contents
7TH EUROPEAN CONFERENCE ON SPACE DEBRIS Temporal Analysis of ENVISAT’s Rotational Motion Debris Attitude Motion Measurements and Modelling by Combining Different Observation Techniques Assessment of Post-Manoeuvre Observation Correlation Using Short-Arc Tracklets Optical Measurements Association Using Optimized Boundary Value Initial Orbit Determination Coupled with Markov Clustering Algorithm Method of Predicting and Processing Breakups of Space Objects GESTRA-Technology Aspects and Mode Design for Space Surveillance and Tracking Information-Theoretic Approaches to Space Object Collision Risk Induced by the Uncatalogued Space Debris Population in the Presence of Large Constellations Sensitivity of the Space Debris Environment to Large Constellations and Small Satellites Status of the Space Environment: Current Level of Adherence to the Space Debris Mitigation Fast Re-Entry Deorbitation with Acceptable Risk Level Architecture and First Achievements of a Simulation for the Approach of an Uncooperative Target E.Deorbit - ESA’s Active Debris Removal Mission Airbus DS Vision Based Navigation Solutions Tested on LIRIS Experiment Data
ISSN 0007-084X www.bis-space.com Publication Date: 15 August 2017 Guest editor International Advisory Board Dr Holger Krag, ESA deputy editor Rachel Armstrong, Newcastle University, UK Duncan Law-Green Peter Bainum, Howard University, USA AssociAte editors Stephen Ashworth Stephen Baxter, Science & Science Fiction Writer, UK Keith Cooper Stephen Gamble James Benford, Microwave Sciences, California, USA Paul Gilster Rob Swinney James Biggs, The University of Strathclyde, UK production AssistAnt Anu Bowman, Foundation for Enterprise Development, California, USA B. Jones Gerald Cleaver, Baylor University, USA promotion G. Norman Charles Cockell, University of Edinburgh, UK JBis office Arthur C. Clarke House, 27/29 South Ian A. Crawford, Birkbeck College London, UK Lambeth Road, London, SW8 1SZ, UK Tel: 020 7735 3160 Adam Crowl, Icarus Interstellar, Australia Fax: 020 7582 7167 Email: [email protected] Eric W. Davis, Institute for Advanced Studies at Austin, USA www.bis-space.com Kathryn Denning, York University, Toronto, Canada If you wish to submit a paper our Guidelines for Authors can be obtained Martyn Fogg, Probability Research Group, UK from the JBIS office or online: www.bis- space.com/what-we-do/publications/ Raghavan Gopalaswami, Aerospace Researcher, India writing-papers distriBution detAils Lamartine Guimarães, Institute for Advanced Studies, Brazil JBIS is distributed worldwide by mail and may be received by annual subscription Mark Hempsell, Hempsell Astronautics Ltd, UK or purchase of single copies. It is available through membership of the British Takuto Ishimatsu, Massachusetts Institute of Technology, USA Interplanetary Society at much reduced rates. Subscription details for members, Les Johnson, Marshall Space Flight Center, USA non-members and libraries are available from the above address. Terry Kammash, University of Michigan, USA JBIS is a publication which promotes the mission of the British Interplanetary Kelvin F. Long, Initiative for Interstellar Studies Society. Opinions expressed in signed articles are those of the contributors and Inoue Makoto, Institute of Astronomy & Astrophysics Academia Sinica, Taiwan do not necessarily reflect the views of the Editor or the Council of the British Interplanetary Society. Security clearance, Gregory L. Matloff, City University New York, USA where necessary, is the responsibility of the author. Koichi Mori, Nagoya University, Japan
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VOL. 70 No. 2/3/4 FEBRUARY/MARCH/APRIL 2017
LIST OF CONTENTS 7TH EUROPEAN CONFERENCE ON SPACE DEBRIS
45 Temporal Analysis of ENVISAT’s Rotational Motion Svenja Sommer, J. Rosebrock, D. Cerutti-Maori et al. 52 Debris Attitude Motion Measurements and Modelling by Combining Different Observation Techniques Jiří Šilha, T. Schildknecht, J.-N. Pittet et al. 63 Assessment of Post-Manoeuvre Observation Correlation Using Short-Arc Tracklets J.A. Siminski, T. Flohrer and T. Schildknecht 69 Optical Measurements Association Using Optimized Boundary Value Initial Orbit Determination Coupled with Markov Clustering Algorithm Carlos Yanez, Juan-Carlos Dolado, Pascal Richard et al. 77 Method of Predicting and Processing Breakups of Space Objects Zach Slatton and Diana McKissock 82 GESTRA-Technology Aspects and Mode Design for Space Surveillance and Tracking H. Wilden, C. Kirchner, O. Peters et al. 85 Information-Theoretic Approaches to Space Object Collision K. DeMars and M. Gualdoni 98 Risk Induced by the Uncatalogued Space Debris Population in the Presence of Large Constellations Bruno Revelin and Juan-Carlos Dolado-Perez 105 Sensitivity of the Space Debris Environment to Large Constellations and Small Satellites H.G. Lewis, J. Radtke, A. Rossi et al. 118 Status of the Space Environment: Current Level of Adherence to the Space Debris Mitigation Stefan Frey and Stijn Lemmens 125 Fast Re-Entry Deorbitation with Acceptable Risk Level Elisabet Cid Borobia, Claire Frémeaux and Jean-François Goester 134 Architecture and First Achievements of a Simulation for the Approach of an Uncooperative Target S. Peters, W. Eidel, R. Förstner et al. 143 E.Deorbit - ESA’s Active Debris Removal Mission Robin Biesbroek, Luisa Innocenti, Andrew Wolahan et al. 152 Airbus DS Vision Based Navigation Solutions Tested on LIRIS Experiment Data A. Masson, C. Haskamp, I. Ahrns et al.
Mission The British Interplanetary Society promotes the exploration and use of space for the benefit of humanity, by connecting people to create, educate and inspire, and advance knowledge in all aspects of astronautics.
41 IntroductionJournal of the to British this Special Interplanetary Issue on SpaceSociety, Elevators Vol. 70, p.42, 2017
The British Interplanetary Society is proud to publish this special, triple issue edition of JBIS, dealing with the critically important subject of space debris. I would like to thank Dr. Holger Krag, Head of the European Space Agency’s Space Debris Office, for agreeing to act as guest editor for this special edition and selecting papers from the recent conference in Darmstadt that he organised. Holger is a world leading expert in this field and his involvement with this special publication is greatly appreciated
Roger Longstaff Editor, Journal of the British Interplanetary Society
The production of this issue was sponsored by
42 Journal of the British Interplanetary Society, Vol. 70,David p.43, 2017Raitt
7th European Conference on Space Debris Guest Editorial
Since 1957, more than 5,250 space launches have led to an on-orbit population today of more than 23,000 tracked debris objects. Only about 1,200 are functional spacecraft. The remaining are classified as space debris and no longer serve any useful purpose. A large percentage of the routinely tracked objects are fragments from the approximately 290 breakups, explosions and collisions of satellites or rocket bodies that are known to have occurred. An estimated 750,000 objects larger than 1 cm and a staggering 166 million objects larger than 1 mm are thought to reside in commercially and scientifically valuable Earth orbits.
Today’s active satellite infrastructure includes telecom, weather, navigation, broadcast and climate-monitoring missions, and these provide a multitude of critical services and daily benefits to citizens and economies. Their loss, due to their orbits being polluted by debris, would severely damage modern society.
As the world’s largest scientific gathering dedicated to space debris, The 7th European Conference on Space Debris saw the best-ever attendance by some 350 participants from space organisations, academia and industry who delivered papers on the latest research into the debris threat and on new technologies aimed at mitigating debris creation and reducing the orbital debris population. The 4-day conference took place over the 18th-21st April at the ESA European Space Operations Centre (ESOC) in Darmstadt, Germany. The conference was co-sponsored by ASI (Agenzia Spatiale Italiana), CNES (Centre National d’Etudes Spatiales), DLR (Deutsches Zentrum für Luft- und Raumfahrt), UKSA (United Kingdom Space Agency), COSPAR (Committee on Space Research), and IAA (Internal Academy of Astronautics).
For the first time in the 24-year history of the quadrennial debris conference series, the media briefing was attended by ESA Director General Jan Wörner and Brigitte Zypries, German Federal Minister for Economic Affairs and Energy and German National Aerospace Coordinator.
The findings were delivered by researchers and specialists of more than 20 space-faring nations in 244 scientific papers. It became apparent that debris mitigation strategies, defined long ago, are important today as never before. However, the venting of residual energy from satellites and upper stages at the end of their missions to prevent explosive break-ups, and the disposal of space objects through a final manoeuvre, remain challenges. Numerous novel solutions were presented to support these important mitigation measures. Many authors emphasized that successful execution of these measures is becoming ever more important in view of upcoming ‘megaconstellations’ comprising thousands of satellites in low Earth orbit.
As already postulated by keynote speaker Donald Kessler decades ago, the number of space-debris objects in some orbital regions grows even if mitigation measures are applied. To prevent this uncontrolled growth, the active removal or deorbiting of selected large defunct space objects is required in addition to the full application of mitigation measures. The technology required for deorbiting is actively being studied today and the remarkable progress was displayed at the conference.
Another important field is the capacity for the surveillance and tracking of defunct space objects, which is a necessary precondition to active collision avoidance and space situational awareness. The progress made by European actorsin this field is notable; space surveillance radars are currently under development in many European countries and laser technology promises high-precision tracking of space debris objects.
It has been a privilege and a major challenge at the same time, to select 14 papers out of the 244 excellent conference contributions. I hope that the present selection provides a reasonable cross-section of the work presented in Darmstadt. On behalf of the Programme Committee, I cordially thank the Journal of the British Interplanetary Society for the opportunity to issue a special edition dedicated to this important topic.
Let this publication be a source of inspiration for the space farers of today in their endeavour to preserve space for the use by the space farer of tomorrow.
Dr. Holger Krag Chair of the Programme Committee Head of ESA Space Debris Office Darmstadt, 3rd July 2017
7th European Conference on Space Debris: https://conference.sdo.esoc.esa.int/ ESA Space Debris Office: http://www.esa.int/debris Conference Movie: http://www.esa.int/spaceinvideos/Videos/2017/04/Space_debris_-_a_journey_to_Earth
43 IntroductionJournal of the to British this Special Interplanetary Issue on SpaceSociety, Elevators Vol. 70, p.44, 2017
70% of all catalogued objects are in low-Earth orbit (LEO), which extends to 2000 km above the Earth’s surface. To observe the Earth, spacecraft must orbit at such a low altitude. The spatial density of objects increases at high latitudes. (ESA)
44 Journal of the BritishTemporal Interplanetary Analysis ofSociety, ENVISAT’s Vol. 70, Rotational pp.45-51, Motion 2017
TEMPORAL ANALYSIS OF ENVISAT’S ROTATIONAL MOTION
SVENJA SOMMER*, J. ROSEBROCK, D. CERUTTI-MAORI AND L. LEUSHACKE Fraunhofer Institute for High Frequency Physics and Radar Techniques, Fraunhoferstraße 20, 53343 Wachtberg, Germany. Email: [email protected]*
The Earth-observing satellite ENVISAT failed in April 2012 and orbits with an uncontrolled attitude. In order to remove ENVISAT from space in a potential de-orbiting mission, the attitude state of the satellite has to be known. We present attitude estimations using ISAR images obtained with the Tracking and Imaging Radar (TIRA) during 2011 - 2017. By matching wire grid models to the 2D ISAR images, the rotation vector can be estimated. After loss of contact, the spin period of ENVISAT decreased and reached the minimum in 2013. Since then, the spin period increased by (75.0 ± 0.9) ms d-1 and reached 226 s in March 2017. An analysis of the rotation axis shows, that ENVISAT tumbles, where the rotation axis describes a nutation with a cone opening of about 80°. Keywords: ISAR, image sequences, attitude estimation, rotational motion, ENVISAT
1. INTRODUCTION
ENVISAT is one of the largest objects in orbit and the largest echoes received from the object are coherently processed to satellite launched by ESA. It is located in low earth orbit at gain 2D high resolution images. 767 km and, therefore, in a highly populated orbit region. ENVISAT lost contact to ground stations in April 2012. After Unlike optical instruments, the resolution of ISAR images efforts to re-establish contact failed, ISAR images, among is independent of range. Furthermore, radar systems are others, where used to determine the cause of the failure. ISAR active systems and can be operated day and night. Another images, together with photographic images from the French advantage compared to optical systems is the fact that radar imaging satellite Pleiades, showed, that no external damages systems are independent of the cloud coverage above the radar could be found. Still, ENVISAT is no longer controlled, or other weather related restrictions. Hence, TIRA is an ideal meaning that it poses an increased danger to other satellites instrument for space reconnaissance and for instance to observe due to possible collision, especially in an orbit with a high (uncontrolled) satellites over long time periods to detect and density of objects. estimate their rotational motion [7], that usually changes over time. Hence, ENVISAT is a possible target for a de-orbiting mission, where robotic satellites would capture ENVISAT and 2. ISAR IMAGING OF SATELLITES pull it into a re-entry orbit. For such manoeuvre, the rotational velocity vector, i.e. rotation axis and angular velocity, of the 2.1 Principle satellite is essential to be known. Several studies have estimated ENVISAT’s attitude and spin velocities with various methods. Radar measures the time delay between transmitting and Satellite laser ranging (SLR) and bi-static laser ranging were receiving a radar pulse that is reflected at an object. That way, used to study ENVISAT’s attitude [1, 2]. Ground based the range between radar and object is determined. To gain an photometry was used by Koshkin et al. [3] and, additional image of the object, not only range information is necessary, to experimental studies, simulations have been performed to but also information about the object structure perpendicular estimate the attitude of ENVISAT. Gómez et al. [4] simulated to range, the so-called cross-range. The range and cross-range the effects of Earth’s gravity gradient and eddy currents. Silha et span the image plane of an ISAR image. The cross-range can al. [5] used the software tool iOTA [6] to perform comparisons be estimated by utilizing the motion between the radar and between modelling and SLR observations. object. For satellite imaging, the radar is usually stationary on the Earth’s surface while the satellite passes over the radar. The In this paper, we present estimations of the rotational motion movement of the satellite and the radar during a pass is shown of ENVISAT from 2011 - 2017 using 2D inverse synthetic in Fig. 1. aperture radar (ISAR) imaging with the Tracking and Imaging The coordinate system used in this paper is the Earth centred Radar (TIRA), operated by Fraunhofer FHR in Wachtberg, inertial (ECI) coordinate system if not stated otherwise. The Germany. ISAR systems exploit the relative motion between x-axis points towards spring equinox, the z-axis is aligned the radar (which is usually stationary) and the object to be with the Earth’s spin axis and the y-axis is perpendicular to the imaged (which is moving and/or rotating). Through its motion, aforementioned. the object is illuminated from different aspect angles. Radar The motion of the satellite can be divided in two parts: This paper was presented at the ESA 7th European Conference on translation and rotation. The translational motion is due to the Space Debris, ESA/ESOC, Darmstadt, Germany, 18-21 April 2017 orbital motion. The range variation from the radar to a salient
45 Svenja Sommer, J. Rosebrock, D. Cerutti-Maori and L. Leushacke
Fig. 1 Observation geometry. point resulting from this motion and from Earth rotation needs to be compensated in order to gain ISAR images. The vector between the radar and object is called the line-of-sight (LOS) and changes while the satellite passes over the radar. The LOS direction relative to the satellite varies due to translational motion and Earth rotation but also due to a possible intrinsic rotation of the satellite. It is exploited to gain information about the object in cross-range as the relative distances between object points change between consecutive pulses causing corresponding phase changes. The effective rotation vector, responsible for the cross-scaling, is orthogonal to the plane spanned by the LOS moving relative to the satellite. Its norm, called rotation speed, is the angular velocity at which the LOS moves within its plane.
The rotation speed scales the cross-range of the ISAR image. That means, that the rotation affects the scaling of Fig. 2 Two ISAR images of one passage with a manually assigned the object in cross-range. Hence, the rotation vector must model (blue) and the projected WGM from the optimization be known a priori to estimate the cross-scaling of an ISAR (green). image. Although radar location, orbit and Earth rotation are usually well known, the intrinsic motion of the object makes the cross-scaling of ISAR images hard to determine. The In both images, the image is centred on the main body, while intrinsic rotation of the object is of great interest, but affects the solar panel is partly cut off. The manually assigned WGM the cross-scaling of the ISAR images, which should be used is shown in blue. to estimate the intrinsic rotation. The next step is to estimate a rotation vector which fits all 2.2 Attitude estimation assigned points in the best way. This step assumes, that the rotation vector ω is constant and does not change over the If the ISAR image planes and their scaling, relative to duration of the passage. If this assumption is not fulfilled, inertial coordinates, were known, the object’s attitude could the passage can be divided in several sub-passage, where the be estimated from its attitude relative to the image plane for assumption of a constant rotation vector can be upheld. The every ISAR image. The attitude relative to the image plane algorithm to determine the rotation vector is sketched in Fig. 3. can be determined by rotating a WGM (requiring that the objects dimensions are known) until its projection matches The initial attitude and rotation vector of the model are the ISAR image after appropriate cross-range scaling. varied. Projections of the WGM corners, synthesized from Unfortunately, neither the image plane nor cross-scaling are these parameters, are then compared to the manually assigned known in advance. points. The mean of squared distances between them is used as an error measure. It can be calculated as To overcome the problem, the WGM is adapted manually 2 to a set of ISAR images. Several WGM corners are assigned ∈2:= R - LT C to the corresponding points in each ISAR image. In order to 0 F assess the validity of each assignment, it is useful to compare the assigned image points against the parallel projection of the and depends on the matrix L, which follows from and rotated and cross-range scaled WGM. An example of two ISAR contains the LOS unit vectors and their temporal derivatives images of ENVISAT from the same pass are shown in Fig. 2. (in a satellite-fixed coordinate system, which depends on the
46 Temporal Analysis of ENVISAT’s Rotational Motion
TABLE 1: TIRA Observation Dates of ENVISAT. No. Start [UTC] 1 29 Aug 2011 10:32:20 2 09 May 2012 10:19:20 3 23 May 2012 10:06:17 4 31 May 2012 11:51:58 5 08 Jan 2013 09:21:55 6 07 May 2013 09:57:07 7 25 Jul 2013 09:42: 00 8 09 Oct 2013 09:43:50 9 21 Nov 2013 10:00:46 10 20 May 2015 09:50:05 11 07 Jun 2016 08:00:03 12 07 Jun 2016 08:04:55 13 06 Sep 2016 18:10:56 Fig. 3 Algorithm outline. 14 06 Sep 2016 19:48:19 rotation vector). The initial attitude is defined by the matrix T0 15 21 Sep 2016 18:53:17 which rotates the WGM coordinates contained in the columns 16 21 Sep 2016 20:32:18 of C to inertial coordinates at reference time. R contains range and range rate for several assigned images. The index F denotes 17 11 Jan 2017 08:24:30 the Frobenius norm, i.e. the square root of the sum of squares 18 27 Jan 2017 10:10:08 of all matrix entries. 19 22 Mar 2017 08:30:08 ω ∈2 By varying and T0 to minimize , the optimal rotation vector and initial attitude for the assigned images can be stabilized attitude, i.e., the same part of the satellite pointed determined. towards Earth’s centre during an orbit [1]. This rotation corresponds to a rotation velocity of about 0.06o s-1 in the The synthesized WGM projections resulting for the rotation inertial frame of reference. Indeed, we estimated a rotation vector for the example, shown in Fig. 2, are indicated in green velocity of 0.06o s-1 before the loss of contact, which is in good and agree well with the manually assigned WGM projections agreement with the actual rotation velocity. (blue). The estimated rotation velocity of all observations are 3. LONG TERM OBSERVATIONS OF ENVISAT presented in Fig. 4. After the loss of contact, the rotation velocity increased from April 2012 until May 2013. In May ISAR observations of ENVISAT have been performed 2013, the highest rotation velocity was estimated to be 2.9o s-1, using the TIRA radar system. TIRA is located in Wachtberg, corresponding to a spin period of 124 s. The actual rotation Germany (50.616° N, 7.126° E). It consists of an elevation- velocity might have been higher, but cannot be resolved here over-azimuth pedestal carrying a 34 m parabolic Cassegrain due to the limited numbers of observations at that time. antenna, a narrowband L-band tracking radar and a broadband Ku-band imaging radar. For more details, see [8]. Here, the The spin period (inverse of rotation velocity) is regarded Ku-band imaging radar was used. It is a broadband coherent separately in Fig. 5 as the temporal development of the spin radar with a centre frequency of 16.7 GHz with circular period might be of interest for possible deorbiting missions. polarization. The 3 dB beam width is 0.031° with a typical The spin period between May 2013 and March 2017 was fitted, peak power of 13 kW. depending on time, with a linear regression of the form y = mx + n (red) and ln(y) = a + bx (blue). It can be found that the In this study, data from the years 2011 - 2017 (see Table 1 linear fit (correlation coefficient 0.996) fits the data better than for exact dates) are used. The first observation of this series an exponential fit (correlation coefficient 0.989). The estimated was conducted when ENVISAT was still active and in a linear fit of the spin periods depending on time is described by stabilized attitude mode. Then, a series of observations have been performed shortly after the loss of contact on 8 April 2012 −1 yD=(0.0750 ± 0.0009)() s d ⋅+ 115.0 ± 0.9 s in order to assess possible external damage. Since, occasional observations have been performed from 2013 until March 2017, with an increase in observation during 2016/2017 to investigate where D is the number of days since 1 January 2013. Hence, the attitude motion in more detail. we estimate that the spin period of ENVISAT seems to increase with (75.0 ± 0.9) ms per day. 3.1 Rotation Velocity, Spin Period
The rotation velocity is the magnitude of the rotation vector in Additional to our data, Fig. 5 shows also fits from two other the inertial frame of reference (ECI coordinates, J2000). Before studies. The green line is based on the study by Kucharski et loss of contact, ENVISAT orbited Earth in a gravitational al. [1] who collected data during 2013 using satellite laser
47 Svenja Sommer, J. Rosebrock, D. Cerutti-Maori and L. Leushacke
Fig. 4 Angular velocity derived by TIRA measurements from August 2011 to March 2017. The red dashed line indicates the date of loss of contact, 8 April 2012.
Fig. 5 Estimated spin periods. The red line is a linear regression of the data obtained with TIRA, the blue an exponential fit. The cyan line indicates the fit of the spin period obtained by Koshkin et al. [3] and the green line by Kucharski et al. [1].
ranging and used a linear fit. The dashed green lines indicates with (75.0 ± 0.9) ms d-1, while Kucharski et al. [1] estimated the possible temporal development extrapolated from their fit. an increase in spin period of 36.7 ms d-1. Koshkin et al. [3] Although their spin period estimation for 2013 does not deviate estimated a spin period increase of 57 ms d-1 for 2013, and based much from our estimation in 2013, the extrapolated values on their fit function, an increase of 104.4 ms d-1 on average for differ widely for later years. 2016. Although our linear fit corresponds fairly well with the quadratic fit of Koshkin et al. [3] with small deviations, the A study by Koshkin et al. [3], indicated by the cyan line, fit of Kucharski et al. [1] shows a far smaller increase in spin using photometry with data from 2013 to 2015, found a period duration. A major reason for this might be the different quadratic fit for their results. Their measurements are, in the first observation periods. Kucharski et al. [1] used observations approximation, in good agreement with our results, although from 2013, while Koshkin et al. [3] used data from 2013 - 2015 there are differences especially in the beginning and end of our and this study data from 2013 to 2017 for the trend analysis of observation period. For 2013, their fit tends to overestimate the the spin period. spin period slightly compared to our results, and the extrapolated seems to overestimate the spin period even more strongly. 3.2 Spin Period Prediction Performance
An overview of the results from this study as well as from To investigate the prediction performance of spin period Kucharski et al. [1] and Koshkin et al. [3] is given in Table 2. estimations using ISAR images, we fitted spin periods for two different time periods in the past and compared the Our estimations for the minimum spin velocity correspond extrapolated spin periods to recent observations. The first set well to the measurements of Kucharski et al. [1] in the way that of spin periods is from 2013 (observation No. 6 - 9). The linear the spin period decreases after the loss of contact until around fit of the spin periods is shown in Fig. 6 in dark blue. The light April/May 2013. blue area indicates the confidence interval of the fit using the 0.95-quantile of Student’s t-distribution. After that, the rotation velocity begins to decrease. The rotation period of ENVISAT is found to increase linearly The next set of spin periods uses data from 2013 and 2015
48 Temporal Analysis of ENVISAT’s Rotational Motion
TABLE 2: Comparison to Other Studies. Study Minimum Spin period Spin period Degree of spin period increase increase polynomial 2013 2016 fit Sommer et al., 2017 124 ms 75.0 ms d-1 75.0 ms d-1 1 Kucharski et al., 2014 128 ms 36.7 ms d-1 36.7 ms d-1 1 104.4 ms d-1 Koshkin et al., 2016 - 57 ms d-1 2 (average)
Fig. 6 Prediction performance of spin period estimates of ISAR imaging with TIRA. The dark blue line indicates a linear fit to data from 2013, the dark green line a linear fit to data from 2013/2015 and the red line to all data (May 2013 - March 2017). The light blue and light green areas indicate the confidence interval of the fits.
(observation no. 6 - 10). The linear fit is indicated in Fig. 6 by the On the other hand, the spin axes for the years 2016/2017 dark green line, the corresponding extrapolation by the dashed show a more coherent pattern. This is examined in detail in Fig. dark green line. The light green area indicates the confidence 8. Here, we show the rotational axis only for the observations interval of the corresponding fit using the 0.95-quantile of in 2016/2017. The rotation axis varies over time, but it can be Student’s t-distribution. The linear fit taking all data since May seen that the rotation axis for two measurements of the same 2013 into account is indicated by the red line. No uncertainty is day show almost in the same direction. Additionally, the vectors shown for this fit as no prediction was made using all data. For appear to lie roughly on a cone, therefore we fitted a cone to the the uncertainty of this fit, see above. data but omitted an outlier (6 September 2016, 18:10:56). The result is indicated by the black circle in Fig. 8. The resulting Comparing the extrapolated values from the first time period cone opening is about 80° and the normalized cone axis points (2013) to the actual data, it can be seen, that the extrapolation towards [-0.22; 0.02; -0.97]. Although there are some deviations agrees quite well with observations taken in 2016/2017. All from the fitted cone, the results indicate that the rotational axis estimated spin velocities lie within the uncertainty of the fit. Taking is not fixed and ENVISAT performs a nutation. Comparing the the observation from 2015 also into account shows that the slope variances of the rotation axes in 2013 and 2016/2017, it seems of this fit is smaller than for the first fit, but still, the extrapolated that the tumbling movement decreased, but ENVISAT still values agree, within the uncertainty, with observed values from tumbles. 2016/2017. Comparing both extrapolated fits to the linear fit of all data (red line) shows that the red line lies between both extrapolated On the other hand, Kucharski et al. [1] found that the spin fits and within the areas of uncertainty. Hence, the extrapolated vector is almost perpendicular to the along-track vector in 2013. values are in good agreement with the actual measurements. The Koshkin et al. [3] found that ENVISAT appears to be spinning prediction performance of radar using ISAR imaging should be around an axis parallel to the normal of the orbit. The analysis compared to model simulations in future studies. of Kucharski et al. [1] relies on assumption that the spin axis of ENVISAT is stable from 10 April to 25 September 2013. 3.3 Spin Axis During this period, we analysed two passages, on 07 May and 25 July 2013. The angle between rotation axes on those dates, Additionally to the rotation velocity estimations, we derived the as they have been estimated using ISAR in conjunction with spin axis of ENVISAT. The different spin axes of ENVISAT, a WGM, is 17.6°. Hence, ISAR imaging provides the means i.e. the normalized rotational vectors in an inertial frame of to estimate the rotation velocity without the assumption of a reference, are shown in Fig. 7 for 2011 - 2017. The temporal long-term stable rotation axis. On the other hand, this method evolution is colour coded. The first two years after loss of contact assumes that the rotation axis is constant for the duration of a (2012/2013, bluish colours) do not show a distinct direction for passage. In case of fast tumbling objects, this might not be the the rotational axis. This might indicate that ENVISAT made a case but can be overcome by dividing a passage in different tumbling movement, meaning the rotational axis is not constant sub-passages, where the assumption of a fixed rotation axis is in the inertial frame of reference. reasonable. In the case for this ENVISAT study, the tumbling
49 Svenja Sommer, J. Rosebrock, D. Cerutti-Maori and L. Leushacke
Fig. 7 Normalized rotation vectors in inertial coordinates (ECI), August 2011 - January 2017.
Fig. 8 Normalized rotation vectors, July 2016 - January 2017, fitted with a cone. The dashed line indicates an outlier and was omitted for the fit.
movement is slow, meaning that the assumption of a fixed used to make simple extrapolations of future spin periods, rotation vector can be upheld for one pass. assuming a linear trend as found in this study. It was shown, that the extrapolated values from short periods of time fit 4. CONCLUSION quite well to later observations. Additionally, ISAR imaging can be used to determine the rotation axis of an object. In the The attitude of a space object can be determined by ISAR case of ENVISAT, it appears that it tumbles with a nutation. imaging in conjunction with wire grid models. This method These information might be helpful for a potential deorbiting can be used for long term studies of the attitude of uncontrolled mission of ENVISAT. In order to verify the linear trend in the space objects, in this case, ENVISAT. The increase in spin spin period, additional observations should be conducted in the period with time, which was found in this study, can also be future.
REFERENCES
1. D. Kucharski, G. Kirchner, F. Koidl, C. Fan, R. Carman, C. Moore, 3. N. Koshkin, E. Korobeynikova, L. Shakun, S. Strakhova and Z. H. Tang, A. Dmytrotsa, M. Ploner, G. Bianco, M. Medvedskij, A. Makeyev, G. “Remote Sensing of the EnviSat and Cbers-2B satellites rotation around Appleby, M. Suzuki, J.M. Torre, Z. Zhongping, L. Grunwaldt and Q. the centre of mass by photometry”, Advances in Space Research, 58, Feng, “Attitude and Spin Period of Space Debris Envisat Measured by pp.358-371, 2016. Satellite Laser Ranging”, IEEE Transactions on Geoscience and Remote 4. N.O. Gómez and S.J.I. Walker, “Earthś gravity gradient and eddy currents Sensing, 52, pp.7651-7657, 2014. effects on the rotational dynamics of space debris objects: Envisat case 2. H. Wirnsberger, O. Baur and G. Kirchner, “Space debris orbit prediction study”, Advances in Space Research, 56, pp.494-508, 2015. errors using bi-static laser observations. Case study: ENVISAT”, 5. J. Silha, T. Schildknecht, J. Pittet, D. Bodenmann, R. Kanzler, P. Karrang Advances in Space Research, 55, pp.2607-2615, 2015. and H. Krag, “Comparison of ENVISAT’s Attitude Simulation and Real
50 Temporal Analysis of ENVISAT’s Rotational Motion
Optical and SLR Observations in order to Refine the Satellite Attitude Technologies Conference, S. Ryan ed., 2015. Model”, in Proceedings of the Advanced Maui Optical and Space 7. J. Rosebrock, “Absolute Attitude From Monostatic Radar Measurements Surveillance Technologies Conference, S. Ryan ed., 2016. of Rotating Objects”, IEEE Transactions on Geoscience and Remote 6. R. Kanzler, T. Schildknecht, T. Lips, B. Fritsche, J. Silha and H. Krag, Sensing (Part 1), 49, pp.3730-3726, 2011. “Space Debris Attitude Simulation - IOTA (In-Orbit Tumbling Analysis)”, 8. D. Mehrholz, “Ein Verfolgungs- und Abbildungsradarsystem zur in Proceedings of the Advanced Maui Optical and Space Surveillance Beobachtung von Weltraumobjekten”, Frequenz, 50, pp.138-146, 1996.
(Received 9 June 2017; Accepted 19 June 2017)
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51 JiříJournal Šilha, of T. the Schildknecht, British Interplanetary J.-N. Pittet, G.Society, Kirchner Vol. et 70, al. pp.52-62, 2017
DEBRIS ATTITUDE MOTION MEASUREMENTS AND MODELLING BY COMBINING DIFFERENT OBSERVATION TECHNIQUES
JIŘÍ ŠILHA1*, T. SCHILDKNECHT1, J.-N. PITTET1, G. KIRCHNER2**, M. STEINDORFER2, D. KUCHARSKI2, D. CERUTTI-MAORI3†, J. ROSEBROCK3, S. SOMMER3, L. LEUSHACKE3, P. KÄRRÄNG4‡, R. KANZLER4 AND H. KRAG5ǂ 1. Astronomical Institute, University of Bern, Sidlerstr. 5, CH-3012 Bern, Switzerland. 2. Space Research Institute of the Austrian Academy of Sciences, Lustbuehelstrasse 46, A-8042 Graz, Austria. 3. Fraunhofer Institute for High Frequency Physics and Radar Techniques, Fraunhoferstraße 20, 53343 Wachtberg, Germany. 4. HTG - Hyperschall Technologie Göttingen GmbH, Albert-Einstein-Str. 11, D-37191 Katlenburg-Lindau, Germany. 5. ESA/ESOC, Space Debris Office, Robert-Bosch-Straße 5, DE-64293 Darmstadt, Germany. Email: [email protected]*, [email protected]**, [email protected]†, [email protected]‡ and [email protected]ǂ
This work will discuss an ESA project “Debris Attitude Motion Measurements and Modeling” (ESA AO/1-7803/14/D/SR) dedicated to the attitude determination of large spacecraft and upper stages. Two major goals are defined for this project. First, the determination of the attitude motion vector in case of a contingency situation, when a short response time is required between the observations themselves and the attitude determination. The second goal is the long term prediction (e.g. 10 years) of the spin rate of selected targets for future potential Active Debris Removal (ADR) missions. The study should in particular fuse the results from passive optical, laser ranging and radar observations. We will discuss a highly modular software tool named ιOTA (In-Orbit Tumbling Analysis) which was developed during the presented activity. This tool performs short- (days) to long- term (years) propagations of the orbit and the attitude motion of spacecraft in Earth orbit and furthermore its post-processing modules will generate synthetic measurements, i.e. light curves, satellite laser ranging (SLR) residuals and synthetic radar images. Last but not least we will present results from a collaborative campaign when four priority targets have been selected for collaborative measurements with radar, SLR and light curves in order to test and validate the ιOTA tool. Keywords: Space debris, attitude motion measurements, active debris removal
1. INTRODUCTION
The population of space debris increased drastically during the Aperture Radar (ISAR) images (i.e. parallel projection of the last years. Catastrophic collisions involving massive objects 3D object model onto the 2D ISAR image plane) that can be produce large number of fragments leading to significant compared with the real measurements. The strength of the growth of the space debris population. An effective remediation approach is the combination of various attitude measurement measure in order to stabilize the population in Low Earth Orbit types to cancel ambiguities of the individual methods and to (LEO) is therefore the removal of large, massive space debris. combine this information with a dynamic model in order to Secondly, satellite malfunctions might lead to loss of contact establish attitude prediction. The validation of the attitude with the spacecraft and an accurate attitude determination can model will be done by comparison to real observations of help to identify the cause. Such scenarios are referred to as targets with known attitude. For more information about the contingency cases. ιOTA tool please refer to Kanzler et al. [1].
Currently, the Astronomic Institute of the University of 2. IN-ORBIT TUMBLING ANALYSIS TOOL Bern (AIUB) in cooperation with three partners is involved in the ESA study Debris Attitude Motion Measurements and ιOTA is a standalone tool programmed in C++. One of the key Modelling (ESA AO/1-7803/14/D/SR) dedicated to the attitude features of the software is the approach of high modularity for determination of large spacecraft and upper stages. One of the the simulation of the relevant effects, as well as regarding the project consortium partners, Hypersonic Technology Goettingen used environmental models, enabling easy updates of existing (HTG), is developing a highly modular software tool ιOTA models and an easy implementation of new models released. to perform short- (days) to long-term (years) propagations Except for the gravitational influence of the Earth, the user will of the orbit and of the attitude motion of a spacecraft, taking be able to choose which particular effects shall be included in into account all the relevant acting forces and torques [1]. the simulation. Furthermore, ιOTA’s post-processing modules will generate synthetic measurements, e.g. light curves, Satellite Laser 2.1 Modular Architecture Design Ranging (SLR) residuals and “synthetic” Inverse Synthetic The ιOTA host process calls the particular submodules of the This paper was presented at the ESA 7th European Conference on software. Figure 1 displays the decomposition of the software, Space Debris, ESA/ESOC, Darmstadt, Germany, 18-21 April 2017 including the software modules, the data flow from the model
52 Debris Attitude Motion Measurements and Modelling by Combining Different Observation Techniques
The post-processing modules comprise: • History module: Output and storage of all relevant (selected) simulation data Light curve modelling Optical image generation in the GUI Radar image generation and Radar Cross Section estimation Satellite laser ranging measurement simulation
The post processing is done during the simulation, providing accessible results to the user while the simulation is running. Using the ιOTA-GUI, the user can visualize the simulation results, i.e. history data for the orbit and attitude motion, as well as acting forces and torques and the synthetic measurements generated.
2.2 Simulation Input and Modelling
Mandatory input for the simulation is the initial spacecraft orbit and attitude, as well as the epoch. Also a surface geometry model of the spacecraft, based on triangular panels, as shown in Fig. 2 for the ENVISAT satellite (international designator 2002-009A) taken from [2], has to be provided by the user. The spacecraft mass, moments of inertia (MoI) and the center of mass (CoM) position within the surface geometry model have to be defined by the user.
Fig. 1 ιOTA process hierarchy and functional architecture [1]. and input data (blue) to the particular modules, as well as the data flow from the simulation (yellow) and propagation (red) modules to the particular destination. The post processing branch (green) provides the final processing and visualization of the simulation results. The simulation part of ιOTA is called from the command line. Before running the software, the simulation setup needs to be defined by the user via configuration files. The environmental conditions for the attitude simulation comprise the modelling of forces and torques resulting from atmospheric drag, gravitational influences from Earth, Sun and Moon, eddy current damping caused by the tumbling motion Fig. 2 ENVISAT 3D model used in ιOTA [2]. inside the Earth’s magnetosphere, solar radiation pressure and impulse transfer through user defined micrometeoroid and small space debris impact events. Simulation modules for The input parameters are: environmental influences are: the attitude state assumption based on real observations, Aerodynamics forces and torque e.g. initial values for spin rate and spin axis direction Eddy current damping determined from SLR data, light curves, from direct Gravitational acceleration and torque (Earth) imaging or from SAR images, Impact events environmental conditions, Solar radiation pressure the 3D surface geometry/shape of the target, Third-body acceleration (Sun and Moon) the CoM determined from International Laser Ranging Service (ILRS) network data or Doppler Orbitography Simulation modules for optional spacecraft related influences and Radio-positioning Integrated by Satellite (DORIS) are: measurements or obtained from models, • Active and Orbital Control System (AOCS) behaviour: the MoI obtained from the manufacturer data or models, Magnetic torquer activation • the surface properties, diffuse and specular reflection, • AOCS behaviour: Reaction wheel behaviour • the retro-reflector positions with respect to the CoM and • AOCS behaviour: Thruster firing to the surface geometry. Moving parts (tank sloshing) Outgassing or leakage 3. OBSERVATION TECHNIQUES Except for the tank sloshing, these internal effects are The attitude states of space objects can be estimated from several managed through user defined events. types of measurement by using the corresponding processing
53 Jiří Šilha, T. Schildknecht, J.-N. Pittet, G. Kirchner et al. methods. Some of them can provide direct information about the object spin behavior, like SLR measurements to cooperative targets [3, 4] or Inverse Synthetic Aperture Radar (ISAR) images performed by radar [5]. Direct optical imaging [6] after processing may provide similar results as the ISAR images. Most cost effective for long term monitoring of the objects behavior and its changes are optical telescope measurements, when a light curve of the object is acquired. By applying time series analysis tools one can extract the rotational frequencies from light curves [7].
3.1 Optical Passive Measurements Fig. 3 Light curve for GLONASS satellite 2001-053C acquired by For targets, such as rotating spacecraft, upper stages, and debris AIUB’s ZIMLAT system. pieces, a sequence of photometric measurements is acquired within a short time interval (few minutes) with a small time coordinate system aligned with the LOS) orthogonal to the step (few seconds), depending on the orbit and attitude of LOS vector. The norm of the effective rotation vector scales the target. The output of such a sequence, i.e. the brightness the ISAR images in cross-range. The image plane is, hence, the variation during the measurement time is a so-called light range/cross range plane that is perpendicular to the effective curve. Light curves are strongly related to the rotation of the rotation vector and contains the LOS vector. The scatterers observed object. To be able to analyze light curves obtained of the object are projected to this image plane spanned by the by optical measurements, i.e. determining the rotation period moving LOS. and the rotation axis direction, several methods can be applied [7]. An example of a light curve for GLONASS satellite 2001- Unfortunately, the image plane and the cross-range scaling 053C acquired by AIUB’s ZIMLAT system (see section 4.1) is of an ISAR image are changing with time and are usually plotted in Fig. 3. unknown. They depend on the satellite’s rotational motion, the satellite’s orbit, the radar location and Earth rotation. All, For more details about the space debris light curves except for the first parameter, are usually known in advance. acquisition and processing please refer to Silha et al. [7]. Therefore, correct cross-range scaling can only be obtained if the rotational motion of the object, i.e. the sequence of its 3.2 Radar Measurements attitudes over time, is known or has been estimated.
3.2.1 ISAR Principle 3.2.2 Attitude Eestimation from ISAR Images
Advantages of radar systems compared to other measurements Two different parametric methods were developed to estimate systems like optical systems are their ability to observe space the rotational motion from a sequence of ISAR images. Both objects at any time a day independently from the weather methods enable the rotational velocity vector to be estimated conditions. for both slowly and fast tumbling objects with ground-based imaging radars. Inverse synthetic aperture radars (ISAR) exploit the rotational motion between radar and object in order to image Parametric attitude estimation requires a suitable rotational the object in 2D. The radar transmits regularly waveforms that motion model. The two methods are based on different models. are backscattered by the object and received by the radar. From The first method assumes a constant rotation vector (whose the delay between transmit and receive, the ranges between the length is the rotational velocity and whose direction is the axis) radar and the different point scatterers, which are distributed in an inertial system over one satellite pass. The second method over the object, can be measured. Over time, the object rotation uses the simulation tool ιOTA, which simulates the temporal causes small variations of these distances. This induces phase evolution of attitude. In both cases, the initial state is given by differences between radar pulses that are proportional to cross- the attitude and the rotation vector at reference time. range (i.e. direction perpendicular to range). Cross-range positions can therefore be separated by spectral analysis of The two methods use a wire-grid model (WGM) of the consecutive pulses. satellite, which is projected to the ISAR images. The projections of the WGM corners can then be compared to salient points in Challenge of ISAR imaging is the estimation of the unknown an ISAR image. Knowing the satellite’s attitude over time, the object motion from the radar data. Indeed, the kinematics of image plane and cross-range scaling for several images of a the object is required in order to form a focused image of the passage can be computed. moving object. The motion of the object can be decomposed into a translational motion of a reference point of the object, 3.2.2.1 First Optimization Procedure which has to be compensated, and a rotational motion around an axis through this reference point, which leads to ISAR Figure 4 shows the optimization procedure under the assumption imaging. of a fixed rotational velocity vector over a satellite pass. It is based on a maximum likelihood (ML) approach. Attitude The object is imaged in the so called image plane. The estimation is accomplished by estimating the parameters of a first direction (range) is in the line-of-sight (LOS) direction rotational motion model. First the WGM is projected manually from the radar to the object. The second direction (cross- on a few ISAR images. Then, for a given initial attitude and a range) is orthogonal to the effective rotation vector, which rotational velocity vector, the WGM is automatically projected is the component of the rotation vector of the object (w.r.t. a on the ISAR image sequence. The algorithm searches for the
54 Debris Attitude Motion Measurements and Modelling by Combining Different Observation Techniques
Fig. 4 Optimization without ιOTA. Fig. 5 Optimization with ιOTA. parameters that match best the automatic projections with the manual projections.
The quality of matching is expressed by an error measure. We took the mean of squared distances between projected corners and assigned image points for this purpose. An alternative error measure was also investigated. If a proper rotation and cross- range scaling of the WGM is found by matching the image content, this rotation can be compared to the rotation predicted by the rotational motion model for given parameters. Both rotations can be described by a rotation vector. The alternative error measure is then the squared Euclidean distance of both vectors. Fig. 6 SLR residuals of ENVISAT measured by the Graz SLR 3.2.2.2 Second Optimization Procedure (with ιOTA) station. ιOTA propagates an initial state over time by computing location and attitude. Since the translational motion is also 4. SENSORS simulated, the initial state, defined by position and velocity of the satellite, has to be specified additionally. This state is Within this study several different sensors have been used to usually known in advance. A single 6-dimensional optimization acquire attitude related measurements of space debris objects. procedure is applied, which is illustrated in Fig. 5. 4.1 ZIMLAT Telescope ιOTA computes the satellite’s attitude relative to the Earth centered inertial (ECI) system as a function of time resulting in One of the main instruments at AIUB’s Swiss Optical the current rotational velocity vector in ECI coordinates. The Ground Station and Geodynamics Observatory Zimmerwald, satellite’s orbital position and the radar location as functions Switzerland (hereafter called Zimmerwald observatory) of time yield the temporal evolution of the LOS direction in (observatory code 026, SLR station code ZIML) is the 1-meter ECI coordinates. This corresponds to rotation of the ECI Zimmerwald Laser and Astrometry Telescope (ZIMLAT). system relative to a coordinate system where one coordinate ZIMLAT is used either for SLR to cooperative targets, permanently points in LOS direction. Subtracting both rotations targets equipped with SLR retroreflectors, or for passive yields the LOS rotational velocity vector relative to the satellite, optical observations (astrometric positions and magnitudes) given in ECI coordinates. Cross-range is orthogonal to both this of artificial and natural objects in near-Earth space. During vector and the LOS. Thus, the image plane is defined as well as daytime the system operates in SLR mode only. During night cross-range scaling. time the available observation time is shared between SLR and optical observations [8] based on target priorities. The 3.3 SLR Measurements switching between the modes is done under computer control and needs less than half a minute. The ZIMLAT telescope is SLR is a technique measuring the time of flight of laser photons shown in Fig. 7. between a ground-based observatory and a satellite. SLR is usually performed to objects equipped with retro-reflector array 4.2 TIRA Radar (RRA), also known as cooperative targets. SLR measurements themselves can directly provide two types of data related to the The space observation radar TIRA (Tracking and Imaging Radar) attitude state, where both are related to the rotation of satellite’s located in Germany is the largest experimental system which RRA around its center of mass (CoM). The first type, is the is unique in Europe. It is operated by the Fraunhofer Institute modulation of the range between the laser and the object’s RRA. for High Frequency Physics and Radar Techniques FHR. The The second type of data is the alternative visible or hidden state system primarily serves as the central experimental facility for of the RRA as seen from the observatory. An example of a SLR the development and investigation of radar techniques for the residuals acquired by Space Research Institute’s (IWF from detection and reconnaissance of objects in space. TIRA also German Institut für Weltraumforschung) Graz SLR station (see provides valuable support for space missions: space agencies section 4.3) can be seen in Fig. 6. from all over the world use the special capabilities of the FHR
55 Jiří Šilha, T. Schildknecht, J.-N. Pittet, G. Kirchner et al.
Fig. 7 AIUB’s ZIMLAT telescope. (Silha and Bodenmann) scientists and their system. As the name implies, the TIRA system comprises a tracking radar and an imaging radar. The narrowband, fully coherent, high power tracking radar has a transmission frequency in L-band (1,333 GHz) and the wideband imaging radar has a transmission frequency in Ku- band (16.7 GHz) and is currently equipped with a high target resolution. TIRA radar is shown in Fig. 8. Fig. 8 FHR’s TIRA system. (Fraunhofer FHR) 4.3 GRAZ SLR STATION
The IWF’s Graz SLR station (station code GRZL) is housed in the Observatory Lustbuehel, Austia. In order to test laser ranging possibilities to space debris objects, the Satellite Laser Ranging (SLR) Station Graz installed 2012 a frequency doubled Nd:YAG pulse laser with a 1 kHz repetition rate, a pulse width of 10 ns, and a pulse energy of 25 mJ at 532 nm (on loan from German Aerospace Center Stuttgart, DLR). This laser was replaced in 2013 by another frequency doubled Nd:YAG pulse laser with 100 Hz repetition rate, a pulse width of 3 ns, and a single pulse energy of 200 mJ at 532 nm, also on loan from DLR Stuttgart.
Additionally, the station is able to acquire single-photon Fig. 9 IWF’s Graz Laser Telescope dome at Observatory light curves recording to cooperative and non-cooperative Lustbuehel, Austria. (IWF) targets [9].
The Graz SLR system is shown in Fig. 9. control system. The satellite is currently in a LEO orbit with a mean altitude around 770 km. ERS-2 was decommissioned in 5. TARGET LIST 2011 and its orbit has been lowered from 750 km to 573 km to decrease its lifetime. Both ERS satellites are equipped with We defined five priority targets to be observed during RRA and have a very similar design. simultaneous observations. Because of the high interest, ENVISAT (2001-002A), an ESA satellite which is non-active The fourth selected target was ADEOS-2 (2002-056A) since 2012, has been selected as priority target. On 8th of April (Fig. 10, right panel), a Japan Aerospace Exploration Agency 2012 the Agency lost contact with the satellite. Currently, (JAXA) satellite. ADEOS-2 was launched in 2002 into a LEO ENVISAT is one of the largest and heaviest objects in Low orbit with a mean orbital altitude around 800 km. After one Earth Orbit (LEO) region, which is the region with the highest year of service the mission ended by a failure of the solar panel. density of man-made objects in space, and poses a big treat Since then the satellite showed several sudden accelerations in to operational spacecraft in case of a collision or break-up rotations. The most current one was observed by ZIMLAT in event. ENVISAT is orbiting at a mean altitude of 766 km. It December 2015. is equipped with a RRA which makes is observable by any SLR system, if the RRA is visible from the station. The 3D Our last target selected was the JAXA upper stage H-2A model of ENVISAT satellite used in the ιOTA tool is plotted rocket body (R/B) (2001-038B). This is the only selected in Fig. 2. object which outside LEO, namely on a highly eccentric orbit with perigee and apogee altitudes of ~260 km and 34,180 km, We selected the decommissioned ESA spacecraft ERS-1 respectively. The vehicle evaluation payload (VEP-2) was (1991-050A) and ERS-2 (1995-021A) (Fig. 10, left panel) as launched in 2001 for testing purposes and has been observed other two priority targets. The ERS-1 mission ended in 2000 several times by radars since then, e.g. by TIRA. The H-2A R/B after 9 years of service due to a failure of the onboard attitude is shown in Fig. 11.
56 Debris Attitude Motion Measurements and Modelling by Combining Different Observation Techniques
Fig. 12 Light curve of attitude-controlled Jason-3 satellite acquired by the ZIMLAT system during the night 2017-03-15 (red line) and synthetic light curves generated by ιOTA for the same Fig. 10 Satellites ESA ERS-2 (left) and JAXA ADEOS-2 (right). pass assuming different factors for the diffuse reflection. (ESA and JAXA)
Fig. 13 SLR residuals of ENVISAT satellite acquired by ZIMLAT during the night 2016-08-22 (blue points) and synthetic residuals generated by ιOTA for the same pass (green points).
night 2016-08-22. The synthetic SLR residuals are the results of adjusting the rotation angular velocity vector of ENVISAT in Fig. 11 Upper stage H-2A R/B. (JAXA) ιOTA to provide the best match with the observations.
6. SOFTWARE VALIDATION 6.3 Long-Term Prediction, ENVISAT Case
Several different modules need to be validated for ιOTA, namely The observed an modelled evolution of ENVISAT’s rotational the generation of synthetic measurements and the modelling of velocity over one year is shown in Fig. 14. In the model we acting torques and forces. In the following sections we show were assuming different acting torques and forces, namely eddy examples of such validations. current, gravitational torque, 3rd body torque and all three types of torques combined. The ιOTA predictions for these forces are 6.1 Light Curves, Jason-3 Case compared to the angular velocities extracted from the ZIMLAT SLR residuals which were processed by AIUB [3]. Figure 14 During the night 2017-03-15 we acquired a light curve of active covers the time period from July 2013 to August 2014. As can satellite Jason-3 with the ZIMLAT telescope. The whole pass be seen from Fig. 14 we have a good agreement between the has been covered. The obtained light curve is plotted in Fig. 12 observed and predicted values of the angular velocity if we (red points). As expected, the light curve showed a relatively include all three mentioned forces in the model. simple change of brightness over time, mostly as a function of the object elevation over the horizon. No apparent satellite 7. COLLABORATIVE OBSERVATION CAMPAIGN rotation is visible in the light curve. The goal of the collaborative observations was to observe the We generated a synthetic light curves for the same pass by same target at the same time with different types of sensors. using ιOTA. Different light curves were generated based on These measurements should allow cross-calibration of the the Jason-3 3D model available from NASA and by assuming different methods and provide testing data for the evaluation different reflective properties for the satellite surfaces (ratio of the ιOTA tool. between diffusely and specular reflected light). All the generated light curves are plotted in Fig. 12. To get a good match between 7.1 Selection of Observation Nights the real and synthetic light curves we had to add a time shift of 150 s to the real light curve. This discrepancy will be further We had three sensors available for the observation campaign, investigated. The vertical axis (magnitude) for the real light curve TIRA, the ZIMLAT telescope and the Graz SLR station. From is in a relative scale and has not been calibrated. Once shifted, the our five priority targets we selected only objects in LEO. The shape of real light curve is in good match with the light curves H-2A R/B could not be observed by any other system than by created by diffusely reflected light (dif=0.6, dif=0.2 in Fig. 12). ZIMLAT (light curve acquisition) due to its high altitude and absence of a RRA. 6.2 SLR Residuals, ENVISAT Case We investigated the visibilities of ENVISAT, ERS-1, ERS-2 Figure 13 shows an example of synthetic SLR ranges of and ADEOS-2 for a time period between Spring and Winter ENVISAT generated by ιOTA (green points) in comparison with 2016 for all three observation sites. For light curve we required real SLR ranges (blue points) acquired by ZIMLAT during the that during the observation the object is illuminated by the
57 Jiří Šilha, T. Schildknecht, J.-N. Pittet, G. Kirchner et al.
collaborative measurements during nights 2016-09-06 and 2016-09-21 only. Unfortunately, the weather conditions at Graz SLR station prevented the station to perform observations during any of the mentioned nights. Therefore, we had simultaneous data from TIRA (ISAR imaging) and ZIMLAT (simultaneous light curve and SLR data). The light curve acquisition at ZIMLAT was performed either by using a CCD camera with frame rates of about 0.75 frames/s or by a sCMOS camera with a frame rates of ~ 5.0 frames/s. The summary of the observations for the nights 2016-09-06 and 2016-09-21 is given in Tables 1 and 2, respectively.
Fig. 14 Inertial angular velocity of ENVISAT satellite determined 7.3 Acquired Measurements, TIRA by AIUB from the SLR residuals acquired by ZIMLAT system during years 2013–2014 (black points) and predicted angular The results were obtained with data acquired with the Tracking velocity by assuming different acting torques/forces. and Imaging Radar (TIRA) of Fraunhofer FHR [10, 11].
Sun while the Sun is below horizon in order to decrease the 7.3.1 Attitude Estimation with ιOTA background noise. We used the following criteria for selecting the correct pass for the simultaneous measurements: Attitude estimation using the simulator ιOTA needs much more computational power than assuming a fixed rotational velocity All objects are illuminated by the Sun vector in the inertial system (several hours for the optimization All objects are above horizon for all stations, preferably with ιOTA vs. less than a minute for the optimization without > +30° for the Zimmerwald station ιOTA). Therefore, only one passage of ENVISAT was analysed • The Sun is below horizon for the Zimmerwald station, by this method (see [5] for the temporal investigation of preferably -5° ENVISAT’s rotational motion using the first optimization Objects are visible from all three sites for at least 3 procedure). Figure 15 shows ISAR images of ENVISAT with minutes overlaid WGMs. For testing purposes, first a CAD model of a At least one pass of ENVISAT during the given night sphere and a corresponding inertia tensor proportional to the fulfills the previously listed criteria unit matrix were applied. Doing so, the ιOTA result essentially gave the same mean square error (MSE) as the algorithm Additionally, we included also the following two criteria: designed for a constant rotational velocity vector, and the initial TIRA is available attitude and rotational velocity vector differed only slightly. Latest 24 hours before the observation campaign the This confirmed the correct modelling of the ιOTA simulation weather predictions were favorable at least for the program. Comparing the attitude quaternions generated by Zimmerwald observatory or the Graz SLR station ιOTA for subsequent time instances, it could be observed that the rotational velocity vector simulated by ιOTA kept nearly By following the mentioned criteria we got one month of constant as expected for a spherical object. overlap when we could observe all four targets within one night from all three observation sites. Finally, we selected five nights In a next step, the sphere was replaced by an ENVISAT CAD for collaborative measurements, namely 2016-08-26, 2016-09- model along with the corresponding inertia tensor. Several 04, 2016-09-06, 2016-09-10 and 2016-09-21. error minimization procedures were tested. First, the estimate for constant rotation vector was taken for initialization. Then, 7.2 Observation Campaigns random initialization was tried, leading in one case to an error reduction. The alternative error measure was also used in Due to the weather conditions, we eventually performed other cases as shown in Table 3. Using this measure led to TABLE 1: Summary of Simultaneous Observations Performed During Night 2016-09-06. Pass AIUB SLR Remark AIUB LC Remark FHR Remark ENVISAT N/A - N/A - YES L-band + Ku-band 2016-09-06, 18:10 UTC ENVISAT ~400 YES YES CMOS ~400s YES L-band + Ku-band 2016-09-06, 19:47 UTC Interrupted signal ERS-1 NO - YES CMOS ~250s YES L-band + Ku-band 2016-09-07, 01:43 UTC ERS-2 NO - YES CMOS ~120s - - 2016-09-07, 01:51 UTC Adeos-2 NO - YES CMOS ~450s YES L-band + Ku-band 2016-09-07, 03:09 UTC ERS-2 N/A - YES CCD ~130s YES L-band + Ku-band 2016-09-07, 03:23 UTC YES – acquisition was successful, data are available, NO – Applicable only for SLR. Attempt to acquire data but unsuccessful, (N/A) – No attempt.
58 Debris Attitude Motion Measurements and Modelling by Combining Different Observation Techniques
TABLE 2: Summary of Simultaneous Observations Performed During Night 2016-09-21. Pass AIUB SLR Remark AIUB LC Remark FHR Remark ENVISAT NO - YES CMOS ~200s YES L-band + Ku-band 2016-09-21, 18:57 UTC ENVISAT ~500s Full YES YES CMOS ~120s YES L-band + Ku-band 2016-09-21, 20:37 UTC signal ERS-1 N/A - N/A - YES L-band + Ku-band 2016-09-22, 00:57 UTC ERS-2 NO - YES CMOS ~50s YES L-band + Ku-band 2016-09-22, 02:13 UTC Adeos-2 CMOS ~100s NO - YES YES L-band + Ku-band 2016-09-22, 02:39 UTC Interrupted ERS-2 NO - YES CMOS ~450s YES L-band + Ku-band 2016-09-22, 03:25 UTC YES – acquisition was successful, data are available, NO – Applicable only for SLR. Attempt to acquire data but unsuccessful, (N/A) – No attempt.
Fig. 15 ISAR images of ENVISAT with superposed WGMs (green: manual projection, grey:automatic projection) after the optimization procedure.
59 Jiří Šilha, T. Schildknecht, J.-N. Pittet, G. Kirchner et al.
TABLE 3: RMS Error of Point Positions for Different Simulation and Computation Procedures. Physical Model for Optimization Initialization RMS Position Error [m] constant rotation vector random 0.14368 iOTA with error from initialized by constant 0.31906 all projected WGM points rotation vector result 0.76028 iOTA with error from 2.52654 random, 4 trials all projected WGM points 0.26897 0.78320 iOTA with alternative error measure constant rotation vector result 0.23773 iOTA Result from previous case 0.20102
TABLE 4: Estimated Rotational Velocity Vectors in ECI Coordinates (1 January 2000, 12:00 UT). Pass Rotation vector [rad/s] Rotational velocity [deg/s] ENVISAT 2.55e-02 1.16e-02 -1.60e-03 1.6066 2016-09-06, 18:11 UTC ENVISAT 2.64e-02 1.16e-02 3.85e-03 1.6683 2016-09-06, 19:48 UTC ERS-1 8.92e-03 4.48e-03 -5.53e-03 0.6540 2016-09-07, 01:43 UTC 3.51e-03 -2.79e-03 -6.96e-03 0.4743 ERS-2 8.57e-03 -5.16e-04 1.41e-02 0.9896 2016-09-07, 03:24 UTC 4.71e-03 -1.65e-03 5.57e-03 0.4282 Adeos-220 NO NO 16-09-07, 03:09 UTC ENVISAT 1.94e-02 2.12e-02 8.69e-04 1.6498 2016-09-21, 18:53 UTC ENVISAT 1.52e-02 2.43e-02 1.93e-03 1.6442 2016-09-21, 20:32 UTC ERS-1 -1.29e-02 3.62e-03 1.45e-03 0.7700 2016-09-22, 00:54 UTC ERS-2 1.30e-02 -1.38e-04 -8.25e-03 0.8829 2016-09-22, 02:10 UTC ERS-1 1.99e-03 -5.99e-04 5.09e-03 0.3149 2016-09-22, 02:34 UTC Adeos-2 NO 2016-09-22, 03:25 UTC NO similar results as the original one. Surprisingly, the original 7.3.2 Attitude Estimation without iOTA error measure was reduced by using the alternative error measure for minimization. The error measure could be further Table 4 gives the estimated velocity vectors for the different radar reduced by taking the result as initialization of subsequent observations under the assumption of a constant rotation vector. error minimization with the original error measure. The ISAR images of the different objects are shown in Fig. 16. resulting root mean square (RMS) position errors are given in Table 3. While the WGM for ENVISAT was derived from a CAD model, the WGMs for the other satellites were derived by hand All results refer to a minimization where WGM projections from data sheets provided by ESA. Therefore these WGMs due to WGM matching to single images were taken as reference might be inaccurate. points in the image. Unexpectedly, for all procedures using iOTA the RMS error was higher than the RMS error for the The assumption of constant rotation vector appears to be constant rotational velocity assumption. The reason for this is satisfied for all ENVISAT and ERS-1 passes. For ERS-2, not yet clear. A possible cause could be that the CAD model this assumption seems to be satisfied only for the pass on and/or its center of gravity and inertia tensor do not sufficiently 22 Sept. 2016. The pass on 07 Sept. 2016 was divided in 3 match reality. Alternatively, the algorithm may not converge to sub-passes. Individual rotation velocity vectors were fitted the absolute minimum of the error function but to a relative under the assumption of constant rotation vector over each minimum. sub-pass.
60 Debris Attitude Motion Measurements and Modelling by Combining Different Observation Techniques
Fig. 16 ISAR images of the observed satellites.
ADEOS-2 is a strongly tumbling object and the assumption during both collaborative observation nights. Examples of of constant rotation velocity vector is not fulfilled. Therefore, it our data is plotted in Fig. 17. The residuals showed a strong was not possible to derive a rotation vector from both passes. trend which was caused by the difference between the used predictions to track the object and its real position. 7.4 Acquired Measurements, ZIMLAT 8. SUMMARY 7.4.1 Light Curves We presented an ESA study dedicated to the attitude We acquired light curves for all priority targets during the determination of space debris objects such as defunct collaborative observation nights 2016-09-06 and 2016-09-21 spacecraft and upper stages by using different types of (see Tables 1 and 2). Light curves for the satellites ENVISAT observation techniques. The techniques discussed are the and ADEOS-2 acquired during the night 2016-09-06 by the acquisition and processing of the Inverse Synthetic Radar ZIMLAT telescope are shown in Fig. 16. For both objects the Images (ISAR), Satellite Laser Ranging (SLR) residuals and light curves showed fast brightness variation over time. We light curves. processed both light curves in order to extract the apparent rotation period by applying the method of epoch folding There are in total four partners involved in the study, each [8]. This method revealed that the apparent rotation period contributing a different expertise. The Hypersonic Technology of ENVISAT was 192.4 s which corresponds to an apparent Goettingen (HTG) (Germany) developed the highly modular rotation velocity of 1.87 deg/s. For ADEOS-2 we got software tool ιOTA to model different types of measurement and inconclusive results for the apparent period, obtaining values to perform short-(days) and long-term (months, years) attitude between 45.6 s to 71.2 s where none of these numbers could predictions by assuming different torques and forces. Another be confirmed. partner, the Astronomic Institute of the University of Bern (AIUB) (Switzerland), which is was also leading the study, was 7.4.2 SLR Residuals responsible for the acquisition and processing of light curves and SLR residuals . Similar expertise was covered by the third We were able to measure SLR residuals only for ENVISAT partner, the Space Research Institute’s (IWF) (Austria). Finally
61 Jiří Šilha, T. Schildknecht, J.-N. Pittet, G. Kirchner et al.
Fig. 17 Light curve of ENVISAT (upper panel) and ADEOS-2 (lower panel) acquired during the night 2016-09-06 by the ZIMLAT telescope using an sCMOS camera. the Fraunhofer Institute for High Frequency Physics and Radar Techniques FHR (Germany) was responsible for the acquisition and processing of radar data.
Five targets have been selected during our study for observations and attitude determination, namely the satellites ENVISAT, ERS-1, ERS-1, ADEOS-2 and the upper stage H-2A R/B. To four of them, all objects in LEO, collaborative observations have been performed during two nights in September 2016 when ISAR images have been acquired by FHR’s TIRA system along with light curves acquired by AIUB’s ZIMLAT telescope. During these nights we were able to measure SLR residuals for the ENVISAT satellite only. Fig. 18 SLR residuals of ENVISAT acquired by ZIMLAT during the night 2016-09-21. Finally, an analysis of ISAR images has been performed by FHR to determine the attitude states of all observed objects. Attitude states could be found for ENVISAT, ERS-1 and ERS-2. Our next step is to fully processes the data acquired during However, ADEOS-2 showed quite tumbling behaviour, which collaborative campaign and further validate the ιOTA tool and was also observed in the light curves by the ZIMLAT telescope. its individual modules.
REFERENCES
1. R. Kanzler, T. Schildknecht, T. Lips, B. Fritsche, J. Silha and H. Krag, Space Debris, ESA/ESOC, Darmstadt, Germany, 18-21 April 2017. “Space Debris Attitude Simulation - ιOTA (In-Orbit Tumbling Analysis)”, 6. R. Dantowitz, “Sharper Images Trough Video”, Sky & Telescope, 96, Proceedings of the Advanced Maui Optical and Space Surveillance pp.48-54, 1998. Technologies Conference, Wailea, Maui, Hawaii, 15-18 September 2014. 7. J. Silha, T. Schildknecht, J.N. Pittet, A. Rachman and M. Hamara, 2. J. Silha, T. Schildknecht, J.-N. Pittet, D. Bodenmann, R. Kanzler, P. “Extensive light curve database of Astronomical Institute of the Karrang and H. Krag, “Comparison of ENVISAT’s attitude simulation University of Bern”, 7th European Conference on Space Debris, ESA/ and real optical and SLR observations in order to refine the satellite ESOC, Darmstadt, Germany, 18-21 April 2017. attitude model”, Proceedings of AMOS Conference, Maui, Hawaii, 20-23 8. J. Silha, E. Linder, M. Hager and T. Schildknecht, “Optical Light Curve September 2016. Observations to Determine Attitude States of Space Debris”, Proceedings 3. J.-N. Pittet, J. Silha and T. Schildknecht, “Single pass attitude determination of 30th International Symposium on Space Technology and Science, of ENVISAT satellite trough the laser ranging measurements”, Advances Kobe-Hyogo, Japan, 4-10 July 2015. in Space Research, in preparation. 9. M. Steindorfer, G. Kirchner, F. Koidl and P. Wang, “Light Curve 4. D. Kucharski, G. Kirchner, F. Koidl, Cunbo Fan, R. Carman, C. Moore, Measurements with Single Photon Counters at Graz SLR”, 2015 ILRS A. Dmytrotsa, M. Ploner, G. Bianco, M. Medvedskij, A. Makeyev, G. Technical Workshop, Matera, Italy, 26-30 October 2015. Appleby, M. Suzuki, J.-M. Torre, Zhang Zhongping, L. Grunwaldt and 10. K. Merz, D. Banka, R. Jehn, M. Landgraf and J. Rosebrock, “Observations Qu Feng, “Attitude and Spin Period of Space Debris Envisat Measured ofinterplanetary meteoroids with TIRA”, Planetary and Space Science, by Satellite Laser Ranging”, IEEE transactions on geoscience and remote 53, pp.1121–1134, 2005. sensing, 12, pp.7651-7657, 2014. 11. D. Mehrholz, “Ein Verfolgungs- und Abbildungsradarsystemzur 5. S. Sommer, J. Rosebrock, D. Cerutti-Maori and L. Leushacke, “Temporal Beobachtung von Weltraumobjekten”, Frequenz, 50, pp.138–146, 1996. analysis of ENVISAT’s rotational motion”, 7th European Conference on DOI:10.1515/FREQ.1996.50.7-8.138.
(Received 26 June 2017; Accepted 13 July 2017)
* * *
62 AssessmentJournal of Post-Manoeuvre of the British Observation Interplanetary Correlation Society, using Vol. 70,Short-Arc pp.63-68, Tracklets 2017
ASSESSMENT OF POST-MANOEUVRE OBSERVATION CORRELATION USING SHORT-ARC TRACKLETS
J.A. SIMINSKI1, T. FLOHRER1 AND T. SCHILDKNECHT2 1. Space Debris Office, ESA/ESOC, Darmstadt, Germany. 2. Astronomical Institute, University of Bern, Hochschulstrasse 4, 3012 Bern, Switzerland.
Satellites maintain or establish their operational orbit by performing impulsive or continuous thrust manoeuvres. When cataloguing resident space objects, these rapid or slow orbital changes complicate a successful correlation. The new orbit remains uncertain and cannot be used for operations such as conjunction detection. This work outlines and assesses a method for the correlation of optical tracklets to already catalogued objects and the following orbit recovery. For that purpose, historic orbital data is analysed to predict possible states after the manoeuvre using kernel density estimation. The resulting probability density function also provides a measure for the association likelihood of a new tracklet. The methods are tested with optical observations from the Zimmerwald observatory. Manoeuvre information and ephemerides are reported by the satellite operator and used as a reference. Keywords: Short-arc problem, tracklet association, manoeuvres
1. INTRODUCTION
When maintaining a catalogue of resident space objects, new measurements must be associated to already catalogued objects. If no matching entry in the catalogue is found, the new observations either originate from an unknown object or from a manoeuvred spacecraft.
Objects in high-altitude orbits are typically observed with ground-based optical telescopes. Due to limited observation time, each object can only be observed for a short duration. The resulting short observation arcs, called tracklets, do not provide enough information to determine the full orbital state after the manoeuvre (cf. [1]). The updated orbital state is essential for operational tasks, such as collision avoidance, but is also required in order to find the object again and keep the number Fig. 1 Time series of inclination (i) determined from optical observations of Meteosat-9. Grey vertical lines indicate reported of duplicate database entries low. As proposed in Siminski et al. North-South station-keeping manoeuvres. [2], a likely candidate state after the manoeuvre can be obtained by analysing and characterizing historic data from the object seven North-South station-keeping manoeuvres, some small in the catalogue to predict the state after the manoeuvre. The slew manoeuvres, and otherwise East-West manoeuvres in this manoeuvre history can be obtained from satellite operators time period. The manoeuvre epochs and types were reported by or estimated from past catalogued states. An example of the EUMETSAT by email. latter estimation is given by Lemmens and Krag [3] who detect manoeuvres from the publicly available Two-line element Before starting the orbit recovery, the measurements must catalogue (space-track.org). Figure 1 shows the time-series be first associated to the catalogued objects. Otherwise the of the inclination of Meteosat-9 determined from tracklets. catalogue size would artificially increase without actually The satellite is observed from the Zimmerwald observatory adding any new objects to the domain. For that purpose, the in Switzerland and serves as a test case throughout this paper. historic data from the figures is used to describe the post- The North-South station-keeping manoeuvre epochs can be manoeuvre state probability. The resulting density function is approximately computed from the figure by identifying the local then used to compute an association likelihood. Alternatively, peaks. Figure 2 shows the time-series for selected mean orbital Holzinger et al. [5] and Singh et al. [6] propose to use a elements (using the mean element formulation by Kamel [4]). control effort distance metric to rank different possible object The elements are derived from the weekly reported reference associations, i.e. the object which realizes the measurement orbits by EUMETSAT. In addition to the North-South station- with the least fuel consumption is the most likely originator. keeping as in Fig. 1, it also shows other types of manoeuvres. In total, the satellite performed one relocation manoeuvre, After the successful association step, the most likely post- manoeuvre state is estimated. In Holzinger et al. [5] the orbital This paper was presented at the ESA 7th European Conference on solution which requires the least amount of fuel is considered as Space Debris, ESA/ESOC, Darmstadt, Germany, 18-21 April 2017 a good estimate. However, realizing the new measurement with
63 J.A. Siminski, T. Flohrer and T. Schildknecht
Fig. 2 Time series of mean orbital elements for Meteosat-9: semi-major axis a w.r.t. to the synchronous λ as, inclination i, longitude , eccentricity e. minimum fuel does not need to return the same optimal result requires a different amount of fuel and depends on the epoch as when performing long-term orbit maintenance manoeuvre (due to luni-solar perturbations). optimization. The approach developed in Siminski et al. [2] overcomes this limitation by augmenting the information The above explained characteristic variables apply to of the new observation with the probability density function manoeuvre strategies with instantaneous changes (which derived from the historic data. The observation correlation and is observable for most of the satellites in the geostationary recovery of the most likely orbital state is briefly illustrated domain). Continuous thrust orbit control strategies require with a simulated example. The two possible approaches, i.e. different variables to group the manoeuvre types, e.g. the rate control effort minimization as in Holzinger et al. and Singh of change of orbital elements over time. However, the available et al. [5, 6] and using historic data as in Siminski et al. [2], dataset contains only satellites with instantaneous orbital are assessed with reference ephemerides and manoeuvres of changes. Therefore, this analysis focuses on these manoeuvre Meteosat-9 and optical observations from the Zimmerwald strategies. observatory collected from 2008 to 2016. The focus of this paper (complementary to the analysis in Siminski et al. [2]), is For each past manoeuvre epoch i = 1 … n, where n is the the assessment of the accuracy of the recovered states using the number of past manoeuvres, the feature vector is then given by real observations. i ii i i c=( eeba,, ∆∆ e ,t ) (1) 2. MANOEUVRE CHARACTERIZATION i where eb are the pre-manoeuvre mean elements (consisting of semi-major axis a, mean longitude λ, inclination i, and As proposed in Siminski et al. [2], manoeuvres are characterized i i eccentricity e), ea are the elements after the manoeuvre, ∆e with so-called feature vectors. The information from the past i states before and after the manoeuvres is compressed in this is the difference between them and ∆t is time difference w.r.t. vector. The vector elements are selected in a way that allows to the last manoeuvre. Instead of using the full set of orbital grouping, i.e. values that should be similar for the same type elements, a subset is used which is sufficient to describe of manoeuvre. geostationary orbits. Figure 3 shows selected components of the feature vectors The feature vector is assembled from the variables described ci for all manoeuvre epochs (illustrated with the ×). As also in the following: observable in the inclination time series, the points can be i. A manoeuvre type is dependent on the current orbital grouped into two types of manoeuvres: one group has no elements, e.g. whenever a geostationary satellite inclination change (accumulation of many samples in the reaches its box boundaries in longitude, it will most middle of the bottom plot) and one dispersed group with likely perform an East-West manoeuvre. Similarly, it inclination corrections. A semi-major axis change is likely will perform a North-South correction when reaching a once a longitude value around 9.5o-9.7o or around 0o is reached certain inclination. (upper plot). The latter described group represents the strategy ii. The change in orbital elements itself also describes the before the relocation in the beginning of 2013. The upper plot manoeuvre, e.g. a similar semi-major axis change is also shows that the manoeuvres after the relocation are typically typically used for East-West station-keeping. performed once every 60 days. iii. Manoeuvres are likely to be performed after similar time-intervals ∆ti (due to similar dynamics causing In addition to the samples, the figure also shows an empirical a deviation from the nominal orbit and due to human density function based on the points of the sample in the feature operator practice). vector space. The probability of and the relationship between the characteristic variables is described with the so-called Station-keeping manoeuvres typically repeatedly require kernel density estimation (cf. [8]). the same amount of fuel described with ∆V. For instance, East- n+1 n+1 West manoeuvres, when performed regularly, need a certain ∆V Given any new state after the manoeuvre ea at t depending on the sub-satellite longitude [7]. Inclination control (described with orbital elements), the probability density can
64 Assessment of Post-Manoeuvre Observation Correlation using Short-Arc Tracklets
Fig. 3 Probability density of orbital changes, pre and post-manoeuvre states and time since the last manoeuvre. be expressed in terms of the historic feature vectors with the these observation vectors with the range and range-rate following equation x = ()ρρ, , a state hypothesis expressed in orbital elements
at ta is given n++11n ni fw()()eb , = ∑ ih kc − c (2) i e()() x= err, (5) a where kh is a smoothing kernel function with bandwidth h, wi are weighting factors, and the tested feature vector where the position and velocity in the inertial frame are
n+1 nn ++ 11 n + 1 n + 1 =+ρ =++ ρρ c =( eeba,, ∆∆ e ,t ) (3) rR s and rR s s (6) is obtained by combining the latest orbital state in the database and R and R denote the station position and velocity. en+1 with the new state en+1 and computing the time difference b + a ∆tn 1 to the last observed manoeuvre. Various choices for The density function for the post-manoeuvre state is then smoothing kernels kh are discussed in the literature along with computed from inserting Eq.(5) into (2) strategies how to select the bandwidth h [9]. Here, a Gaussian kernel is selected with Silverman’s rule of thumb for the n i bandwidth selection. In order to allow for strategy changes fw()x= ∑ ih k() cx () − c (7) (e.g. the relocation), weights are used to decrease the impact i of old samples on the density function. A forgetting factor φ is introduced to scale the kernel. The respective weights are ∆ The approximate t is computed from ta and the last computed with estimated manoeuvre epoch. All other orbital elements required for c are computed from x and the new observation vectors s i ttni+1 − w = φ (4) and s . This effectively reduces the high-dimensional feature vector density function to a 2-dimensional one. The size of the weights thus depends on how old the manoeuvre of the sample is. A typical choice for φ is 0.99. A The most-likely orbital solution using this density function smaller value will decrease the weight for older samples. This is then given by weighting scheme explains why some accumulations in Fig. 3 do not contribute much to the empirical density function (e.g. xxˆk == arg max f () (8) the samples with a longitude λ around 0o). x∈c
3. ASSOCIATION OF NEW OBSERVATIONS and consequently if multiple catalogue states are tested with AND RECOVERY one new measurement, the one with the largest probability is the most promising candidate for the association. As the After receiving a new tracklet, it must be first associated to density function in Eq. (2) is not necessarily unimodal, the a catalogue object. If no match in the catalogue is found, corresponding density function in range and range-rate can the closest objects flagged as a manoeuvrable spacecraft is be multi-modal as well and thus allows for multiple feasible assessed. In addition, the probability that they manoeuvred solutions. or not can be estimated and considered (e.g. as suggested in Shabarekh et al. [10]). The probability that the observation Figure 4 shows the density for a simulated observation of originates from a specific object is then calculated to select Meteosat-9. A series of observations is simulated using the the most-likely candidate. If multiple candidate objects can reference states at the post-manoeuvre epochs and deriving be associated with a similar probability, each one can be the line-of-sight and its time-derivative thereof. The reference loosely associated using the probability as an association ephemerides before and after the last manoeuvre (East-West) weight. of the dataset obtained from the weekly reference orbits. The maximum of the probability density function w.r.t. to the The computation of the likelihood is explained in the reference solution in the centre is indicated with the white cross following. The catalogued object state before the manoeuvre ×). The error in range and range-rate for this simulated example is now denoted with eb at tb for notational simplicity (dropping is around 100 m and 0.1 m/s. The density as shown in Fig. 3 the superscript index). A new tracklet at ta is represented with is computed from about 50 pre- and post-manoeuvre states of the line-of-sight s and its time-derivative s . When augmenting Meteosat-9 before the last manoeuvre.
65 J.A. Siminski, T. Flohrer and T. Schildknecht
An alternative approach is proposed by Holzinger et al. [5] and Singh et al. [6], where the orbit of a satellite after a manoeuvre is recovered assuming that the measurement is realized using the least amount of fuel ∆V. Similar to the first approach, a function is optimized to find the most likely candidate. The function and minimum is shown in Figure 5 and is explained in the following paragraphs.
Let eb at tb be the known orbital state of a catalogued object right before the manoeuvre and ea at ta the unknown after it. The fuel consumption is approximated using the quadratic loss [5]
1 tb P = min ∫ uu()()t ttd (9) 2 ta where u is the thrust control and is included as an additional acceleration in the equations of satellite motion. The quadratic loss describes the minimum energy solution of a trajectory Fig. 4 Probability density function of orbital state given a new connecting eb and ea. It is found with optimal control problem solvers (here the one by Houska, Ferreau [11] is used) and is measurement. Range and range-rate are centred around the commonly easier to find than the direct solution giving the reference solution (+). The white cross (×) depicts the maximum of the density function. smallest possible ∆V. More details about the approach can be obtained from [2, 5, 6].
The required ∆V is bounded with
∆V()()eeba,2 ≤− t a tP b (10) and the most likely state after the manoeuvre, using Eq. (5) and the minimum energy trajectory, is accordingly given by
xˆm =arg min ∆V ()eeba , (11) x
The observed error of the optimal point xˆm for the simulated example in Fig. 5 is approximately one order of magnitude worse when compared to the solution of the first method using historic data.
4. ACCURACY ASSESSMENT
This section compares the accuracy of the resulting post- ˆ manoeuvre state of the kernel-density estimate xk and the Fig. 5 ∆V requirement depending on x (relative to the reference ∆V minimum xˆm . The accuracy using simulated observations solution (+) in the centre). The minimum ∆V solution is depicted is discussed in Siminski et al. [2]. Here, tracklets collected at with the (×). the Zimmerwald observatory are used. A set of measurements observed at most 7 days after a manoeuvre is selected. As using the same numerical optimization routine (optimize. occasionally Meteosat-9 is not observed for a longer duration, minimize) from the SciPy library [12]. The synchronous semi- not every manoeuvre can be tested in this analysis (compared major axis (42,164 km) serves to compute an initial starter for to when using simulated observations as in Siminski et al. the optimization. In case of the kernel density function f, a bad [2]). However, the accuracy of the results should be more starter can fall into a region with numerically zero probability. representative of what is achievable with the methods. Hence, the iterative optimizer will not find a gradient or better value in the close vicinity of the starter and will fail to The last 8 manoeuvre epochs, which fulfil the criterion above, converge. This behaviour was only observed when artificially are used to select the states before and after the manoeuvres placing starters far away from the solution. However, the from the weekly orbits. The analysis is performed for the density function can be initially sampled on a grid to find the latest manoeuvres in the data set in order to guarantee that the local maxima. From there on the iterative solvers are capable of empirical density function is sufficiently sampled. The kernel finding the most likely solution. density estimation for each test considers only states in the past. Seven of the observed manoeuvres within this sequence The difference between reference and obtained solutions are East-West station keeping (EWSK) manoeuvres and one is shown with the errors in range and range-rate all selected is a small slew manoeuvre (SLEW). The manoeuvres and the epochs. The different correlation methods and solutions xˆk , * corresponding tracklet epochs are summarized in Table 1. xˆm , and the reference x , are illustrated in Fig. 6. All points lie on the same line-of-sight and have the same topocentric The density function and the ∆V-function are optimized angular velocity. The comparison results are shown in Fig. 7.
66 Assessment of Post-Manoeuvre Observation Correlation using Short-Arc Tracklets
TABLE 1: Manoeuvre Epochs and Observation Epochs. # Type Manoeuvre Observation 1 EWSK 2014-01-08 07:13 2014-01-08 21:50 2 EWSK 2014-03-11 08:43 2014-03-12 03:49 3 SLEW 2014-04-08 10:58 2014-04-10 03:13 4 EWSK 2014-08-27 05:48 2014-09-01 20:45 5 EWSK 2014-10-22 07:13 2014-10-23 17:55 6 EWSK 2014-12-17 22:58 2014-12-18 23:09 7 EWSK 2015-02-09 06:58 2015-02-10 02:11 8 EWSK 2015-09-29 05:28 2015-09-30 18:47
Fig. 6 Accuracy assessment using reference range and range-rate * xˆa after manoeuvre. The different solutions xˆm and xˆk are compared to the reference in range – range-rate space.
The kernel density function estimate predicts the reference state after the manoeuvre better by one order of magnitude. This relative performance difference agrees with the theoretical assessment in Siminski et al. [2] using only simulated observations. Due to errors in the tracklets, the overall accuracy Fig. 7 Difference between predicted and estimated post-manoeuvre decreased when compared to the previous analysis. states using the historic data (upper plot) and the minimum energy solution (lower plot) for 8 manoeuvre epochs of the Meteosat-9 5. CONCLUSIONS dataset. The grey circles depict the range differences and the black squares depict the range-rate differences. The accuracy of solutions obtained after a manoeuvre has been determined for a real measurement set. The preliminary results In the framework of space object behaviour understanding, show that the accuracy of the kernel density method appears to objects are classified into groups e.g. by the different be one order of magnitude better. However, this is only true as operational manoeuvre strategies [13]. The catalogue data (e.g. long as the manoeuvres are predictable. The minimum energy orbital states, measurements) can be merged with additional solution can always serve as a fall-back option when no historic information sources (e.g. operator data, news articles, etc.) to information is available. The analysis is only performed for a describe the expected spacecraft motion. If such a database is single satellite with a repeating pattern of manoeuvres. Future available, individual methods to predict the post-manoeuvre studies will have to investigate the accuracy for more satellites state depending on the satellite class could be developed. The and different manoeuvre types and strategies. Furthermore, here used kernel density estimation is a simple and robust way future research should identify the extent of the historic data of describing the orbital change. However, more advanced necessary to obtain accurate post-manoeuvre estimates, i.e. prediction methods and more available object information can from which point on is the method capable to predict the improve the performance. The principle idea of merging the future manoeuvres. Additionally, the quality of the resulting new observations with the probable state density remains the orbits will be assessed further, e.g. if it suffices to successfully same and could be also applied when using another density correlate the following observations with the determined state. prediction tool.
REFERENCES
1. A. Milani et al., “Orbit determination with very short arcs. I admissible orbit recovery considering maneuvers”, in Proceedings of the 27th AAS/ regions”, Celestial Mechanics and Dynamical Astronomy, 90, pp.57-85. AIAA Space Flight Mechanics Meeting. 2017. 2004. 3. S. Lemmens and H. Krag, “Two-line-elements-based maneuver detection 2. J.A.Siminski, H. Fiedler and T. Flohrer. “Correlation of observations and methods for satellites in low earth orbit”, Journal of Guidance, Control,
67 J.A. Siminski, T. Flohrer and T. Schildknecht
and Dynamics, 37, pp.860-868, 2014. 9. B.W. Silverman, Density estimation for statistics and data analysis, Vol. 4. A.A. Kamel, “Geosynchronous satellite perturbations due to Earth’s 26. CRC press, 1986. triaxiality and luni-solar effects”, Journal of Guidance, Control, and 10. C. Shabarekh et al. “A Novel Method for Satellite Maneuver Prediction”, Dynamics, 5: pp.189-193, 1982. in Advanced Maui Optical and Space Surveillance Technologies 5. M.J. Holzinger, D.J. Scheeres and K.T. Alfriend, “Object correlation, Conference, 2016. maneuver detection, and characterization using control distance metrics”, 11. B. Houska, H.J. Ferreau and M. Diehl, “ACADO toolkit: An open-source Journal of Guidance, Control, and Dynamics, 35, pp.1312-1325, 2012. framework for automatic control and dynamic optimization”, Optimal 6. N. Singh, J.T. Horwood and A.B. Poore. “Space object maneuver detection Control Applications and Methods, 32: pp.298-312, 2011. via a joint optimal control and multiple hypothesis tracking approach”, 12. E. Jones et al., SciPy: Open source scientific tools for Python. http:// in Proceedings of the 22nd AAS/AIAA Space Flight Mechanics Meeting, www.scipy.org/. (Last Accessed 19 July 2017) 2012. 13. R. Furfaro et al., “Resident Space Object Characterization and Behavior 7. E.M. Soop, Handbook of geostationary orbits, Vol. 3. Springer Science & Understanding via Machine Learning and Ontology-based Bayesian Business Media, 1994. Networks”, in Advanced Maui Optical and Space Surveillance 8. E. Parzen, “On Estimation of a Probability Density Function and Mode”, Technologies Conference, 2016. The Annals of Mathematical Statistics, 33, pp.1065-1076 1962.
(Received 11 June 2017; Accepted 13 July 2017)
* * *
68 Optical Measurements AssociationJournal using of the Optimized British Interplanetary Boundary Value Society, Initial Vol. Orbit 70, Determination... pp.69-76, 2017
OPTICAL MEASUREMENTS ASSOCIATION USING OPTIMIZED BOUNDARY VALUE INITIAL ORBIT DETERMINATION COUPLED WITH MARKOV CLUSTERING ALGORITHM
CARLOS YANEZ1*, JUAN-CARLOS DOLADO1, PASCAL RICHARD1, IVAN LLAMAS2 AND LAURENT LAPASSET3 1. CNES, 18 av. Edouard Belin, 31401 Toulouse Cedex 9, France. 2. GMV Innovating Solutions, 17 rue Hermès, 31520 Ramonville St. Agne, France. 3. ENAC, 7 Avenue Edouard Belin, 31000 Toulouse, France. Email: [email protected]*
Identification of new circumterrestrial space objects is essential for building up and maintaining a catalogue of Resident Space Objects (RSO). It is a recurrent task that we have to deal with in a day-to-day catalogue maintenance and that will become more intensive with the increasing awareness on space debris risks as more sensors get dedicated to the space surveillance effort. Robust algorithms are therefore needed in order to envisage automatic measurements associations that enable us to process large quantities of sensors data. This paper addresses this problem combining a method for optical tracklets association with a clustering method used in big data problems. Performance of this approach is assessed in real scenarios using measurements taken by a ground based robotic telescope located at Chile that belongs to the TAROT (Rapid Response Telescopes for Transient Objects) network. Keywords: Space Debris, Correlation, Initial Orbit Determination, Optical Measurements, Graph Clustering
1. INTRODUCTION
One of the main missions of Space Surveillance is the detection pairs with a score below a predefined threshold are filtered and cataloguing of space objects. Maintenance of this catalogue out as a true association. However, we cannot guarantee the is fundamental in order to enable the database to be used for, absence of false associations among the filtered pairs. These among others, collision risk assessment and re-entry analysis. false associations, usually coming from observations of close This maintenance comprises a twofold task. On one hand, it objects, will prevent the correct distinction between objects is necessary to keep track of known objects and reduce the and, in this way, a synthetic object generated from observations uncertainty on their state vector. On the other hand, catalogue of several real objects will come up from computations with a is expected to be enriched with objects that either were not high risk of not being able to correlate to future observations. identified up to then or coming from already catalogued Novelty of the present work consists in introducing the notion object that have endure a fragmentation event (collisions or of graph to store the correlation relationships and applying explosions). Tackling the latter problem is the scope of this to this graph the Markov clustering algorithm to tackle the paper. Of special interest is the case concerning close objects problem of false associations. This approach leads to a more (originated from a recent fragmentation, or belonging to a robust distinction between different objects observed, specially cluster of satellites), for which identification can be messy and the clustered ones. robust methods are therefore needed. Performance of this approach is investigated by means Association of uncorrelated tracks and initial orbit of simulated observations concerning three objects in determination is essential in the cataloguing task and, for this geostationary orbit (GEO). This work includes analysis on reason, it has been the object of intense research in recent years. the accuracy of the estimated orbit, observation residuals and Siminski et al. [1] have developed a method based on a boundary association goodness-of-fit. Moreover, an analysis is presented value formulation. It uses the solution of the Lambert’s problem processing a real set of optical measurements taken by French to calculate orbit candidates which are then discriminated TAROT telescope located at Chile [3] that comprises a sky comparing angular rates by means of the Mahalanobis distance. region where a cluster of three co-located GEO satellites are One of the advantages of this Optimized Boundary Value Initial orbiting. All the analysis and results presented in this paper Orbit Determination (OBVIOD) method compared to others is have been performed using BAS3E, the CNES tool which a less sensitivity in orbit accuracy with respect to measurements simulates a whole space surveillance system. noise. We can then apply this method to the identification of new objects [2], processing each possible combination of two 2. OPTIMIZED BOUNDARY VALUE INITIAL uncorrelated tracklets in order to give a likelihood score based ORBIT DETERMINATION (OBVIOD) on the loss function (the Mahalanobis distance), and those The Boundary Value method developed in Siminski et al. [1] This paper was presented at the ESA 7th European Conference on is used in this study to compute an association probability Space Debris, ESA/ESOC, Darmstadt, Germany, 18-21 April 2017 between two tracklets, as well as to have an initial estimate
69 Carlos Yanez, Juan-Carlos Dolado, Pascal Richard et al. of the orbit that best fits these two tracklets. Hereafter, a brief Notice that the hat variables refer to computed values in description of the method is presented along with some results contrast to non-hat variables ( z and z ) that refer to observed concerning the precision of the method and considerations on values. Each possible hypothesis p leads to a different the way it is used. Lambert’s problem and, consequently, to a different candidate orbit. The quality of a candidate orbit is evaluated by assessing 2.1 Method Description the agreement between computed and observed angle rates. An optimization scheme is then followed to obtain the best The OBVIOD method deals with the association of optical candidate orbit, p* , based on the minimization of a loss observations. Optical sensors provide a series of close function defined as follows: images (very short arc), each image containing, at an epoch t, an observation composed of a pair: right ascension α and T t L() pk, =−−zz zˆˆC −1 z declination δt of an object. A series of observations forms a ( ) ( ) tracklet if they all belong to the same object. This correlation inside a tracklet is performed by simple linear correlation where C is a covariance matrix that accounts for the algorithms. Hence the importance that the series of images are uncertainties on both the observed and the computed angular close enough, so that they can be unambiguously fit. In the case rates. This loss function represents the Mahalanobis distance of TAROT telescopes, a tracklet is made of three observations between separated 20 s, each observation subject to a noise of 1 arcsec ˆ in both angular coordinates. The advantage of leading with z and z tracklets instead of with individual observations lies in the fact A characteristic of this distance is that it is distributed according that we can make use of angular rates. Within this study, angular to a χ 2 distribution. Tracklet information is used in a twofold rates are always computed by fitting a linear regression from a way: series of three observations. Equivalently, angular coordinates are taken directly from the linear fit as the value at the central a. Angular coordinates are used to define candidate orbits. epoch of the tracklet. Raw values of any particular observation Each candidate orbit is the solution of a Lambert’s are, therefore, not used. The information contained in a tracklet problem considering range hypotheses. is compressed into an attributable vector [4] at epoch t in the b. Angular rates are used to discriminate the most suitable following form: orbit among all candidate orbits. T The ()pk, -space is not considered unbounded for the At = ()ααδδ,,, t optimization search, but, on the contrary, some constraints Following [5], measurement noise associated to this are imposed in the orbital elements depending on the type attributable can be approximated to: of object we can encounter. This entails the definition of a compact subset, also known as admissible region [4]. We follow [1] and define the admissible region in terms of allowed 221 semi-major axis interval ()aa, and greatest allowed σσθ = raw min max N eccentricity, emax . This leads to the following allowed range interval: 12 σσ22= θ 2 raw ∆tN 22 2 ρmin,, i=−+c i cr i + min − r s i where θ is either the right ascension or the declination, N is 22 2 the number of measurements contained in the tracklet and ∆t ρmax,, i=−+c i cr i + max − r s i the separation between observations.
The boundary value problem formulation is built up from where i is an index that stands for the first or second tracklet, the angular coordinates of the tracklets at both observation rs is the norm of the sensor position, c is the dot product epochs: between sensor position and line-of-sight, and the allowed radius interval is defined as follows:
T z = (αδα, , , δ ) 11 2 2 ramin= min()1 − e max
Orbital state is completely defined with hypotheses on the ramax= max()1 + e max range at t1 and t2 . We form then a hypothesis variable denoted as p = ()ρρ12, , that permits us to define the position vectors and, therefore, a Lambert’s problem. Lambert’s problem refers Additionally, the constraint on the semi-major axis also to the orbital boundary value problem constrained by two defines bounds on the allowed interval of orbital revolutions: position vectors and the elapsed time ( dt = t21 – t , in this case). We also need to specify the number of complete revolutions k= dt/ P() a made during the transfer, k . In this work, solution of the min max Lambert’s problem is obtained by the method developed in [6], which considers non-perturbed two-body dynamics. The orbit kmax = dt/ P() amin solution permits us to obtain computed angular rates:
3 T where Pa= 2/πµ() is the orbital period from Kepler’s ˆ z = (αδα11,, 2, δ 2) third law.
70 Optical Measurements Association using Optimized Boundary Value Initial Orbit Determination...
2.2 Loss Function Topography
The topography of the loss function in the p-hypotheses space should be sufficiently smooth in order to succeed in the function minimization and, in consequence, in finding the hypothesis that better fits the observations. This minimization is performed verifying some inequality constraints that define the admissibility region. Techniques of convex optimization [7] are used, requiring twice continuously differentiable multivariate real functions.
We have performed extensive simulations for a GEO object to assess the sensibility of the loss function topography against separation between tracklets. Tracklets are composed of three consecutive images separated 20 s containing angular measurements of 1 arcsec centered Gaussian noise. The admissible region is defined under the following constraints: 40000 << a [] km 50000 and emax = 0.2 . This admissible region is used all along this work in the case we look for near-geostationary Fig. 1 Loss function for a GEO object in the case of tracklets objects. In general, the loss function is smooth enough as we can separated by 8 hours. see in Fig. 1. Nevertheless, we have encounter two situations where topography deformation complicates the problem: the nearly linear relation between accuracy and noise, which is a. Exact number of orbital periods separation. In the evidence of the robustness of the OBVIOD method. vicinity of exact number of revolutions the loss function begins to become deformed (see Fig. 2a), until it gets 3. MARKOV CLUSTERING ALGORITHM completely stretched (see Fig. 2b) and, in consequence, The OBVIOD method states that a pair of tracklets is correlated no optimization can be performed. This singularity is ** not specific to GEO orbits, but we have found the same if the minimum of the loss function, Lmin = Lp(), k , lies behaviour in other orbital regimes (highly elliptical and below a predefined threshold. Passing the threshold gate, then, medium earth orbits). We claim that this feature shall means correlation. For object identification, we only consider be taken into account as a constraint in the definition of those pairs that pass the threshold gate. By doing so, we can surveillance strategies. If, for example, we are intended handle pairs that are actually correlated but we can also face the to survey the geostationary ring, employing this method case of a false positive correlation (see Table 1). Definition of implies, in consequence, to prevent looking at the same this threshold stays somehow subjective and conditioned on two longitude bands at the same hour every night. opposite types of reasoning: either we take a quite low threshold b. Regions with no solution of Lambert’s problem. There is to try to process only true positive correlations with the drawback a maximum number of revolutions for transfer between of considering few tracklets of the total, or we take a higher two tracklets given a hypothesis p . In the optimization threshold to process more pairs, increasing, at the same time, scheme, we look for a minimum of the loss function for the number of false positives. In a real case, especially when objects are too close (for example, with co-located geostationary each kkk∈()min, max k. In that way, we apply optimization techniques to a problem with a fixed k . For a given k, it is satellites, or few time after a fragmentation event) we cannot possible that a solution to the Lambert’s problem exists, guarantee the absence of false positives. The reason why true within the admissible region, for a set of p -hypotheses and false positives can have similar values of the loss function is but not for others. This is the case of Fig. 2c where a mainly due to, both, the measurement noise, and the dynamical chaotic region can be seen. This region corresponds to model simplification in the Lambert’s problem solution. the set of p -hypotheses for which no solution exists for k = 1 and, consequently, the Lambert solver does Only one false positive would lead to grouping tracklets not converge. In those cases where no convergence is from two different objects into one identified object with found, we jump to the solution for k −1. This prevents the clear risk of not being able to recover it in subsequent the optimizer to fail, and, in doing so in our example, the observations. Dealing with this problem is therefore essential loss function topography passes from Fig. 2c and Fig. 2d in object identification. enabling the global minimum to be found. 3.1 Graph Construction 2.3 Orbit Precision A graph is a mathematical structure formed by a set of objects, One of the reasons of having selected the OBVIOD method usually called nodes or vertices, that can be related in one-to- for linkage is the precision in the initial orbit obtained and, in one relationship via edges. In this work, nodes correspond to particular, the stability against measurement noise. Figure 3(left) the tracklets and edges correspond to the correlation gating test shows the accuracy of the orbit depending on the separation of (1 if the pair passes the test or 0 otherwise). Order of tracklet in the two tracklets. It is worth noting the increase of accuracy the pair has no incidence in the correlation relationship. Thus, on the semi-major axis for longer intervals, and the typical we speak of undirected graphs, in contrast to directed graphs concave shape for the eccentricity with a minimum around half where the sense of the relationship does play a role. Graphs can an orbital period. This indicates that we should favour tracklets be represented as a matrix, where columns and rows refer to separated as much as possible within one night or belonging to tracklets and the element ()ij, of the matrix to the relationship two consecutive nights. Figure 3(right) presents the sensitivity between tracklets i and j . Such a matrix is symmetric in the of the solution against measurement noise, it is worth noting case of undirected graphs.
71 Carlos Yanez, Juan-Carlos Dolado, Pascal Richard et al.
(a) Minimization is still possible. (b) Stretched topography preventing minimization.
(c) Solution k = 1. The upper right triangle of the figure chaotic( (d) Solution k = 1, except for the previous chaotic region regions) has no Lambert solution for one complete revolution. where a value k = 0 is taken. Fig. 2 Loss function topography difficulties.
Fig. 3 Precision of OBVIOD method for a GEO object as a function of the separation between tracklets (left) and as a function of the sensor noise (right). Left: Measurement noise is 1 arcsec in both angular coordinates. Right: Circle markers correspond to 4 hours separation between tracklets, squares to 8 h, triangles to 16h and diamonds to 20h. Statistical values are computed from a sample of 100 executions.
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TABLE 1: Possibilities in Gating Association. Test says “Correlation” Test says “Not correlation” Correlation True positive False negative Not correlation False positive True negative
3.2 Graph Clustering
Graph clustering is a field of intense research, especially with the advent of big data that aims to recognize communities from a large amount of data [8]. These communities or clusters are characterized by having many edges within their nodes, and few edges with nodes of other clusters. In our case of study, these clusters correspond to the set of tracklets defining one object and the few edges between clusters correspond to the false positives. Representing our problem is such a way assumes implicitly the following: a. A sufficiently great amount of observations are processed in order to big data techniques apply. b. A relative low threshold of the loss function is set and, in that way, false positives are scarce compared to true positives.
One popular graph clustering method is the Markov Clustering (MCL) algorithm developed in [9], that has been successfully used in different domains as protein families identification in biology [10] or lexical acquisition and word sense discrimination [11]. Markov Clustering partitions a graph via simulation of random walks. The idea is that random walks on a graph are likely to get stuck within dense subgraphs rather than shuttle between dense subgraphs via Fig. 4 (Top) A graph representing one only cluster. Circles are sparse connections. This approach results in a sequence of nodes (tracklets) and lines are edges (correlation relationships). algebraic matrix operations (normalization, expansion in (Bottom) Same graph split into two clusters with the Markov powers and inflation) that converge in such a way that inter- Clustering algorithm using an inflation parameter ∈()1.5,3.5 . cluster interactions are eliminated and only intra-cluster parts stay (see Fig. 4). Three parameters have to be specified in the MCL algorithm: self-loop, power and inflation parameters. (see Section 2.3) and its associated initial orbit is Self-loop parameter indicates if there is a relationship of considered the initial guess in a least-squares (LS) filter each node with itself. In this study, self-loops are considered, where all tracklets of the cluster are taken into account. meaning that in the matrix representation of the graph all the Aberrant tracklets are rejected and the orbit is refined diagonal elements are set to 1. Also, the power parameter is solving another LS problem. The criterion of aberrant set to 2, that is to say, in the expansion step we always take the tracklets is defined with an Euclidian distance to the square of the matrix. The only parameter which is not fixed corresponding simulated tracklet (computed from the within this study is the inflation parameter. This parameter determined orbit) weighted with the telescope noise; affects the granularity of the solutions (see [9]). The higher if this distance is abnormally long (higher than 20, for this parameter is, the denser and smaller are the clusters of the example), tracklet is rejected. solution. 4. METHOD ASSESSMENT 3.3 Use of Clustering in Object Identification In this section we present results of the application of this Our approach can be summarized in the following steps: method to simulated objects first and then to real data extracted a. Application of the OBVIOD method to all possible from observations of TAROT telescope. combinations of two tracklets (except those at the same epoch) with a correlation gating test defined by a 4.1 Application to Simulated Objects * threshold L for Lmin . b. Building up the associated matrix representing the Simulations have been carried out considering three objects in graph where nodes are tracklets and edges are set to the geostationary ring (see Table 2). These objects are observed 1 if it relates nodes that have passed the gating test in three consecutive nights within an observation interval (correlated) or 0 otherwise (not correlated). duration of 3 hours each night. The two last intervals start c. Application of Markov clustering algorithm to the 22 and 51 hours after first interval, respectively. Inside these previous graph. Identified clusters correspond to intervals, we have 50% chance of having one tracklet every 10 tracklets belonging to a same object. minutes which is assigned to one of the three objects randomly. d. Orbit determination and refinement. For each cluster, This procedure along with the measurement noise considered we select one pair of tracklets sufficiently separated (1 arcsec in both angular coordinates) makes each simulation
73 Carlos Yanez, Juan-Carlos Dolado, Pascal Richard et al.
TABLE 2: Keplerian Elements of the Three GEO Objects Considered in Simulations. Object 1 Object 2 Object 3 Semi-major axis [km] 42164.2 42165.4 42164.6 Eccentricity [-] 0.00024 0.02030 0.00009 Inclination [deg] 0.01 0.11 2.02
Ω+ ω + M [deg] 0.035 0.031 0.023 different. Two of these simulations are hereafter presented, called GEO3_1 and GEO3_2. Observations characteristics are those of a typical TAROT working scheme.
A test is performed beforehand in order to characterize the shape of the minimum loss function when an all-vs-all approach is considered for building up the tracklets pairs (see Fig. 5). There is in total 30 observations (13 corresponding to object 1, 10 to object 2 and 7 to object 3). Thus, there are 435 possible tracklet pairs ( nn⋅−()1 /2 where n is the number of tracklets), of which 144 pairs correspond to tracklet of the same object. In view of Fig. 5, we draw up the following considerations:
• Clouds of pairs of the same or different object are well separated when tracklets are taken in the same night, whereas these clouds are partly mixed when tracklets are 1 or 2 nights separated. This fact is an evidence of a Fig. 5 Minimum of loss function for all combinations of tracklets recurrent paradox when we tackle jointly the correlation pairs coming from 3 geostationary objects. and initial orbit determination: we can confidently correlate two close observations but the issued orbit is not very precise and, on the contrary, it is hard to correlate two distant observations but the computed orbit is, in general, of better precision. • Singularity for a number exact of revolutions is present. We see the divergence of minimum loss function values around 1 and 2 sidereal days. This is related to the distorted topography of the loss function (see Section 2.2). • Definition of the threshold L* is not straightforward. If we set L* = 1, we would consider 200 associations, including 63 false associations ( 31.5% ). Whereas for L* = 0.1 , 48 associations are considered, of which 8 are false (16.7% ). We decide to set the former value as threshold for the upcoming simulations.
In GEO3_1 simulation, the telescope takes 31 tracklets distributed 14, 7 and 10 for objects 1, 2 and 3, respectively. Fig. 6 Minimum of loss function for all combinations of tracklets pairs in first three days of TAROT data. There are 60 associations (7 false) that pass the threshold criterion concerning 27 of those 31 tracklets. A graph is then built up represented by a symmetric matrix of dimension correlation relationships (6) and tracklets that are involved in 31 × 31. Markov clustering algorithm is then applied and three false associations (2). These clustering results are stable for an objects (clusters) are identified using 24 tracklets (distributed inflation parameter in the range ()1.8, 2.6 . 11/6/7). There are two reasons for the 7 discarded tracklets in the clustering: 4 of them have no correlation relationship to any In both cases, clustering algorithm succeeds to filter out other, and 3 of them belonging to object 1 and taking within false associations, improving, in consequence, the objects an interval of 30 minutes are densely associated to each other identification. Similar simulations have been also performed forming a separated cluster which is not considered because of with GTO and MEO objects showing the same robust its small size. These clustering results are stable for an inflation performance (where GTO object of study: sma 24371 km, parameter in the range ()1.6,3.0 . ecc 0.73 , inc 4.0 deg and MEO object of study : sma 29600 km, ecc 0 , inc 56 deg). In GEO3_2 simulation, 30 tracklets are available distributed 8/10/12. There are 48 associations (3 false) that pass the 4.2 Application to Real TAROT Telescope Observations threshold criterion concerning 24 tracklets. Markov clustering algorithm identifies 3 objects using 22 tracklets (distributed We have applied this method to observations taken by TAROT 7/8/7). Discarded tracklets come from tracklets that do not have telescope located at Chile during 9 nights, from 4th to 12th
74 Optical Measurements Association using Optimized Boundary Value Initial Orbit Determination...
November 2014. They point towards a sky region concerning 609 raw observations out of 1223 are exploitable (49.8%). We the geostationary ring around a longitude of 107.3 deg W. At apply the method to each interval of three days independently. this longitude, three co-located geostationary satellites are It is worth noting that, in this real case, we cannot differentiate orbiting. These satellites, part of the ANIK series, belong to clouds of pairs in Fig. 6 for those tracklets belonging to a same the communications company Télésat Canada (NORAD IDs night. This feature complicates the choice of the loss function 26624, 28868 and 39127). threshold, L* . As we expect to identify at least three objects and according to results from previous section, we set a threshold A total of 1223 optical observations are available. L* = 0.001 that cuts off around 80% of combinations. Association of these raw observations into tracklets is done with a linear correlator based on the Euclidian distance In the first interval, 373 out of 1830 possible pairs are selected normalized to 3-sigma value. A group of observations are and we correlate 56 out of 61 tracklets (inflation parameter is correlated only if this distance is below 0.1. We obtain a total set to 2.25). Tracklets from first days are only correlated to one of 203 tracklets distributed as follows: 61 the first three days, object but in the next two days, correlation clearly identifies 63 the following 3 days and 79 the last three days; that is to say, three objects as expected (see Fig. 7). In the second interval, Fig. 7 Correlation of real optical observations. Circles correspond to real observations, empty if they are not correlated to any object, full if they are correlated to the object of the same colour. Solid lines correspond to simulated observations of the identified objects.
75 Carlos Yanez, Juan-Carlos Dolado, Pascal Richard et al.
548 out of 1953 combinations are selected and we succeed to jointly with the real TAROT measurements and an indication of correlate 62 out of 63 tracklets identifying, again, three objects. which observations have been correlated and used in the orbit Inflation parameter is kept to 2.25. Comparing the objects determination. obtained in first and second interval, we have differences of less than 250 m in semi-major axis, 5⋅ 10−5 in eccentricity and 5. CONCLUSION 3 mdeg in inclination. Last interval is somehow different, there are more observations that in previous ones (+25%) and we A robust procedure for processing uncorrelated tracks in the can hardly see the presence of three objects as simultaneous context of object identification has been presented. It mainly three tracklets are only present in first day of this interval. combines two methods: a method that provides an initial There are 1135 out of 3081 possible pairs that pass the loss orbit and a correlation likelihood for a pair of optical tracklets function threshold gate, what means 36.7% of the total, the and a clustering algorithm for object identification. First highest percentage of the three intervals. This could be simply applications of this procedure are promising, showing good due to the fact of having, in principle, less objects at sight, so, behaviour against false associations. Further investigations more combinations contain tracklets of the same object. Two are also needed to determine criteria for setting the inflation objects are only identified in this case using 64 out 79 tracklets parameter, analysing the number of nights which is optimal to (inflation parameter = 1.75). For visualizing the goodness of be considered as a function of the orbital regime and assess the the correlation, it is worth examining Fig. 7 where simulated case when data from multiple telescopes is available. observations of the identified objects are plotted in each case,
REFERENCES
1. J.A. Siminski, O. Montenbruck, H. Fiedler and T. Schildknecht, “Short- Aerospace and Electronic Systems, 48, pp.2628-2637, 2012. arc tracklet association for geostationary objects”, Advances in Space 6. D. Izzo, “Revisiting Lamberts problem”, Celestial Mechanics and Research, 53, pp.1184-1194, 2014. Dynamical Astronomy, 121, pp.1-15, 2015 2. M. Weigel, M. Meinel and H. Fiedler, “Processing of optical telescope 7. S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge observations with the space object catalogue BACARDI”, 25th University Press, 2004. International Symposium on Space Flight Dynamics ISSFD, 2015. 8. S.E. Schaeffer, “Graph clustering”, Computer Science Review, 1, pp.27- 3. C. Thiebaut, A. Klotz, J. Foliard, B. Deguine and M. Boër, “CNES optical 64, 2007 observations of space debris in geostationary orbit with the TAROT 9. S. Van Dongen, Graph Clustering by Flow Simulation, University of telescope: IADC campaign results”, 35th COSPAR Scientific Assembly, Utrecht, Ph.D. Thesis, 2000. 35, p.984, 2004. 10. A.J. Enright, S. Van Dongen and C.A. Ouzounis, “An efficient algorithm 4. A. Milani, G. F. Gronchi, M. D. M. Vitturi and Z. Knežević, “Orbit for large-scale detection of protein families”, Nucleic Acids Research, 30, determination with very short arcs I. Admissible Regions”, Celestial pp.1575-1584, 2002. Mechanics and Dynamical Astronomy, 90, pp.57-85, 2004. 11. B. Dorow, J.P. Eckmann, and D. Sergi, “Using curvature and markov 5. K.J. DeMars, M.K. Jah and P.W. Schumacher, “Initial orbit determination clustering in graphs for lexical acquisition and word sense discrimination”, using short-arc angle and angle rate data”, IEEE Transactions on Workshop MEANING-2005, 2004.
(Received 21 June 2017; Accepted 13 July 2017)
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76 JournalMethods of the British of Predicting Interplanetary and Processing Society, Breakups Vol. 70, ofpp.77-81, Space Objects 2017
METHODS OF PREDICTING AND PROCESSING BREAKUPS OF SPACE OBJECTS
ZACH SLATTON1 AND DIANA MCKISSOCK2 18th Space Control Squadron, 1521 Utah Ave, Bldg 8401, Vandenberg AFB, CA 93437, USA. Email: [email protected] and [email protected]
The 18th Space Control Squadron (18 SPCS) has created new techniques to predict, detect, process, and catalogue breakups. It has done so on behalf of Air Force Space Command (AFSPC), in support of U.S. Strategic Command’s Joint Functional Component Command for Space, which is charged with executing USSTRATCOM’s presidentially assigned Space Operations mission area. This paper presents the process of predicting propulsion system-related breakups through the detection of outgassing, which has led to the successful prediction of the breakup of a rocket body. 18 SPCS methods for tasking, correlating uncorrelated tracks (UCTs), and finding breakup pieces are shown. Also presented are existing and new approaches to finding the time and location of a breakup, which assists in determining the cause. Finally, we explore a new method for determining the parent piece of a breakup, which was essential in finding the main body of an active payload and six rocket bodies in past breakup events. These methods have optimized breakup processing and increased the responsiveness of 18 SPCS. Keywords: Space Object Breakups, Prediction, Detection, Processing
1. PREDICTING BREAKUPS
The 18th Space Control Squadron (18 SPCS) is the tactical unit is highly eccentric, or may not happen at all if the argument under the 21st Space Wing (21 SW) responsible for maintaining of perigee is in the southern hemisphere. Therefore, 18 SPCS and providing foundational space situational awareness (SSA) cannot rely solely on headcount reports from the SSN for timely for the U.S. Department of Defense, as well as interagency, detection of breakups. This has motivated the squadron to commercial and foreign partners around the globe. The core develop a procedure for predicting breakups due to the failure functions of 18 SPCS include maintaining the space catalogue of propulsion systems. through space surveillance and tracking, generating spaceflight safety data, and processing high-interest events such as On Friday, October 1, 1999, a 1 SPCS analyst noticed launches, reentries, and breakups. In years past, this role was outgassing by object 21734, listed in the satellite catalogue as accomplished successively by the Space Control Center (SCC), an SL-14 rocket body. The analyst increased sensor tasking 1st Space Control Squadron (1 SPCS), and most recently the before the weekend, and identified that the rocket body broke 614th Air Operations Center (614 AOC), also referred to as the up the following Monday. This was the first prediction of Joint Space Operations Center (JSpOC). an unintentional breakup in history, and demonstrated that outgassing could precede a breakup for events related to 18 SPCS defines a breakup as the usually destructive propulsion systems. disassociation of an object, often with a wide range of ejecta velocities. A satellite breakup may be accidental or the result The 18 SPCS uses the Astrodynamics Support Workstation of intentional actions. 18 SPCS also processes anomalous (ASW) to maintain the high accuracy catalogue. ASW employs debris-causing events which are the unplanned separation, a calculated parameter, Adaptive Linear Element (ADALINE), usually at low velocity, of one or more objects from a satellite, to detect events based on user-set thresholds specific to each which remains essentially intact. Anomalous debris-causing space object. If an object has event detection turned on and the events can be caused by material deterioration of items such observations that come in after the epoch of the state vector as thermal blankets, protective shields, or solar panels, or by break the defined ADALINE threshold, then the object will fail the impact of small particles. The number of debris generated automatic processing and transfer to a manual processing list. and/or the operational status of the spacecraft is not indicative This notifies the analyst that the object has deviated from normal of the type of event; both breakups and anomalous events may orbital motion, and requires manual intervention to update its result in few or many pieces, and may or may not affect the orbital parameters in the catalogue. Traditionally only active capability of the spacecraft. This paper will focus on breakups satellites have event detection turned on to detect manoeuvres. as the destructive disassociation of an object. However, event detection can be used to detect other Traditionally, 18 SPCS relies on the Space Surveillance activities in addition to manoeuvres. For example, if a rocket Network (SSN) to deliver multiple headcount reports to detect body outgasses, the resultant observations will break the breakups. This can take an extended period of time if an object ADALINE threshold. If event detection has been turned on for this rocket body, it will be placed onto the manual intervention This paper was presented at the ESA 7th European Conference on list, which will alert the analyst that something abnormal has Space Debris, ESA/ESOC, Darmstadt, Germany, 18-21 April 2017 occurred or is occurring.
77 Zach Slatton and Diana McKissock
The objects designated as SL-12 (AUX MOTOR) in the space catalogue have fragmented more than any other space object in history. Due to the long time between tracking by the SSN, their high eccentricity, and the rapid separation of the debris pieces from the parent, many times a multiple headcount is not detected immediately after breakup. For example, in one case, a JSpOC analyst identified a SL-12 (AUX MOTOR) breakup several months after it had taken place. Similar to the event in 1999, 18 SPCS analysts recently noticed that SL-12 auxiliary motors often outgas before breaking into pieces. In response, new procedures have been put into place that increase tasking on objects when analysts notice outgassing, which increases the likelihood that the SSN will catch a multiple headcount at the time of breakup.
During post-event analysis of the June 1, 2016 breakup of space object #33473, designated as an SL-12 (AUX MOTOR), JSpOC analysts realized they had identified outgassing prior to the breakup; they also observed outgassing by the parent piece Fig. 2 Delta time vs. time plot of object #33472 showing outgassing for days after the event (Fig. 1). prior to breakup.
Based on these findings, a post-event analysis of the March 26, 2016 breakup of space object #33472, also listed as SL-12 (AUX MOTOR), was conducted. It revealed that outgassing occurred prior to the breakup and continued for days afterwards, as well (Fig. 2).
On July 25, 2016, 18 SPCS analysts identified outgassing of object #29680, another SL-12 (AUX MOTOR). Analysts immediately increased tasking, and two days later, on July 27, they detected the object’s breakup. Outgassing continued for days afterwards. This demonstrated the second successful prediction of an unintentional breakup in history (Fig. 3).
As of February 2017 ASW’s event detection has found three possible collisions and five outgassing events including the outgassing of SL-12 (AUX MOTOR), #33472, which previously broke up a year earlier. Fig. 3 Delta time vs. time plot of 29680 showing outgassing prior Knowing that outgassing can occur before propulsion- to breakup. related breakups happen allows 18 SPCS to predict that a fragmentation may occur. This is especially important when successive tracking is hours apart, such as for highly eccentric 2. TASKING, CORRELATION, AND rocket bodies. By activating event detection in ASW for rocket FINDING PIECES OF THE BREAKUP bodies and dead payloads, 18 SPCS will be able to monitor abnormal behaviour such as outgassing, and in turn, predict The first step in processing a breakup is tasking sensors to breakups that could threaten spaceflight safety. collect observations on the debris. Phased array sensors typically perform the best as they can put up a debris-sensing Fig. 1 Delta time vs. time plot of 33473 showing outgassing prior “fence” ahead of the parent satellite’s last known orbit and to breakup. collect observations for several minutes after it has passed. This effectively assesses the spread of the debris since the pieces usually disperse faster in-track than cross-track or radially. Large explosions or collisions pose exceptions because the inclination and right ascension of the node can spread several degrees due to the energy of the breakup. Unlike a mechanical tracker, a phased array radar can collect many tracks in a very short amount of time, making them invaluable in the detection of the pieces. Once adequate data is collected and assessed, the 18 SPCS Breakup Officer may confirm the event as a breakup, which results in notifications to interagency and security partners. Beginning in 2015, 18 SPCS added additional notifications specifically to all operators of active spacecraft, as well as the general public through Space-Track.org and social media, to support spaceflight safety and increase transparency on debris-causing events.
Once tasking and tracking are accomplished, 18 SPCS
78 Methods of Predicting and Processing Breakups of Space Objects analysts associate the resultant uncorrelated tracks (UCTs) to the breakup. The JSpOC mission system, SPADOC, does this automatically, but 18 SPCS analysts can increase the association parameters to pull in UCTs that may have been missed. Once initial pieces are created and correlated to the breakup, the parameters can be refined so that pieces that do not belong are not correlated.
Timely identification of the breakup pieces is important so that they can be used for conjunction assessment, to refine the breakup cloud model, and to determine the time of the breakup. When a piece is found and correlated to an event, it is created in the analyst catalogue, usually designated by the satellite catalogue number range 80000 to 80999. Initially designating these debris pieces as analyst objects allows their two line element set (TLE) history to mature and refine. Once a piece Fig. 4 In-track vs. time plot of Hitomi/ASTRO-H breakup. has a sufficient TLE history and analysts are convinced that its orbit can be maintained by the mission system automatically, implements special perturbations (SP) predictive modelling. 18 the piece is entered into the public catalogue. SPCS analysts have adapted it to find the mean separation time and the standard deviation or error of that time. It also gives a There are several methods for finding pieces of a breakup. delta-v or separation velocity of the pieces. This directly relates The quickest and easiest is visually finding strings of UCTs that to the energy of the breakup, which indicates the cause of the correlate to each other on a delta-time vs. time plot (Fig. 4). breakup. A highly energetic event could be due to a collision Delta-time is the measurement of how far off the observations or significant explosion, whereas lower-energy events could are from the prediction or propagation. If delta-time is negative, be due to small explosions or drag. Other methods can also the object has arrived before it was expected. If positive, the be employed. AFSPC’s Astrodynamics Standards software object has arrived later than expected. The advantage of this has a tool named the Breakup Analysis Module (BAM) which method is that people can recognize a trend that computers employs pinch point analysis and has been used in breakup cannot. processing for many years.
Other methods include UCT processing and UCT trending. Figure 5 shows the results of applying conjunction UCT processing mathematically determines which UCTs assessment software to NOAA 16 versus the NOAA 16 pieces correlate to each other; this is more sophisticated, but can after the breakup. The results are in miss distance (km) vs. time. take much longer due to the power required for computer Where the miss distances converge is the time of the breakup. processing. Many UCT processors use a different method, UCT trending. This method plots the Keplerian elements of the Another way to determine the type of event is to evaluate UCTs individually and visually strings them together, which the separation times of the pieces. If they separate hours or can be very reliable for finding outliers of a breakup. Overall, days apart, the event is most likely due to shedding or coolant there is no wrong way to find a debris piece as long as the end leaking, as demonstrated by Cosmos 1818 and Cosmos 1867 result is of good quality. [1]. If the pieces separate all at once, the event may have been an explosion or collision. 3. FINDING THE TIME AND CAUSE OF A BREAKUP The easiest way to investigate the cause an event for an active payload is to communicate with the owner/operator (O/O) of the Finding the time of the breakup up is important for two reasons. satellite. For instance, if the O/O states that they lost communication First, it can be used to find the latitude, longitude, altitude, and at a certain time, it can lead to identifying or confirming the time of location in the orbit of the breakup by propagating the parent the event. In the case of the Hitomi/Astro-H, the O/O verified that object before the time of the breakup to the time of the breakup. The latitude, longitude, and altitude reveal which part of the world the satellite was over when the event happened. If the Fig. 5 Conjunction assessment of NOAA 16 breakup. satellite broke up while intersecting with a launch trajectory when a launch occurred, there may have been a collision. The location in the orbit can also help determine the cause of the breakup. If a satellite is close to reentry and fragments on a perigee pass, then the breakup is most likely aerodynamic.
The second reason the time of the breakup is important is debris modelling. Along with the energy of the breakup, the time is needed to model the debris cloud appropriately and determine the risk to surrounding satellites. There are many methods for modelling clouds of breakup debris, but they are all useless if they do not know when and where to start modelling. 18 SPCS can determine the time of the breakup in several ways.
The most straightforward is using conjunction assessment software, specifically ASW’s SuperCOMBO, which
79 Zach Slatton and Diana McKissock the satellite spun itself apart [2]. If an O/O maintains contact with a satellite and can still control it, the 18 SPCS Breakup Officer will not categorize it as a breakup, except in extreme cases; rather, it will be deemed an anomalous debris-causing event, and the pieces will be expeditiously catalogued for conjunction assessment purposes.
4. FINDING THE PARENT PIECE
The parent piece of a breakup is the main body of the original object or the biggest piece. Finding the parent piece of the debris is important for two reasons. First, there needs to be an object in the place of the original number in the catalogue Fig. 6 AGOM plot of Hitomi breakup. to keep the catalogue in order. Second, the parent object may break up again, as has happened with several SL-12 auxiliary motors. To determine the biggest piece, 18 SPCS relies on the radar cross-section (RCS) calculated by the SSN. This has many limitations, the most significant of which is that the RCS data can be erratic and sparse depending on sensor coverage and availability. Another factor is that the RCS depends on the frequency of the radar, so two different radars will give two different values for RCS. Additionally, some radars have limits on how many objects per pass they can track. Also, for most SL-12 auxiliary motors there are usually two objects that contend for the largest RCS.
With this in mind, 18 SPCS analysts have developed a Fig. 7 BC plot of Hitomi breakup. method that works extremely well to determine the parent object of a breakup. 18 SPCS maintains a history of the special perturbations state vectors which include the Ballistic Coefficient (BC) and the measurement of radiation pressure measured as Area Gamma Over Mass (AGOM). Both are functions of area-to-mass ratio. When viewing the breakup pieces’ BC/AGOM histories with that of the parent object prior to the breakup, the main body should have similar BC/ AGOM values to that of the original object. Note, however, that this may not always be the case for catastrophic breakups. Depending on the altitude of the perigee of the pieces and the parent, either AGOM or BC may be more definitive than the other. Fig. 8 AGOM plot of #33473 and biggest pieces. This method was essential in finding the main body of Hitomi (ASTRO-H) when it fragmented. In this case, the main body was not the largest piece, marking a flaw in traditional 18 SPCS methodology. Figures 6 and 7 shows the AGOM and BC histories of the original object, #41337 (red), plotted against the largest piece, #41442 (green), and the main body after the breakup, also numbered 41337 (red). Note that the post-breakup #41337 piece matches the pre-breakup parent object closer than the largest piece. Upon realizing this, sensor resources were allocated to track the main body as opposed to the biggest piece.
In Figs. 8 and 9, the pre-breakup AGOM and BC histories of SL-12 auxiliary motor #33473 (red); is compared to the largest Fig. 9 BC plot of #33473 and biggest piece. post-break up pieces 80503 (green), 80500 (blue), and 80504 (white), all of which have similar RCS. As seen, 80503 matches the pre-breakup parent before the breakup better than the other despite these challenges, for the cases shown 18 SPCS was able pieces, indicating that it is the main body. to determine the post-breakup parent object significantly faster using BC/AGOM history correlation than they would have The primary drawback to this method is the time that it using traditional methods. takes to build a decent AGOM/BC history for each object. Calculating a high-fidelity AGOM and BC requires a minimum 5. CONCLUSION span of three days of observations. This is hindered by the fact that the main body may still be outgassing for days after the Through the development of new analytical methods, 18 breakup, which is the case of SL-12 auxiliary motors. However, SPCS can now detect, process, and catalogue breakups
80 Methods of Predicting and Processing Breakups of Space Objects faster than traditional approaches allowed. By using event in the past few years has also expedited the cataloguing processing for dead payloads and rocket bodies, many of post-break up pieces, as well as determining the parent breakups are detected sooner, and some can even be piece of the event. In short, 18 SPCS is now more efficient predicted. The employment of new processing techniques at processing breakups than ever before.
REFERENCES
1. NASA, “New Debris Seen from Decommissioned Satellite with Nuclear spacenews.com/jaxa-closing-in-on-cause-of-hitomis-breakup. (Last Power Source”, Orbital Debris Quarterly News, 13, pp.1-2, 20009. Accessed 21 June 2017) 2. J. Foust, “JAXA closing in on cause of Hitomi’s breakup”, http://
(Received 2 June 2017; Accepted 19 June 2017)
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81 H.Journal Wilden, of theC. Kirchner,British Interplanetary O. Peters et al. Society, Vol. 70, pp.82-84, 2017
GESTRA-TECHNOLOGY ASPECTS AND MODE DESIGN FOR SPACE SURVEILLANCE AND TRACKING
H. WILDEN1*, C. KIRCHNER1, O. PETERS1, N. BEN BEKHTI1, R. KOHLLEPPEL1, A. BRENNER1 AND T. EVERSBERG2 1. Fraunhofer FHR, 53343 Wachtberg, Germany. 2. German Space Agency DLR, 53227 Bonn, Germany. Email: [email protected]* and [email protected]
On behalf of the Federal Government the German Space Administration (DLR RFM) commissioned the Fraunhofer Institute for High Frequency Physics and Radar Techniques (FHR) in 2015 to design and develop a phased–array based radar for monitoring the low Earth orbit. This so-called German Experimental Space Surveillance and Tracking Radar (GESTRA) will support the German Space Situational Awareness Centre to generate a catalogue of orbital data for all objects with a minimum radar cross section (RCS) at altitudes of less than 3000 km. Keywords: GESTRA, tracking radar, catalogue of orbital objects
1. INTRODUCTION
The strong dependency of human society on infrastructure in space demands for continuous space surveillance activities. Considering potential sensor technologies, operational radar- based space surveillance systems play an important role in detecting debris objects in the earth orbit. On behalf of the Federal Government the DLR Space Administration (DLR RFM) commissioned the Fraunhofer Institute for High Frequency Physics and Radar Techniques (FHR) in 2015 to design and develop a state-of-the-art phased –array radar to monitor the low Earth orbit. This so-called German Experimental Space Surveillance and Tracking Radar (GESTRA) will support the German Space Situational Awareness Centre to generate a Fig. 1 Beam strategy for track-while-scan mode. catalogue of orbital data for all detected objects at altitudes of less than 3000 km. Incorporating most challenging phased- array technologies, the concept of the GESTRA radar system explains the detailed requirements defined by DLR-RFM will provide high quality data sets. This radar sensor gives the concerning high standards in product assurance and quality basis for future scientific investigations within the cooperation management, documentation and verification, which were frame of the contributing nations. derived from the ECSS standards of the European space agencies. 2. REQUIREMENTS OF THE RADAR SENSOR 3. DEVELOPMENT OF THE GESTRA Monitoring the low Earth orbits up to an altitude of 3000 SYSTEM AT FHR km and assuring the detection of all objects with a certain minimum radar cross section can only be achieved with a The subsystem complexity and the high transmit power lead to radar system based on phased-array principles and newest the design of a close-monostatic pulsed phased-array radar in module and beamforming technologies. Once, space objects L-band (1280-1390 MHz). have been detected, special track-while-scan- radar modes focus energy and timing in order to improve the data quality The transmit subsystem and the receive subsystem are and information about the object orbit parameters (see Fig. integrated individually in large-size shelters of 18 m × 4 m × 1). Due to the main orbit trajectories, the strategy for space 4 m being separated by about 100 m. In order to extend the field surveillance is to form and monitor a wide angle fence of of view beyond the scan area of the array, each array antenna closely separated transmit beams and to detect all objects is mounted on a 3-axes positioner with wide angle mechanical passing this fence. rotation features (see Fig. 2). Integrated scissors lifts allow to move the antenna frontends from transport position into The partly mobile radar sensor is developed to allow an operational position within the 5 m-radome on the shelter roof. experimental operation for 12 years. This long term operation Both antenna apertures consist of 256 active cavity-backed This paper was presented at the ESA 7th European Conference on stacked patch antennas distributed on a triangular grid of Space Debris, ESA/ESOC, Darmstadt, Germany, 18-21 April 2017 the planar circular array. The transmit elements excite a
82 GESTRA-Technology Aspects and Mode Design for Space Surveillance and Tracking
is mandatory. Each high power single radiator is connected to a transmit module with high efficiency.
The solid state transmit modules developed at FHR are designed to deliver a pulsed output power higher than 1000 W with a duty cycle of maximum 25%.
The transmit module shown in Fig. 4 depicts the 3-stage structure of the amplifier design. Several programmable features in the transmit path allow the output pulse to be compliant with ITU concerning out of band spectrum. Assuring mode-adapted pulse length large buffer capacitors mounted on the planks store the necessary electrical energy. By means of 6 bit-phase shifters the beam shape is switched from beam broadening in surveillance mode to pencil beam in track mode.
5. RECEIVE SYSTEM
To guarantee a low system noise figure independent of the ambient temperature the receiver system utilizes the same liquid-cooling system as the transmit system. The receiver is based on the so-called “software defined radio” principle with the received signal being sampled by each element on the carrier frequency. The associated receiver module (see Fig. 5) contains two identical analog microwave pre-amplifying paths having Fig. 2 Mechanical model of the antenna with 3-axes- positioner. adjustable gain and filter centre frequency. A 12-bit dual-channel A/D converter digitizes the dual-polarized received signal, linear polarization and the receive elements are designed for which is fed into the central FPGA. A firmware was developed dual polarization in order to cope with ionospherical wave that implements digital downconversion, baseband filtering and propagation effects (Faraday Rotation). The demonstrator of an the first-level beamforming. Thus the radar frequency can be antenna quarter is shown in Fig. 3. switched from pulse to pulse enabling flexible waveforms.
On the backside of the antenna plate the element outputs are The optical digital outputs are combined using adapted connected to the corresponding modules for receive and transmit beamforming units. These units allow to arbitrarily shape respectively. For maintenance reasons the modules of both multi-beam pattern of the receiving antenna. Only this digital antennas are arranged on so-called plank structures enabling beam processing in combination with a beam broadening array liquid-cooling and power supply to the modules. The planks weighting on transmit allows to meet the requirements of high form the least replaceable units additionally accommodating speed space surveillance. To improve the sensitivity of the radar decentral power supplies and the necessary control units. The system for given transmit power and noise figure, multiple radar mass of all planks summarizes to nearly 2 tons for each of the pulses are combined with a sophisticated high-performance two subsystems being carried by the antenna plate. radar processor, having a thermal power loss of 40 kW.
4. TRANSMIT SYSTEM 6. MODE DESIGN OF THE RADAR
Due to the high radiated average power needed to meet the In order to facilitate the operation of space surveillance, range requirements of the radar, a separate transmit subsystem several operational modes are implemented with different
Fig. 3 Demonstrator of an antenna quarter, front side (left) and backside (right) with large backplane PCB.
83 H. Wilden, C. Kirchner, O. Peters et al.
will be remotely controlled by the German Space Situational Awareness Centre in Uedem. This makes it necessary to monitor the status of vital subsystems and processes permanently, as well as of all system components. More than 2000 sensors measure moisture levels, air and water pressures, flow rates of the coolant, and currents in both GESTRA shelters to ensure safe operation.
In total the shelters weigh more than 90 tons each.
7. OUTLOOK
Fig. 4 Transmit module. In November 2016 the Fraunhofer FHR successfully completed the critical design review of the GESTRA system. Thus all of the subsystems will now be built and tested. Algorithms as well as firmwares will be further optimized. Starting in March 2017 all of the subsystems will be integrated into the shelters. After the final verification, the system will be handed over to the German Space Situational Awareness Centre in Uedem.
ACKNOWLEDGMENT
The work presented in this paper was performed on behalf of the German Space Agency with funds of the German Federal Fig. 5 Dual polarized Digital Receive Module. Ministry of Economic Affairs and Technology under the grant No. 50LZ1401. scan strategies. Due to the main orbits of the space debris the The authors deeply appreciate and thank for the tremendous beam directions form of a fence with up to 90° coverage, either support of the development team consisting of up to 34 formed in azimuth or in elevation. Once an object has been members. Additionally, special thanks are devoted to the detected, a track beam is fixed to the object and tracks it within main sub-contractors Kniel (development of the adapted the area of the antenna beam coverage. The resulting object power supplies), MBM/AlpinaTec (development of the path information is improved by the increased observation 3D-positioner), innovatek (development of the antenna fluid time. The detection performance enhances, if a-priory orbit cooling system) and Weiss Umwelttechnik (chiller and shelter knowledge of the observed object is taken into account, based climate) for their precious component optimization activities, on catalogue information. interactive concept discussions and very helpful contributions to the development of this innovative surveillance and tracking After system delivery to the contractor the GESTRA system phased-array-radar.
REFERENCES
1. J. Ender, L. Leushacke, A. Brenner and H. Wilden, “Radar techniques for 5. H. Wilden, C. Kirchner, O. Peters, A. Brenner, J. Vera, J.M. Hermoso, J. space situational awareness”, Proceedings of 2011 International Radar Torres, M. Sciotti and P. Besso ,“Low-cost Radar Receiver for European Symposium (IRS), 2011. Space Surveillance”, Proceedings of IET Radar 2012, International 2. M. Sciotti, P. Besso, T. Flohrer and H. Krag, “Low Earth Orbit objects Conference on Radar Systems, Glasgow, UK, 2012. tracking and orbit determination from ground-based phased array radar 6. M. Mendijur, M. Sciotti and P. Besso, “Management of radar resources systems”, Proceedings of 2011 International Radar Symposium (IRS), for space debris tracking”, Proc. of SPIE2012 ”Defence, Security, and 2011. Sensing Symposium”, Baltimore, USA, April 2012. 3. E. Brookner, “Phased-array and radar astounding breakthroughs-an 7. H. Wilden, C. Kirchner, O. Peters, N. Ben Bekhti, A. Brenner and T. update”, Proceeding of 2008 Radar Conference, 2008. Eversberg, “GESTRA- A phased array based surveillance and tracking 4. H. Krag, H. Klinkrad, T. Flohrer and E. Fletcher, “The European radar for space situational awareness”, Proceedings of 2016 IEEE Surveillance and Tracking system- Services and Design Drivers”, Proc. International Symposium on Phased Array Systems and Technology of SpaceOps 2010 Conference, Huntsville, US, 2010. AIAA-2010-1927. (PAST 2016), Boston, USA, 2016.
(Received 10 July 2017; Accepted 13 July 2017)
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84 Journal of Information-Theoreticthe British Interplanetary Approaches Society, Vol.to Space 70, pp.85-97,Object Collision 2017
INFORMATION-THEORETIC APPROACHES TO SPACE OBJECT COLLISION
K. DEMARS1 AND M. GUALDONI2 Missouri University of Science and Technology, Rolla, MO 65409, USA. Email: [email protected] and [email protected]
In view of the high value of space assets and a growing space debris population, collision analysis is of great significance. Collisions between space objects can, at best, be determined in a probabilistic manner. Collision probability between objects is closely related to close approaches of the objects, where the traditional approach to determining the collision probability is predicated upon finding a time of closest approach and bounding this with a deterministic time interval. This paper investigates the application of information theory to the determination of a conjunction interval. Cases of two and more-than-two objects in close proximity are considered, and methods for determining the interval in which the objects are interacting are developed. Simulations are carried out to compare the developed methods to more conventional techniques. Keywords: Collision assessment, information theory, space object tracking
1. INTRODUCTION
The population of tracked space objects is constantly This paper investigates the connection between concepts increasing due to new launches, increases in sensor tracking in information theory, such as information divergence and capabilities, fragmentation of existing space objects, and the entropic information, and those of collisions between space generation of new debris caused by random or intentional objects. Such methods naturally enable the inclusion of the collisions. Collisions between space objects (either active uncertainty of the objects and generalize the time of closest spacecraft or space debris) can only be determined in a approach to a window of time over which the two objects probabilistic manner due to the lack of perfect knowledge are in close proximity. The developments are first considered regarding the parameters that characterize the motion of for the case where the uncertainties in the space object states space objects, i.e. the translational and rotational state of the are taken to be Gaussian, and then this assumption is relaxed space objects as well as the environment in which the space to handle the situations where the uncertainties are non- objects are operating. Fundamentally, collision analysis Gaussian. that is predicated upon nominal orbit parameters without taking into consideration the uncertainty in the parameters Another generalization to the problem of multi-object is inaccurate. collisions is also considered. Whereas a minimum approach distance can be employed for the close encounter of two The probability of collision between two space objects objects, there is no natural extension to the case where more provides a quantitative measure of the likelihood that the than two objects are in close proximity other than pairwise space objects will collide with each other. Collision probability considerations of two objects at a time. Close proximity between two objects is closely related to close approaches of multiple objects can readily occur in multi-spacecraft of the two objects. The traditional method for initializing a formations, such as those assembled from small satellite collision probability assessment is to determine the time of platforms. The information theoretic approaches, unlike the closest approach (TCA) based on predictions of the space traditional methods, can be naturally extended into multi- object motion that are solely made with estimates of the object domains in order to provide a single framework for states of the objects. Determining the TCA can be carried out handling these problems. in several ways. One approach is to numerically propagate the state estimates and find the time at which the propagated Simulations are carried out to highlight the efficacy of estimates come closest, particularly within a combined hard the developed methods using synthetic data for space object body radius [1]. More sophisticated approaches employ Taylor collision scenarios. Two-object and three-object collision series expansions [2] and minimization of the relative position scenarios are considered, and the results of the information vector using surrogate based optimization [3] to improve upon theoretic approaches are compared to more traditional the determination of the TCA. These approaches, however, approaches for determining the relevant characteristics neglect the influence that the uncertainty of the space object involved in space object collisions. states may have on determining when the objects are in close proximity to one another. While the omission of such effects 2. PROBLEM STATEMENT may be appropriate for regularly tracked objects, it begins to break down as the uncertainties in the estimates of the states The central focus of this paper is on the determination of an grows larger. interval during which two or more space objects are in close This paper was presented at the ESA 7th European Conference on proximity and exhibit positional interactions, where the Space Debris, ESA/ESOC, Darmstadt, Germany, 18-21 April 2017 uncertainty of the space objects, in addition to their nominal
85 K. DeMars and M. Gualdoni locations, is taken into account. As such, a probabilistic ()()()()ij, i ii quantification of the states through the use of a probability x~p xmP ;, density function (pdf) is required. Assume that M objects are g( xx) considered. The states of the objects at time t are defined as (i,j) th th k where x denotes the j sample of the i object. These samples can then be partitioned into position and velocity components ()i (i,j) (i,j) T (i,j) T T ()i r as x = [(r ) (v ) ] . As only position interactions are of x = k k ()i interest, the velocity samples are not required. Given a sample vk position from each object, the distance between the samples is computed as where ()()()j2, jj 1, ()i r =rr − iM∈{}1,2,..., ,rk ()i is the position of the ith object at time t , and v is the velocity k k where ⋅ represents the Euclidean norm. If the distance is of the ith object at time t . Additionally, the uncertainties in ()j k ()i not greater than a specified cutoff distance, c, i.e. if rc≤ , the object states are represented by the pdfs p (xk ) . In this then the jth samples of the objects’ positions are deemed to be paper, the pdfs of the single-object states are taken to be either in close proximity. This process is carried out for a set of N Gaussian distributions or Gaussian mixture (GM) distributions. samples taken from the pdfs of both of the objects. The total Regardless of the distribution, it is assumed that the pdf is number of interacting samples, i.e. the number of samples ()j known at a sequence of times, and these pdfs are the inputs to satisfying rc≤ , is denoted S, and the percentage of the different methods described herein to determine when the interacting samples is computed as T = 100(S/N). A tolerance, objects are or are not in close proximity. For ease of notation, T , can then be set on the percentage of interacting samples, the time index will be dropped in the following developments, 0 and any time at which T > T0, the objects are in close proximity with the understanding that the results can be applied at any to one another. time. There is no restriction of this method to operating on 3. TWO-OBJECT APPROACHES Gaussian distributions. While the preceding discussion has focused on the Gaussian case, it is straightforward to extend Assume that there are two objects with states given by x(i) = (i) T (i) T T it to non-Gaussian distributions, provided that the distribution [(r ) (v ) ] , where i {1,2}. Additionally, it is assumed that can be sampled. the uncertainties of the objects are Gaussian, such that the pdf th ∈ of the i object is 3.2 Mahalanobis Distance ()i= ()()() i ii pp()xg( xmP;, xx) While the distribution sampling approach provides a direct method for determining an interval over which two objects are where pg(x;a,A) represents the Gaussian pdf in x with mean a T in close proximity, it also requires significant computational and covariance A = A > 0, such that effort. Therefore, alternative methods are sought which can also provide a method for determining the relevant interval −12 1 T −1 pg =()xaA; , = 2π A exp −−()() xa A xa − while accounting for the uncertainties of the objects. 2 Let y be defined as the joint state of the two objects, i.e. The mean and covariance of the Gaussian distribution can be partitioned into position and velocity elements as x(1) y = (1) ()i ()()ii (2) ()iimr () PPrr rv x mP= and = xx()i ()()ii mv PPvr vv Provided that the two objects are uncorrelated and that their
th ()i ()i individual distributions are Gaussian, the pdf of y is also where, for the i object, mr is the position mean, mv is ()i ()i Gaussian, or the velocity mean, Prr is the position covariance, Pvv is the velocity covariance, and p(y) = pg(y;my, Py) T ()()ii= PPrv() vr where the mean and covariance of y are is the position-velocity cross-covariance. ()11() m P0 mP= xxand = 3.1 Distribution Sampling yy()22 () mxx 0P One straightforward approach to determine the interval of When the two objects are correlated, the pdf of y is still interaction between two objects is to generate a number of Gaussian; however, in this case, the covariance of y will not be samples from the pdfs of the objects and determine the number block diagonal. of samples that are within close proximity to one another. This process can be carried out at any time, which enables Now, define z to be the relative position of the two objects, the determination of the interval in which the objects are which is to say interacting. Given the pdfs of the two objects, samples can be drawn from the pdfs as z = r(2) − r(1)
86 Information-Theoretic Approaches to Space Object Collision
It is clear that z is a linear transformation of y, where the the probability gate, P, and the degrees of-freedom, nr), is the transformation is given by interval over which the objects are in close proximity. Much as the distribution sampling approach relies on selecting the z = [−I 0 I 0]y = Hy cutoff parameter, the Mahalanobis distance approach relies on selecting the probability gate. (i) (i) If the dimension of r is nr, then the dimension of x is 2nr, and the dimension of H is nr ×4nr. The individual elements 3.3 Kullback-Leibler Divergence that comprise H are of dimension nr × nr. Since z is a linear transformation of a Gaussian random variable, it directly The Mahalanobis distance approach improves upon the follows that z is also Gaussian. The pdf of z is distribution sampling approach by removing the computational complexity, but it is restricted to operate on Gaussian distributions p(z) = pg(z;mz, Pz) in order to establish a probability gate. To begin generalizing the interval determination to the realm of information-theoretic where the mean and covariance are quantities, which also provide the means for handling non- Gaussian pdfs, the information divergence is considered. mzy= Hm P= HP HT Generally speaking, an information divergence is a measure zy of similarity or dissimilarity between two pdfs. Given a generic Alternatively, by applying the relationship for the linear information divergence describing the directed distance from p(x) to q(x) denoted by D[p||q], the “distance” is called a metric mapping, the mean and covariance of z can be found to be if [8]: ()()21 1. D[p||q] ≥ 0 with equality if and only if p(x) = q(x) (non- mmzr= − m r negativity and positive definiteness), ()()12 PPz= rr + P rr 2. D[p||q] = D[q||p] (symmetry), and
* 3. D[p||r] ≤ D[p||q]+D[q||r] (sub-additivity/triangle Given a sample from the distribution p(z), denoted by z , the inequality). squared Mahalanobis distance is [4] Information divergences that only satisfy the first condition T d 2=−− zm * Pzm− 1* are not metrics and are referred to as asymmetric divergences. ()()zz z Satisfaction of the second condition necessarily removes the restriction of referring to the divergence as asymmetric. It is well known that the squared Mahalanobis distance, when calculated for samples drawn from Gaussian distributions, is The most often used information divergence is the Kullback- statistically described by the chi-squared distribution, which Leibler (KL) divergence, which is given by [9, 10] is characterized by a parameter that is known as the degrees- of-freedom. The degrees-of-freedom employed in the chi- p ()x squared distribution is equal to the dimension of the random DKL pq = p()xxlog d (3) ∫x q ()x variable; hence, it follows that the distribution of the squared Mahalanobis distance is [5] The KL divergence is defined for arbitrary pdfs, p(x) and q(x), d 22 where x ∈⊆ . It is, however, only possible to determine pd= p2 d; n ()()χ r closed-form relationships for certain cases, such as the case where both pdfs are taken to be Gaussian. Let p(x) be a Gaussian where pχ 2 () ak; represents the chi-squared pdf in the variable a pdf with mean a and covariance A, and let q(x) be a Gaussian with parameter k (with k degrees-of freedom). Making use of the pdf with mean b and covariance B; that is, chi-squared distribution, a probability gate, or threshold, can be used to associate (or reject association of) a sample. If the probability pp()()()()x= gg xaA; , and qp x= xbB;, (4) of accepting the sample is denoted by P, then it is possible to tabulate values of γ such that d2 ≤ γindicates an associated sample. Substituting p(x) and q(x) from Eq. (4) into the KL divergence
For instance, when the probability gate is set to accept 90% of the of Eq. (3), it can be shown that the KL divergence for Gaussian samples for a 2 degree-of-freedom case, the chi-squared distribution distributions is dictates that γ = 4.6052. This method is often employed to establish confidence intervals for data association [6, 7]. 1 −−11T − 1 DKL pq = logBA+ tr{} BA +−()() ab B ab −−d 2 In the context of determining whether two objects are in close proximity, the objective is to determine if the origin, z = where tr{·} represents the matrix trace. ∗ 0, is associated to the relative position distribution, pg(z;mz, Pz). The Mahalanobis distance, with respect to the origin and the One downside to the KL divergence is that it is an asymmetric relative position distribution, is divergence. While this does not prevent one from forming the
directed “distance” between the two distributions p(x) and T −1 21T − ()()21()() 12()() 21 q(x), it does mean that the “distance from p(x) to q(x)” is not ==−+ − d mPmmmz z z() r r() PP rr rr() mm r r the same as the “distance from q(x) to p(x)”. For instance, the (2) reverse KL divergence, which is given by 1 −−11T − 1 2 DKL qp = logAB+ tr{} AB +−()() ba A ba −−d Then, the interval over which d ≤ γ, (where γ is dictated by 2
87 K. DeMars and M. Gualdoni
is not equivalent to DKL[p||q]. Thus, an interval determination 4. MULTIOBJECT APPROACHES using the KL divergence would differ from an interval determination using the reverse KL divergence. To circumvent The methods described thus far are predicated and built upon this, the symmetric KL divergence is defined as the assumption that the interval determination for the interaction of the objects is determined for the case of only two objects. 1 As described, the distribution sampling, Mahalanobis distance, DS = pq( DKL + pq DKL qp) 2 and symmetric KL divergence methods necessarily depend upon the restriction to two objects. One way of overcoming this Substituting for the relationships for the KL and reverse KL shortcoming is to consider all possible pairwise combinations divergences, it follows that the symmetric KL divergence can of the set of M ≥ 2 objects and apply the methods as described be expressed for Gaussian distributions as previously. Even when advanced screening methods are employed to reduce the number of objects considered [11, 12], 1 −−11 T −−11 the combinatoric growth associated with pairwise combinations DS pq =tr{BAAB +} +() ab −() A + B() ab − −2d 4 can significantly increase the required computational burden. (5) 4.1 Information Entropy The relationship for the symmetric KL divergence given in An alternative approach is to further investigate information- Eq. (5) holds for any Gaussian distributions p(x) and q(x). theoretic methods, like the symmetric KL divergence, but The symmetric KL divergence is now specialized to the space within the context of multitarget tracking. A related idea to the object collision case. First, note that “collisions” in the velocity information divergence is the information entropy, or simply space are not of interest; only collisions that occur in position entropy. space are of interest. Therefore, p(x) and q(x) are chosen to be the position marginal densities Information entropy originated in the context of quantifying the amount of uncertainty in the generation of a ()1= ()()() 1 11 pp()rg( r;, mP r rr ) received message or in the amount of “choice” present in the transmission of a message in communication [13], which built ()2= ()()() 2 22 qp()rg ( r;, mPr rr ) upon earlier works that investigated descriptions of the amount of information present in an event space [14]. Essentially, the entropy is a measure of the “size” of the uncertainty of a random As the symmetric KL divergence is under consideration, it is variable. The entropy is minimal when there is no uncertainty not relevant which object is represented by p(x) and which present, i.e. the random variable becomes deterministic; the object is represented by q(x); for either the KL or reverse KL entropy is maximal as all possible outcomes of the random divergence, this is not the case. With this specialization of the variable become equiprobable; and the entropy monotonically pdfs, the symmetric KL divergence is increases as the uncertainty increases. 1 = ΛΛ()()()()21+ 12 For the communication case, the random variable is discrete DS pq tr{ rrPP rr rr rr } 4 in nature, and the uncertainty of the random variable is
T ()()12()() 1212()() described in terms of a probability mass function (pmf). The +−mmr rΛΛ rr + rrmm r − r −2n r () ()() resulting entropy is termed the Shannon entropy, which is [13]
(6) ∞ −1 H[]ρ= − ρρ()() nnlog{} ()()ii ∑ Λ = n=−∞ where rr()P rr . An interesting connection between the symmetric KL where n is the random variable and ρ ()n is the pmf of n. divergence and the Mahalanobis distance can be established in Subsequently, this definition was extended to continuous the special case where the position covariances of the two objects random variables. For a probability density p(x) with support ()()12 d are identical. Let PPrr= rr = P rr ; then, it can be shown that the over the entire state space ⊆ , the Shannon (differential) symmetric KL divergence given in Eq. (6) can be expressed as entropy, Hp[] , is defined to be
T 1 ()()21−1 ()() 21 DS pq =mmPmm rrrrrr − − Hp[] = − p()()xlog{} p xx d (7) 2 () () ∫
In a similar fashion, the squared Mahalanobis distance given in The terminology differential entropy is often used to distinguish Eq. (2) becomes between the entropy for discrete and continuous random variables, but this distinction will be omitted herein. Whereas T 211 ()()21− ()() 21 the Shannon entropy for discrete random variables is absolute, d =−−mmPmm 2 ()rrrrrr() the entropy of Eq. (7) is relative to the coordinate system. That is, if the coordinates are changed, including the units of x, the Thus, when the two objects possess the same position entropy will change. covariance, the symmetric KL divergence and the squared Mahalanobis distance (computed with respect to the origin) While Shannon entropy provides a scalar measure for coincide. This is, of course, a rather specialized case. It does, characterizing the uncertainty of a random variable, it is not however, provide some insight into the nature of the symmetric the only option available. Shannon’s definition of entropy was KL divergence. generalized by Rényi to produce a family of entropy measures
88 Information-Theoretic Approaches to Space Object Collision
[15, 16], which were originally termed “informations of order α, ” but which are now referred to simply as Rényi entropy. The Rényi entropy is defined as
()α 1 α Hp[] = log p()xx d (8) 1−α {}∫ where α is a control parameter. The Rényi entropy is undefined for α = 1, but in the limit as α → 1, it is well known that the Rényi entropy reproduces the Shannon entropy. Similar to the Shannon entropy, the Rényi entropy is relative to the coordinate system.
Entropy can be used to describe the relative concentrations of uncertainty for different scenarios. That is, a smaller entropy indicates a more highly concentrated, or more highly localized, uncertainty. As an example, consider the schematic representation of collisions occurring between three objects shown in Fig. 1. In the beginning frame, which is the one denoted t , the three objects are distinctly separated. As time 1 Fig. 1 Schematic representation of collisions between three continues, Objects #2 and #3 begin to interact, as observed objects. in frame t2. This interaction continues through frame t3, at which time Object #1 begins interacting with the other two objects. Finally, in frame t4, the interaction between three objects has returned to interaction between two objects. This where n is the cardinality of the RFS, ρ ()n is the cardinality distribution, and s(x(i)) is the single target spatial density of the example shows that concentrations of uncertainty are exactly representing interactions between objects. ith target, which is taken to be a valid (single-target) pdf. Further descriptions can be obtained within the i.i.d. cluster process by Shannon entropy, as defined in Eq. (7), cannot be used to modelling the cardinality distribution as a Poisson distribution, describe the level of interaction between multiple objects, as it which is given by is the entropy obtained from a pdf representing the uncertainty of a single object. Augmenting the state to include multiple 1 n −λ objects, such as is done in Eq. (1), also does not work. When ρλ()ne= (10) n! the objects are independent, it is straightforward to show that the entropy of the distribution for the augmented state is equal where λ is the rate parameter. It is also well known that λ is both to the sum of the entropies of the distributions of the individual the mean and the variance of the Poisson distribution. objects. In essence, since the state space is extended to represent the multiple objects, there is no collision between the objects in Moment approximation methods are often employed this space. Instead, the appropriate approach is to work within in multitarget tracking due to their ability to provide the realm of multitarget tracking. computationally tractable solutions. Two such methods, referred to as the probability hypothesis density (PHD) [19, 4.2 Random Finite Sets 20] and cardinalized probability hypothesis density (CPHD) [21, 22, 23] filters, approximate the multitarget Bayes filter by When considering multi-object collisions using multitarget operating on the intensity function, v(x), which is the first order tracking, the use of random vectors is no longer appropriate for moment of the multitarget pdf. The intensity function is defined representing the state of the system. Instead, random finite sets such that integrating over the entire support of the intensity (RFSs) are used to represent the multitarget state as [17, 18] resolves to the expected cardinality of the set, or
X = {x(1),x(2),...,x(M)} λ = v()xxd (11) ∫ where there are M objects, or targets, in the multitarget state. Each of the distinct elements x(i) X, i {1,...,M} is a For an RFS with a Poisson cardinality distribution, the intensity conventional target state, such as the position and velocity of function is given by an object. ∈ ∀ ∈ v(x) = λs(x) (12) An RFS can also be described statistically with a density, albeit a multitarget pdf, in a similar way to describing a random The intensity function is commonly expressed as a weighted vector using a conventional (single-target) pdf. This is a sum of Gaussian distributions of the form [18, 20] fundamental element of multitarget filtering using concepts from L finite set statistics (FISST) [17, 18]. One common assumption ()()() v()x = wpxm;, P (13) is to take the RFS, X, to be an independent and identically ∑ g () =1 distributed (i.i.d.) cluster process; then, the multitarget pdf can be represented as It is important to note that the GM of Eq. (13) is slightly n different from that of [24, 25] and subsequent works in GM ()k f()()Xx= nn!ρ ∏ s() (9) filtering methods. The difference is that the conventional k =1
89 K. DeMars and M. Gualdoni
GM representation is constructed to represent a pdf, and the weights must sum to unity. From Eqs. (11) and (13), it directly ∞ L () Hf= − ρρ nlog n ! n follows that λ = w . That is, when the GM is used to [] ∑ ()(){} ∑=1 n=0 describe an intensity function, the expected number of objects ∞ n in the state space is equal to the sum of the weights in the GM ()i() ii() − ρ ()nsxlog s xx d ∑∑∫ () {}() representation of the intensity function. ni=01 = 4.3 Shannon Entropy While the variable x(i) has been maintained up to this point to distinguish between the multiple integration dimensions, Just as the random vector is lifted to an RFS, the single-target it is recognized that the i.i.d. assumption can now be used to integral becomes a set integral; thus, the Shannon entropy simplify the expression by replacing x(i) with a non-indexed x defined in Eq. (7) may be recast for RFSs via the set integral, since each n-tuple integral has been reduced to a single integral such that over the state space . The result of dropping the index is a sum of n identical integrals, or Hf[] = − f()()Xlog{} f XXδ (14) ∫s ∞ Hf()()()= −∑ ρρ nlog{} n ! n This definition of the multitarget Shannon entropy depends = n 0 upon the coordinate system in much the same way that the ∞ Shannon entropy of Eq. (7) does. For the multitarget problem, − nnρ ()()() sxlog{} s xx d ∑ ∫ however, the situation is compounded since the units change n=0 with the cardinality of the RFS. As such, a more appropriate definition for the multitarget Shannon entropy is [26, 27] The summation in the second term is simply the definition of the mean of the cardinality distribution. Denoting this mean by µ, it follows that (16) Hf[] = −∫ f()Xlog{} ufx () XXδ (15) s ∞ Hf()()()= −−ρ nlog{} n ! ρµ n s()()xlog{} s xx d −|X| ∑ ∫ where u is the units of the FISST density, f(X), and |X| is n=0 the cardinality of the RFS X. For simplicity and consistency (16) with existing results, the naive form of the multitarget Shannon entropy will be used in proceeding. Equation (16) is the Shannon entropy for an RFS under the assumption that it is distributed according to an i.i.d. cluster Substituting the i.i.d. cluster RFS distribution of Eq. (9) and process, which is defined by Eq. (9). applying the definition of a set integral [18] to Eq. (14), the Shannon entropy of an i.i.d. cluster RFS is given by The expression for the Shannon entropy of an i.i.d. cluster process given in Eq. (16) can be specialized by making an ∞ n 1 ()k assumption on the cardinality distribution. Substituting the Hf[] = − n nn!ρ () sx ∑ ∫ ∏ () Poisson cardinality distribution given by Eq. (10) into the n=0 n! k =1 entropy relationship of Eq. (16), while noting that µλ= , it can n ()in()()1 be shown that the infinite summations are eliminated, resulting lognn !ρ ()∏ s()xxxdd in i=1 Hf[] =−−λλlog λλ ss()()xlog{} xx d (17) where n is the Cartesian product of n copies of the state ∫ space. The benefits of the logarithm become apparent quickly, as this allows the logarithm to be decomposed into Solving for the spatial density in terms of the intensity function terms dependent on the single target spatial densities and from Eq. (12) and substituting the result into Eq. (17), it follows terms dependent only on the cardinality n. Thus, the entropy that the Shannon entropy may be expressed solely in terms of may be expressed as the rate parameter, λ, and the intensity function, v(x), as
∞ n Hf[] =−−λλlog λ v()()x log{} v x d x+ vd() x xlog λ ()k ()1 ()n ∫∫ Hf[] = − ρρ() nn sx log{} n !() n dxx ...d ∑ ∫� ∏ () n=0 k =1 ∞ n n The integral in the final term can be replaced by recalling from ()ki() ()1 ()n − ρ ()nsn xlog s x d xx ...d Eq. (11) that it is simply the rate parameter, λ; therefore, ∑∑∫ ∏ () {}() ni=01k =1 = Hf[] =λ − v()()xlog{} v xx d (18) The product of the single-target spatial densities applies a ∫ sifting-like effect; since each logarithm term is only dependent upon x(i), the remaining n − 1 integrals can be evaluated over The result of Eq. (18) is also given in [28]. each spatial density. The result of each of the n − 1 evaluations is unity, as the single-target spatial densities are taken to be Equation (18) is the Shannon entropy for an RFS under the valid pdfs. Therefore, only a sum of integrals over the target assumption that it is distributed according to an i.i.d. cluster state space, , remains, and the result is that the entropy is process, with the further stipulation that the cardinality given by distribution is Poisson. The result shows that the entropy
90 Information-Theoretic Approaches to Space Object Collision is composed of a cardinality entropy term and a spatial Equation (19) is the Rényi entropy for an RFS under the entropy term. It should be noted that the spatial entropy term assumption that it is distributed according to an i.i.d. cluster in Eq. (18) still contains cardinality elements through the process. Unlike the Shannon entropy equivalent given in Eq. representation of the intensity function. It is interesting to (16), there is no clear separation between cardinality-induced note that the spatial entropy term is of the exact form of the entropy and spatial-induced entropy. single-target entropy given by Eq. (7), but with the multitarget intensity function in place of the single-target pdf. Thus, the The Rényi entropy for an i.i.d. cluster process may be spatial term will tend to exhibit the same characteristics specialized by providing a further restriction on the cardinality observed with the single-target entropy, lending intuition to distribution. The Poisson cardinality distribution defined by Eq. the analysis of multitarget entropy, and the cardinality term (10) is now considered. Substituting Eq. (10) for the cardinality will cause the entropy to rise as the number of targets in the distribution in Eq. (19) and reducing yields multitarget state increases. ∞ n ()α 11−αλ α Except in special cases of the intensity, such as an intensity Hf[] = log e()λ s()xxd (20) ∑ ∫ that is Gaussian, the Shannon entropy of Eq. (18) cannot 1!−α n=0 n be found in closed-form. For instance, when the intensity is represented as in Eq. (13), no closed-form solution to the From the series expansion of the exponential function, ∞ entropy of Eq. (18) can be found. In such situations, numerical zn= e∑n=0 zn! , it can be seen that the summation term solutions to the integral, such as those obtained through Monte appearing in Eq. (20) may be written as an exponential, such Carlo integration, must be used. that
4.4 Rényi Entropy ()α 1 −αλ α Hf[] = log e+ ()λ s()xxd 1−α { ∫ } Similar to the concept of extending the Shannon entropy into the multitarget domain, the Rényi entropy is lifted from Eq. (8) which may be further reduced by taking the logarithm to be through the definition of the set integral to yield base e to yield
α 1 () α ()α 1 α Hf[] = log{∫ f()XXδ } Hf[] = −+αλ() λs ()xxd 1−α s 1−α ∫ α where is the control parameter. Just the same as limα→1 From the definition of the intensity function for a Poisson RFS (α) (α) H [p] = H[p], it can be shown that limα→1 H [f] = H[f]; that in Eq. (12), the Rényi entropy is given in terms of the rate is, the multitarget Rényi entropy is a generalization of the parameter, λ, and the intensity function, v(x), to be multitarget Shannon entropy. As with the Shannon entropy, the naive extension of Eq. (8) is considered herein; however, an ()α αλ 1 α extension similar to Eq. (15) to consider the units of the FISST Hf[] =−+ v ()xxd (21) density for the multitarget Rényi entropy can be carried out. 11−−αα∫
The definition of the set integral and the i.i.d. cluster process Equation (21) is the Rényi entropy of order α for an RFS definition from Eq. (9) can be applied to give the Rényi entropy under the assumption that it is distributed according to an i.i.d. for i.i.d. cluster processes as cluster process, with the further stipulation that the cardinality distribution is Poisson. The result, much like the Shannon ()α 1 entropy, shows that the entropy is composed of a cardinality Hf[] = 1−α entropy term and a spatial entropy term, where it is worth noting ∞ α that the spatial entropy term in Eq. (21) contains cardinality 1 ()11()nn()() log n!ρ () nsx s xdd xx elements through the representation of the intensity function. ∑ ∫ n () () n=0 n! Unlike the Shannon entropy, however, the spatial element of the Rényi entropy does not take on the same form as the single- Distributing the exponent to each term within the integrals and target Rényi entropy, which can be seen by comparing Eqs. (8) noting that each of the integrals can be separated, it follows that and (21).
()α 1 In contrast to the Shannon entropy of Eq. (18), the Rényi Hf[] = 1−α entropy of Eq. (21) can be found in closed form for certain ∞ choices of the control parameter a when the intensity function 1 α αα()11() α ()nn() log()()n ! ρ nsxxd s xd x is given by Eq. (13). For instance, when α = 2, the Rényi ∑ ∫∫() () n=0 n! entropy is
()2 As before, the indices on the x(i) have been used to distinguish Hf[] =2dλ − ∫ v2 ()xx (22) between individual integration dimensions; however, now that (i) the integrals involving each of the x terms have been separated Substituting for the GM representation of the intensity into a product of n integrals, this index can be dropped to yield function, it can be shown that
∞ L LL α 11α n ()2 () ()()()()()()ij i j i j () αα H() f=2, w − ww Γ−m mP + P Hf[] = log∑ ()()()n ! ρ ns∫ xxd ∑ ∑∑( ) 1!−α n l=1 ij = 11 = n=0 (19) (23)
91 K. DeMars and M. Gualdoni
where where Fk−1 is the state transition matrix of the CW model, which is taken to be −12 1 − Γ=()a, A2π A exp −aAT 1 a 2 ΦΦ F = rr rv k −1 ΦΦ The first term in Eq. (23) is the cardinality entropy and is simply vr vv given as the sum of the weights of the GM representation of the intensity; for a constant number of guaranteed existing objects, where it is constant. The spatial component of Eq. (23), i.e. the double summation term, is of prime interest when considering the 4− 3cosψ 0 determination of an interval of close approaches. From Eq. Φrr = (23), the spatial element of the Rényi entropy may be expressed 6() sinψψ− 1 as 12 sinψψ() 1− cos nn LL Φrv = ()2 ()()()()()()ij i j i j 21 H ()Θ =−ww Γ−m mP, + P ψ−− ψψ s ∑∑( ) ()cos 1() 4sin 3 ij=11 = nn (24) 3n sinψ 0 Φ = vr 6n() cosψ − 1 0 where Θ is the collection of parameters that defines the GM representation of the intensity for which the spatial entropy is cosψψ 2sin Φvv = computed, i.e. −2sinψψ −+ 3 4cos ()()() L Θ = w ,,mP { } = 1 and ψ = n(tk −tk−1), where n is the mean motion of the reference when all parameters of the GM representation of the intensity object. Note that the CW model is only one of many available are considered. relative motion models. Other options for relative motion [29, 30, 31, 32] can be used, or non-relative motion, such as inertial, central body motion, can also be employed. The CW model 5. RESULTS AND DISCUSSION is chosen here because of its linear nature, which allows for simple state propagation. The methods developed for the determination of an interval during which two or more objects are interacting, or the The reference object is chosen to have a mean motion of interval during which the calculation of the probability of n = 15.91 rev/day and the time step is taken to be a constant collision should be carried out, are applied to three test cases. ∆t = tk − tk−1 = 10 sec. In all three examples, initial pdfs for the The first test case examines a two-object collision case, where objects under consideration are specified by either Gaussian or the uncertainty in the states of the objects is Gaussian, and GM pdfs through the specification of means, covariances, and, compares all of the techniques presented in this work. The for the case of GMs, weights of the GM. All weights are held second test case examines a three-object collision case, again constant, and all of the means and covariances are propagated with Gaussian uncertainty, and compares the distribution using the linear dynamics of the CW model. sampling method to the Rényi entropy method. The final case examines a two-object collision case with non-Gaussian 5.1 Example #1 uncertainties and compares the distribution sampling method to the Rényi entropy method. The initial means of the two objects considered for the first example are given in Table 1. In addition, the uncertainties For simplicity, the dynamic motion of the objects considered of the two objects are Gaussian, with diagonal covariance in this work is taken to be represented using relative motion matrices. The standard deviations are given in Table 2. dynamics. A fictitious reference object is used to describe the center of a rotating frame, and the motion of nearby objects The time history of the means for the two objects is is taken to be described by the relative motion with respect computed for 300 time steps, and the resulting trajectories to this reference object. The reference object is taken to be are illustrated in Fig. 2. Similarly, the covariance histories are in a circular orbit, and a local-vertical, local-horizontal frame (with the x-axis representing the cross-track direction and the y-axis representing the along-track direction) is attached to TABLE 1. Initial Means for Example #1. the reference object. Furthermore, only planar motion will be considered in order to simplify the analysis. The Clohessy- Object x[m] y [m] x [mm/s] y [mm/s] Wiltshire (CW) model is used to represent the dynamics of 1 5.0 36.3 4.4 -11.2 the nearby objects, such that, for a state defined as the relative position and velocity of the form 2 5.4 18.5 -7.2 -7.7 T TT x=rk kk v TABLE 2: Initial Standard Deviations for Example #1. the dynamics of the state are given by the linear, discrete-time, Object x[m] y [m] x [mm/s] y [mm/s] noiseless system 1 1.0 0.5 1.0 2.0 2 0.5 1.0 2.0 1.0 xk =F kk−−11 x
92 Information-Theoretic Approaches to Space Object Collision
Fig. 2 Mean trajectories for Example #1. Fig. 4 Application of the distribution sampling method to Example #1.
Fig. 3 Uncertainty trajectories for Example #1. computed and plotted at 5 step intervals in Fig. 3. Based on Fig. 5 Application of the Mahalanobis distance method to Example #1. these figures, it is observed that there is likely a time interval for which the two objects experience close interaction. To determine when the two objects are in close interaction, the distribution sampling, Mahalanobis distance, symmetric KL divergence, and Rényi entropy methods are applied at each step of the simulation. For each method, the position marginal distributions are obtained from the propagated means and covariances of each object.
First, consider the distribution sampling, Mahalanobis distance, and symmetric KL divergence methods. The position marginal distributions are sampled 1×106 times, the relative distance between the samples are computed, and the number of samples with a relative distance less than c = 1 m are counted. This provides the percentage of interacting samples shown in Fig. 4. The position marginal distributions are used to compute the squared Mahalanobis distance from Eq. (2). The Mahalanobis distance, along with a 90% confidence Fig. 6 Application of the symmetric KL divergence method to interval, which is obtained from the chi-squared distribution, Example #1. is illustrated in Fig. 5. The position marginal distributions are furthermore used to compute the symmetric KL divergence Now, consider the Rényi entropy method. The propagation from Eq. (5). For scaling, the square root of the symmetric KL of the means and covariances for the two objects yields the ()i divergence is shown in Fig. 6. Each of these three methods position marginal means as mr and the position marginal ()i shows a similar time of closest approach for the two objects, covariances as Prr for i {1,2}. To each of these means and (i) where the uncertainty is included in each method. The covariances, a weight of w = 1 is assigned, indicating one symmetric KL divergence, however, provides an analysis from target per mean and covariance.∈ These parameters are then used Θ()()()()i= i ii which it is difficult to determine the interval over which the two to form {w ,,mPr rr } as the set of parameters for each ΘΘ=()()12 ∪ Θ objects are interacting. For this reason, this method will not be object. The total set of parameters is denoted . considered in the following analyses. Using the parameters Θ , the spatial Rényi entropy is computed
93 K. DeMars and M. Gualdoni from Eq. (24), and the result is illustrated in Fig. 7. Inspection TABLE 3. Initial Means for Example #2. of Fig. 7 shows that the interval in which the objects are interacting is obscured by other trends contained in the spatial Object x[m] y [m] x [mm/s] y [mm/s] Rényi entropy. As the entropy accounts for changes in the size of the individual distributions, as well as the translational 1 0.0 50.0 0.0 0.0 motion of the individual distributions, the interval of interaction 2 0.0 -30.0 -68.9 52.8 is not immediately apparent. To more clearly see the interval 3 30.0 0.0 -87.7 -17.3 of interaction, the relative spatial Rényi entropy (not to be confused with the concept of relative entropy) is defined as TABLE 4: Initial Standard Deviations for Example #2. M ∆=()()22ΘΘ − ()() 2i HHss() ∑ H s() Object x[m] y [m] x [mm/s] y [mm/s] i=1 1 1.0 0.5 1.0 1.0 The relative spatial Rényi entropy can be viewed as the difference between the spatial entropy and the spatial entropy 2 0.8 1.2 1.0 1.0 under the assumption of no interaction between the objects. 3 0.6 0.5 1.0 1.0 The relative spatial Rényi entropy is illustrated in Fig. 8, from which the interval of interaction is immediately clear. The time histories of the means and covariances for the Comparing Figs. 4 and 8, it is seen that the relative spatial three objects are computed for 200 time steps, and the resulting Rényi entropy method provides excellent agreement to the trajectories are illustrated in Fig. 9. The resulting covariances more computationally expensive distribution sampling method. histories are plotted at 3-step intervals in Fig. 10.
5.2 Example #2 Based on the analysis of Example #1, the distribution sampling and relative spatial Rényi entropy methods To further investigate the methods developed in this paper, a are implemented to determine when the three objects three-object case is considered. The initial means of the three are interacting. For each method, the position marginal objects are given in Table 3, and the initial standard deviations distributions are obtained from the propagated means and are given in Table 4. As with the first example, the initial covariances of each object. covariances are taken to be diagonal. At each time step, the position marginal distributions are Fig. 7 Application of the spatial Rényi entropy method to Example #1. Fig. 9 Mean trajectories for Example #2.
Fig. 8 Application of the relative spatial Rényi entropy method to Example #1. Fig. 10 Uncertainty trajectories for Example #2.
94 Information-Theoretic Approaches to Space Object Collision sampled 1 × 106 times, the relative distance between the samples is it is illustrated in Fig. 12. The separate intervals of interaction computed, and the number of samples with a relative distance less are clear from Fig. 12, and remarkable agreement with the than c = 1 m are counted. The percentage of interacting samples is distribution sampling method is again observed. One downside to then determined, and this is shown in Fig. 11. Figure 11 illustrates the relative spatial Rényi entropy method is that the information the pairwise interactions between the three objects based on the on the pairwise interactions is lost. This could be recovered by pairwise percentage of interacting samples, as well as the total considering pairwise combinations of the objects in a similar percentage of interacting samples obtained from considering all manner to that undertaken in the distribution sampling method, three objects. From Fig. 11, it is observed that the second and third but this would come at an increase in computational burden. objects begin interacting first, then the first and second objects interact, and finally the first and third objects interact. 5.3 Example #3
The position marginal means and covariances are obtained The final example considered applies and compares the from the uncertainty propagation for each object, and these distribution sampling and relative spatial Rényi entropy ()i ()i are denoted by mr and Prr respectively, for i {1,2,3}. methods to a non-Gaussian problem. The first object in this To each position marginal distribution, a weight of w(i) = 1 is problem is taken to be described by a GM pdf, where the pdf assigned, indicating one target per mean and covariance.∈ These is constructed for demonstration purposes only, and is not parameters are the set of parameters for each object: intended to represent a real-world scenario. It is assumed that the uncertainty of the first object is uniform in angular space, Θ()()()()i= i ii o {w ,,mPr rr } centered at zero in the cross-track direction, with a ±20 extent in the angular direction. Additionally, the range is taken to be
The total set of parameters is denoted 50.0 m from the origin, with a Gaussian uncertainty (1σ) of 2.0 m. The initial velocity is taken to be Gaussian with zero mean ΘΘ=∪∪()()()123 Θ Θ and standard deviations of 1.0 mm/s in both directions. Each component has equal weight in the GM representation of the The relative spatial Rényi entropy, as defined previously, is then pdf, and there are L components in the mixture. computed from the individual and collective parameter sets, and
Fig. 11 Application of the distribution sampling method to The second object is taken to be described by a Gaussian Example #2. distribution. The mean of the Gaussian distribution is m = [−25.0 25.0 11.6 50.0], with position units of meters and velocity units of mm/s. The covariance of the Gaussian distribution is diagonal with position standard deviations of 1.0 m and velocity
standard deviations of 1.0 mm/s. Contours of the initial position distributions are illustrated in Fig. 13. The pdfs of the two objects are propagated for 350 time steps, and the trajectory of the mean of the distribution for the second object is shown in Fig. 13. As the mean of the first object has zero initial velocity and is in only the along-track direction, it remains stationary. The distribution, however, moves in time, but this is not illustrated.
As with the preceding examples, the position marginal distributions are obtained for each object at each time step. These distributions are sampled 1×106 times, the relative distance between the samples are computed, and the number of
samples with a relative distance less than c = 1 m are counted. The percentage of interacting samples is shown in Fig. 14. It is interesting to note that this example of a two-object collision exhibits two separate collisions between the objects. Fig. 12 Application of the relative spatial Rényi entropy method to Example #2. Fig. 13 Trajectories for Example #3.
95 K. DeMars and M. Gualdoni
Fig. 15 Application of the relative spatial Rényi entropy method Fig. 14 Application of the distribution sampling method to to Example #3. Example #3.
Examination of Fig. 13 shows that the second object “loops around” and passes nearby the first object twice.
Given that the first object is represented by a GM pdf, the position marginal pdf is obtained by collecting the position elements of the mean and covariance while preserving the weights of the GM pdf. These parameters are denoted by
L Θ()()()()1= 1, 1, 1, L ()1, = ww,mPr , rr , where ∑ =1 1 { }=1
The second object is represented by a Gaussian pdf, meaning that its parameters are simply given by
Θ()()()()2= 2 22 {w ,,mPr rr } Fig. 16 Comparison of the distribution sampling and relative where w(2) = 1. The total set of parameters is denoted spatial Rényi entropy methods for Example #3. ()()12 ΘΘ= ∪ Θ. The relative spatial Rényi entropy is computed from the parameters and is shown in Fig. 12. the objects. Conventional methods are discussed, and new approaches based on the information-theoretic concepts of To provide a more direct and visceral comparison of the information divergence and information entropy are developed. relative spatial Rényi entropy and the distribution sampling The methods are implemented and compared for two-object methods, the results from Figs. 14 and 15 are plotted together in and three-object close approach scenarios, assuming both Fig. 16, except that the relative spatial Rényi entropy is negated Gaussian and nonGaussian state uncertainties. It is found to possess the same sign as the percentage of interacting that the information entropy approach that makes use of the samples. From Fig. 16, it is seen that the two methods perform multitarget Rényi entropy produces intervals of close proximity identically, modulo scaling, in determining the intervals that are nearly identical to a more standard distribution sampling during which the two objects are in close proximity and the technique while naturally supporting close approaches between distributions are interacting. more than two objects and uncertainties that are represented by Gaussian mixture probability density functions. 6. CONCLUSIONS ACKNOWLEDGMENTS This paper addresses the problem of determining an interval during which two or more objects are in close proximity This work was supported by a US Department of Education to one another, including the effects of uncertainty in the GAANN Fellowship (P200A150309). The authors would also states of the objects, with the motivation of better informing like to acknowledge the many fruitful discussions with Mr. James the determination of the probability of collision between McCabe of Missouri University of Science and Technology.
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5. A. Papoulis, Probability, Random Variables, and Stochastic Processes, 21. R. Mahler, “PHD filters of higher order in target number”, IEEE 2nd edn, McGraw-Hill, 1984. Transactions on Aerospace and Electronic Systems, 43, pp.1523–1543, 6. Y. Bar-Shalom and T.E. Fortmann, “Tracking a Single Target in Clutter”, 2007. in Tracking and Data Association, Vol. 179, Academic Press, pp.157– 22. B.-T. Vo, B.-N. Vo and A. Canton, “The cardinalized probability 190, 1988. hypothesis density filter for linear Gaussian Multitarget models”, 40th 7. T. Kirubarajan and Y. Bar-Shalom, “Probabilistic data association Annual Conference on Information Sciences and Systems, pp.681–686, techniques for target tracking in clutter”, Proceedings of the IEEE, 92, 2006. pp.536–557, 2004. 23. B.-T. Vo, B.-N. Vo, and A. Canton, “Analytic implementations of the 8. A. Cichocki and S. Amari, “Families of alpha- beta- and gamma- cardinalized probability hypothesis density filter”,IEEE Transactions on divergences: Flexible and robust measures of similarities”, Entropy, 12, Signal Processing, 55, pp.3553–3567, 2007. pp.1532–1568, 2010. 24. D.L. Alspach and H.W Sorenson, “Nonlinear Bayesian estimation using 9. T.M. Cover and J.A. Thomas, Elements of Information Theory, 2nd edn, Gaussian sum approximations”, IEEE Transactions in Automatic Control, John Wiley & Sons, 2006. 17, pp.439–448, 1972. 10. S. Kullback and R.A. Leibler, “On information and sufficiency”, The 25. H.W. Sorenson and D.L. Alspach, “Recursive Bayesian estimation using Annals of Mathematical Statistics, 22, pp.79–86, 1951. Gaussian sums”, Automatica, 7, pp.465–479, 1971. 11. S. Alfano, “Toroidal path filter for orbital conjunction screening”, 26. E. Baser, Multitarget MultiBernoulli Tracking and Joint Multitarget Celestial Mechanics and Dynamical Astronomy, 113, pp.321–334, 2012. Estimator, Ph.D. thesis, McMaster University, Hamilton, Ontario, 12. F.R.Hoots, L.L. Crawford and R.L. Roehrich, “An analytic method Canada, 2016. to determine future close approaches between satellites”, Celestial 27. M. Rezaeian, and B.-N. Vo, “The entropy of random finite sets”, Mechanics, 33, pp.143–158, 1984. Proceedings of the International Symposium on Information Theory, 13. C.E. Shannon, and W. Weaver, The Mathematical Theory of 2009. Communication, University of Illinois Press, 2002. 28. P.M. Dames, MultiRobot Active Information Gathering using Random 14. R.V.L. Hartley, “Transmission of information”, Bell Labs Technical Finite Sets, Ph.D. thesis, University of Pennsylvania, Philadelphia, Journal, 7, pp.535–563, 1928 Pennsylvania, 2015. 15. I. Csiszár, Stochastics: Information Theory, Springer, 2006. 29. D.-W. Gim, and K. T. Alfriend, “State transition matrix of relative motion 16. A. Rényi, “On measures of entropy and information”, Proceedings of the for the perturbed noncircular reference orbit”, Journal of Guidance, fourth Berkeley symposium on mathematical statistics and probability, 1, Control, and Dynamics, 26, pp.956–971, 2003. pp.547–561, 1961 30. G. Inalhan, M. Tillerson and J.P. How, “Relative dynamics and control of 17. I.R. Goodman, R.P.S. Mahler and H.T. Nguyen, Mathematics of Data spacecraft formations in eccentric orbits”, Journal of Guidance, Control, Fusion, Kluwer Academic Publishers, Norwell, MA, USA, 1997. and Dynamics, 25, pp.48–59, 2002. 18. R.P.S. Mahler, Statistical MultisourceMultitarget Information Fusion, 31. K.A. LeGrand, and K.J. DeMars, “Bearings-only initial relative orbit Artech House Inc., 2007 determination”, Journal of Guidance, Control, and Dynamics, 38, 19. R. Mahler, “Multitarget Bayes filtering via first-order multitarget pp.1699–1713, 2015. moments”, Aerospace and Electronic Systems, IEEE Transactions on, 32. M.T. Stringer, B. Newman, T.A. Lovell and A. Omran, “Second order 39, pp.1152–1178, 2003. nonlinear initial value solution for relative motion using Volterra theory”, 20. B.-N. Vo, and W.-K. Ma, “The Gaussian mixture probability hypothesis Proceedings of the 23rd AAS/AIAA Space Flight Mechanics Conference, density filter”, IEEE Transactions on Signal Processing, 54, pp.4091– pp.2133–2149, 2013. Paper No. AAS 13-469. 4104, 2006.
(Received 10 July 2017; Accepted 13 July 2017)
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97 BrunoJournal Revelin of the andBritish Juan-Carlos Interplanetary Dolado-Perez Society, Vol. 70, pp.98-104, 2017
RISK INDUCED BY THE UNCATALOGUED SPACE DEBRIS POPULATION IN THE PRESENCE OF LARGE CONSTELLATIONS
BRUNO REVELIN1 AND JUAN-CARLOS DOLADO-PEREZ2 1. CS-SI, 5 Rue Brindejonc des Moulinais, 31506 Toulouse, France. 2. CNES, 18 Avenue Edouard Belin 31401 Toulouse, France. Email: [email protected] and [email protected]
The number of artificial objects in orbit continues to increase and, with it, a key threat to space sustainability. In order to avoid such situation, several responses outlining mitigation procedures, including the Inter-Agency Space Debris Coordination Committee (IADC) Space Debris Mitigation Guidelines, the United Nations Committee on the Peaceful Uses of Outer Space Mitigation Guidelines, the International Organization for Standardization Space Debris Mitigation Standards and a multitude of other national and international documents have been, and continue to be, developed to limit the expected growth of the debris population. Planned, large constellations of satellites in low Earth orbit (LEO) raise new questions about space sustainability, which previous studies started to tackle. On this paper we analyse the effects of these constellations on the long term evolution of the orbital environment when more realistic conditions, than those used on previous studies, are considered (e.g. explosions, lower respect of mitigation practices, objects < 10cm). Keywords: Space debris, mega-constellations, MEDEE, sustainability, mitigation, catalogued objects, CNES, explosions, fragmentation, collision, Monte-Carlo, long-term evolution
1. INTRODUCTION
Since the first orbital launch in 1957, the number of artificial started to characterise and comprehend the impacts of such objects in Earth orbit has been increasing [1]. This has led to new space uses [1, 7], the present study aims at enhancing our a corresponding increase in the threat to active satellites from vision of the risks and threats they entail in a more pessimistic hypervelocity collisions, putting in jeopardy crucial services environment. that benefit human society. Therefore there is growing pressure on space users to implement mitigation measures aimed at 2. SIMULATIONS CHARACTERISTICS preventing the proliferation of space debris and enabling the sustainable use of space [2]. 2.1 General Model Settings
Several responses outlining mitigation procedures, A Monte-Carlo (MC) approach was used to simulate the including the Inter-Agency Space Debris Coordination evolution of the orbital population over a period of 200 years Committee (IADC) Space Debris Mitigation Guidelines [3], from 2013, with the Model for the Evolution of Debris on the United Nations Committee on the Peaceful Uses of Outer the Earth’s Environment (MEDEE) [8], the evolutionary Space Mitigation Guidelines [4], the International Organization model at the French space agency (Centre National d’Etudes for Standardization Space Debris Mitigation Standards [5] Spatiales, CNES). Previous studies [9, 10] have shown that a and a multitude of other national and international documents limited amount of MC simulations (i.e. >40) give statistically have been, and continue to be, developed to limit the expected significant results for the mean number of space objects growth of the debris population.. These guidelines, standards present in the population, while a significant higher number of and laws aim to prevent the generation of debris in the short- realisations (>100) are needed to reach such significance for the term, through measures typically related to spacecraft design standard deviation. The solar activity used in our propagation and operation, and the growth of the debris population over model (a key factor to drive the evolution of objects in LEO) the longer-term, by limiting the lifetime in key orbital regions is of medium strength, as it consists in a repetition of an 11 after the end of mission. A fundamental assumption was that year-long cycle, with maximum F10.7 solar flux at 180 and nature and scale of future space activities would continue to minimum at 70. be similar to what was observed during the 1990s. However the proposed deployment of constellations of satellites in 2.2 Background Population LEO to provide regular internet access to regions lacking necessary infrastructure [6], and the enhancement to space For the purposes of all the simulations, the background traffic beyond what was anticipated, represents a potential (non-constellation) population consists of all objects larger source of disruption to the long term sustainability of the or equal to 10 cm in size, wholly or partially residing in or space environment. While previous studies have already crossing the LEO region on 1 January 2013, and derived from the Meteoroid and Space Debris Terrestrial Environment This paper was presented at the ESA 7th European Conference on Reference (MASTER)-2009 model [11, 12]. Additionally, the Space Debris, ESA/ESOC, Darmstadt, Germany, 18-21 April 2017 non-constellation launch traffic repeats launches to LEO from
98 Risk Induced by the Uncatalogued Space Debris Population in the Presence of Large Constellations the historical period January 1st 2005 to December 31th 2012 The first topic is the main objective of the present study, but in 8 years cycles. the other ones are both scarcely studied in the literature and prone to generate large number of debris, thus their importance in our Moreover: work. However, in order to keep the problem computationally feasible, we have decided to analyse the effect of the uncatalogued Payloads are maintained on their initial orbit, and a population in LEO apart from the last two variables. mean mission lifetime of 8 years is considered (i.e. a Keplerian propagation with J2 effect is considered for 2.4.1 Uncatalogued Space Debris Population payloads during their mission lifetime) (< 10 cm), Scenarios Group A Payloads ensure 100% collision avoidance with the catalogued population during their mission (i.e. objects Studies performed with reference space debris evolutionary > 10cm). models usually focus on objects > 10cm for 2 main reasons: Payloads (at the end of their mission) and Rocket Bodies (R/B) are immediately disposed on lower orbits Computation time (i.e. including smaller objects that ensure a maximum post-mission lifetime in LEO of increase substantially the number of objects in the 25 years, at success rates depending on the scenarios (cf. population and therefore the computation time) §2.5). Catalogues of objects in LEO are limited to objects bigger than 10 cm (order of magnitude) due to current 2.3 Constellation Description limitations on sensor capabilities.
The constellation we model throughout all our simulations However, debris of sizes lower than 10cm (that we call corresponds to a generic constellation (i.e. none of the large- “small” debris in the scope of this paper) can still harm or constellations projects have been specifically considered) destroy operational objects in a collision [15]. A limitation of having the following characteristics [13]: our study is that the initial background population is composed of objects residing or crossing the LEO region bigger than 10 • 1080 satellites at 1100 km of altitude, and 85 degrees of cm, therefore we use the standard NASA Break-up model to inclination, as of January 2021 (includes spare satellites) introduce the “small” objects (> 1 cm) on the environment All satellites have 200kg of mass and 1m² effective after collisions and explosions. Such approach still allows to cross-section study the effect of the uncatalogued population on the long- • All satellites have 5 years of operational lifetime, during term evolution of the space debris population, as such small which they are maintained on their orbit population is characterized by high area to mass ratios, and All launcher stages comply with immediate direct re- therefore by having a high decrease rate of the semi-major axis, entry, and therefore do not appear in our simulations and the analysis is performed for 200 years. No mission-related objects are released 18 objects per launch (for constellation build-up and 2.4.2 Non-Collisional Explosions, Scenarios Group B replenishment) 20 orbital planes Previous studies focused on other key drivers like solar activity 20 launches in 2018, 2019 and 2020 each to build up [16, 17, 18], or PMD success rate [19, 20]. In most of these studies, constellation and either to isolate specific effects or to study the long term 12 launches per year for replenishment inserted in the evolution of the environment under optimistic hypothesis the “no nominal orbit (starting in 2021, last replenishment explosion” hypothesis was retained. However, explosions still launches in 2070). It means that for the first 4 years occurs nowadays [14]. Therefore, we have decided to analyse the after operational start, there will be more satellites than effect of non-collisional explosions on the long term evolution of required, and after operational end, still 4 years with the environment, with the following approach: operational satellites. After mission, objects are disposed of at success rates • Random number of explosions between 5 and 12 per depending on the scenarios, to ensure a maximum year, based on real statistics [14] post-mission lifetime in LEO also depending on the Debris are generated with the standard NASA Break-up considered scenario (cf. §2.5) Model [21, 22], with a higher limit of 250 debris for the • 50 year global mission duration (2021-2071) objects bigger than 10 cm. Such limit is empirical and is Collision avoidance is performed during LEOP and derived from the analysis of catalogued debris by space- during the 5 years mission, with respect to constellation track (www.space-track.org) for objects exploding and non-constellation objects > 10cm, at success rates during the last years. depending on the scenarios (cf. §2.5). • Only objects heavier than 50kg may explode. Only R/B and background payloads, in the initial population or 2.4 Topics of the Study and Scenarios Groups launched before January 1st 2020 may explode (i.e. we consider that after January 1st 2020 all R/B and payloads In this study we focus on the analysis of the effect of three are 100% passivated). variables on the long term evolution of the space debris Constellation satellites are always 100% passivated. population, in the presence of large constellation: 2.4.3 PMD Success Rate, Scenarios Group B uncatalogued debris (i.e. objects smaller than 10 cm in LEO) The 90% PMD success rate baseline scenario (computed on objects Explosions [14] having an orbital lifetime > 25 years), is consistent with previous Up to date Post Mission Disposal (PMD) success rate studies [1, 7, 20, 23], which have shown that compliance to [14]. mitigation guidelines is of paramount importance regarding space sustainability in the future. However, the actual rate of compliance
99 Bruno Revelin and Juan-Carlos Dolado-Perez in recent years shows that the mitigation guidelines compliance, TABLE 3: Scenarios Group B. and in particular the 25 years rule, is far from the hypothesis of 90% [24, 25]. Therefore, more pessimistic assumptions concerning Explosions PMD success rate has been considered in this study: SB1 Background PMD 20% For the background population, two different PMD No constellation success rates hypothesis (the PMD success rate is Explosions computed based on objects having orbital lifetimes Background PMD 20% to 90% in 2050 greater than 25 years) have been considered depending SB2 on the scenario (cf. §2.5.3): (linearly), then 90% 20% of PMD success rate for the whole No constellation simulations SB2 + PMD increasing from 20% in 2013 to 90% in 2050 (linearly) and 90% after 2050. Constellation at 600km: For the constellation, 80% or 90% PMD success rate is Direct injection at 600km assumed, depending on the scenario (cf. §2.5.3). SB3 100% collision avoidance during 5 year mission 2.5 Detail of the Considered Scenarios 100% success rate electric PMD in 2 years 2.5.1 Baseline PMD90 Scenario SB2 + Constellation at 1100km: Our baseline scenario has only background population, with no Electric deployment from 450km to constellation, and no explosion. PMD success rate is set to 90% SB4 1100km in 50 days throughout the whole simulation (Table 1). 100% collision avoidance during 5 year mission TABLE 1: Baseline PMD90 Scenario. 80% success rate electric PMD in 2 No constellation years Baseline PMD90 No explosion SB2 + Background PMD 90% Constellation at 1100km: Electric deployment from 450km to 2.5.2 Scenarios Group A SB5 1100km in 50 days 90% collision avoidance during 5 Simulations in this group show the effect of objects < 10 cm year mission over two reference scenarios: baseline and a constellation 90% success rate electric PMD in 2 scenario (Table 2). years SB2 + TABLE 2: Scenarios Group A. 3 simultaneous constellations at 600km, Baseline PMD90 + 1100km and 1200km: Baseline + small 1cm < Debris < 10 cm generated by Electric deployment from 450km to collisions SB6 altitude in 50 days 90% collision avoidance during 5 Baseline PMD90 + year mission Constellation at 1100km: 80% success rate electric PMD in 2 Direct injection at 1100km years SA1 100% collision avoidance during 5 year mission 90% success rate impulse PMD on Fig. 1 Mean population of objects > 10 cm in LEO for group A an eccentric orbit aiming at 25 years scenarios. lifetime (same as background PMD) SA1 + SA1 + small 1cm < Debris < 10 cm generated by collisions
2.5.3 Scenarios Group B
Our 2nd group of scenarios focus on explosions and PMD rates (Table 3). All objects are above 10 cm.
3. RESULTS
3.1 Group A: Effect of Debris < 10 cm
On this paragraph we analyse the effect of the un-catalogued population on the long term evolution of the environment,
100 Risk Induced by the Uncatalogued Space Debris Population in the Presence of Large Constellations particularly concerning the effect of “small” debris on the proliferation of the mean number of objects > 10cm (cf. Fig. 1) and on the number of collisions (cf. Fig. 3).
As we can see on Fig. 1, the constellation scenarios clearly show the > 10 cm population steeply rise, stabilise, and then decline after the end of the constellation mission [13]. It then reaches equilibrium with a slow rise, because of the 10% constellation PMD failures in itself and its consequences in terms of collisions.
Moreover there is little to no difference in terms of mean- number of objects > 10 cm, when the small debris are considered at least in our 200 years scope. Such difference falls well within the dispersion of the results.
Additionally, Fig. 2 shows a very steep increase of the small objects population, starting from 0 as there is no small object in our initial population. The small objects population after 200 years is approximately 7 times larger than the objects > 10 cm. When constellations are considered, the increase of small debris is bigger, due to additional collisions with abandoned constellation objects. Fig. 3 Mean catastrophic collisions distribution in 50 km altitude bins, in group A. No collision between small debris. Fig. 2 Mean population of 1 cm < objects < 10 cm in LEO for group A scenarios.
In terms of collisions, Fig. 3 confirms the results of Fig. 1: new collisions at 1100 km for the SA1 scenarios with respect to the baseline one, and just a few additional catastrophic collisions in the “small” scenarios when compared to their Fig. 4 Mean non-catastrophic collisions distribution in 50 km respective counterpart. altitude bins, in group A. No collision between small debris. object, its consequences from an operational point of view However, Fig. 4 clearly demonstrates the consequences may range from a loss of power input, to loss of control means of small debris on the environment: 10 times more non- and other functions, or complete loss of the mission and of the catastrophic collisions, at all altitudes, than the “non small” satellite. scenarios, especially in crowded altitudes (800 km, 1000 km, and 1100km with constellation scenarios). This increase on Therefore, in our otherwise optimistic scenarios, small non-catastrophic collisions is tightly linked with an increase on objects may not generate many catalogue size objects, but at the risk induced by the space environment. least create much harder conditions in terms of collision risks and mission sustainability, for mega-constellations as well as It is not surprising that collisions with small debris are background traffic. mostly non catastrophic, from an energetic point of view, as the mass of colliding objects is key to determine the amount of In terms of risk, the integrated collision risk, induced by energy involved. the increase of the uncatalogued objects, to the operational constellation satellites is less severe than expected (i.e. low However, even if a non-catastrophic collision with a 1 cm number of collisions with operational satellites) as their to 10 cm object may not completely fragment the bigger operational lifetime is relatively low (i.e. 5 years) compared to
101 Bruno Revelin and Juan-Carlos Dolado-Perez the time needed for uncatalogued objects to build up at these altitudes. However, the consequences may be more severe for any subsequent space activity.
Additionally, even if we have scarce knowledge of the uncatalogued objects density in the present space environment, we can suppose that their density vs altitude pattern follows that of the catalogued objects. Therefore, it is likely that if we had a realistic population of uncatalogued objects in our initial population, their impact would be notable in dense regions like 800km and 1000km, but not in the somewhat unpopulated 1100km region.
3.2 Group B: Effect of Explosions and PMD Success Rates
Before focusing on the population, and in order to give an idea to the reader about the explosions fragments, let’s have a look Fig. 6 Mean population of objects > 10 cm in LEO for group B at the number of debris produced by the explosions for SB1 scenarios with no constellation. and SB2. Similar figures are reproduced for all the scenarios considering explosions. 9 times more objects after 200 years clearly the explosion rate, and the induced chain effect by the generated fragments, and Figure 5 shows that most of the explosions generate around not so much the PMD success rate, as the final population level 220 objects, when the fragmented mass is enough. Therefore in scenario SB2 with 90% PMD from 2050 to 2213 is only 1/6th when the fragmented mass is higher, the mass of the respective lower than SB1. debris are higher. Figure 7 shows the mean population evolution for all the non- constellations and constellation scenarios. First, we observe that all scenarios present a significantly bigger population than the baseline population which is due, as explained before, to the acceleration of the space debris proliferation due to explosion fragments.
Additionally, the introduction of constellation at low altitude (SB3 at 600km) appears to have no effect in the long run with respect to its reference scenario SB2.
Then, from Fig. 7 two main drivers on the proliferation of space debris can be observed: The PMD success rate, as already shown on previous work [5, 6, 21, 24]. The number and distribution of constellations, coupled with the previous variable. SB6 with three constellations (two of them at high orbits) results in a significantly higher population than SB3.
Fig. 7 Mean population of objects > 10 cm in LEO for group B scenarios.
Fig. 5 Number of debris depending on the mass of the fragmenting object, as generated by the NASA Break-Up Model, for a given MC run.
On the interpretation of Fig. 6, the reader should bear in mind that the considered scenario generates around 1700 explosions in 200 years, and a mean number of 220 debris each. Therefore, the non-collisional fragments will be on the order of 374000, without counting the fragments induced by collisions with them.
Let us focus now on the population evolution for the non constellation scenarios: baseline, SB1 and SB2, in Fig. 6.
The striking result here is that low PMD success rate combined to a relentless occurrence of explosions produce steeply rising space objects population in our model, reaching
102 Risk Induced by the Uncatalogued Space Debris Population in the Presence of Large Constellations
Interestingly, the sensitivity of the population to the PMD success rate is way higher than the sensitivity to the collision avoidance success rate, as can be clearly seen when we compare the results of SB4 and SB5. This is due to the fact that lower PMD success rate has a direct impact on the number of objects staying at the constellation altitude, whereas lower collision avoidance success rate’s impact lasts only for the mission duration.
Additionally, Fig. 8 shows the direct impact of a lower PMD success rate for the constellation at 1100km, from SB5 to SB4 or SB6, 10% less PMD success rate induce 3 times more catastrophic collisions.
The higher collision level in SB6 at 1100km than SB4, may result from the 10% lower collision avoidance success rate (in SB6), as well as the interactions between collision induced debris at 1100km and 1200km.
4. CONCLUSION AND PERSPECTIVES
The study presented on this paper deviates a little bit from Fig. 8 Mean catastrophic collisions distribution in 50 km altitude the optimistic scenarios usually on previous studies, on bins, in group B. which no-explosions and a very good compliance with post- mission disposal (PMD) measures are considered. Moreover high LEO altitudes poses two major concerns. First, passivation the uncatalogued population of objects (<10 cm) has been success and PMD success rate remain of paramount importance also consider in order to study its influence on the long term to avoid proliferation of debris and protect the sustainability evolution of the space environment. of the concerned regions (1100km or 1200km), on which any abandoned satellite or fragment thereof will remain virtually Scenarios implementing the uncatalogued space debris forever. Second, even in virtuous conditions of PMD success population, between 1 cm and 10 cm, highlights the fact that rate and passivation, a small number of collisions is bound such low sized population present a major threat to any mission to induce in the long run a build up of uncatalogued objects success, especially at key altitudes, even if it does not induce a population, which in turn constitutes an important threat for the Kessler-like effect in the population of objects above 10 cm. sustainability of space activities in these region.
Scenarios implementing less optimistic hypothesis including ACKNOWLEDGEMENTS explosions and an actual PMD success rate, ends with a vast amount of objects above 10 cm. The authors would like to thank the ESA space debris office, that have kindly provided the initial ESA MASTER 2009 In this context, the introduction of large constellations at population used for the study presented on this paper.
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1. Space Debris Program Office, “Monthly Number of Objects in Earth 9. J.C. Liou, “A Statistical Analysis of the Future Debris Environment”, Orbit by Object Type”, Orbital Debris Quarterly News, 21, p.12, Acta Astronautica, 62, pp.264-271, 2008. February 2017. 10. J.C. Dolado-Perez, B Revelin and R. Di-Costanzo, “Sensitivity Analysis 2. R. Crowther, “Space Junk – Protecting Space for Future Generations”, of The Long-Term Evolution of the Space Debris Population in LEO”, Science, 296, pp.1241-1242, 2002. The Journal of Space Safety Engineering, 2, pp.12–22, 2015. 3. Inter-Agency Space Debris Co-ordination Committee, “IADC Space 11. C. Wiedemann, S. Flegel and C. Kebschull, “Additional orbital Debris Mitigation Guidelines”, IADC-02-01, 2007. fragmentation events”, 65th International Astronautical Congress, 4. Scientific and Technical Subcommittee of the Committee on the Peaceful Toronto, Canada, 29 September - 3 October 2014, Paper No. IAC-14. Uses of the Outer Space, “Space Debris Mitigation Guidelines of the A6.P.57. Scientific and Technical Subcommittee of the Committee on the Peaceful 12. S. Flegel, J. Gelhaus, M. Möckel et al., Maintenance of the ESA Uses of the Outer Space”, pp.42-46, http://undocs.org/A/AC.105/890. MASTER Model – Final Report, European Space Agency, ESA Contract (Last Accessed 13 July 2017) Number: 21705/08/D/HK.n 2011 5. A. Kato, B. Lazare, D. Oltrogge and P.H. Stokes, “Standardization by ISO 13. B. Bastida Virgili, J.C. Dolado, H.G. Lewis, J. Radtke, H. Krag, B. to Ensure the Sustainability of Space Activities”, Proceedings of the Sixth Revelin, C. Cazaux, C. Colombo, R. Crowther and M. Metz, “Risk European Conference on Space Debris, ESOC, Darmstadt, Germany, 22- to space sustainability from large constellations of satellites”, Acta 25 April 2013. European Space Agency Publication SP-723. Astronautica, 126, pp.154–162, 2016. 6. United Nations, Broadband Commission for Cultural Development, The 14. J.C. Dolado-Perez, C. Pardini and L. Anselmo, “Review of uncertainty state of Broadband 2015, September 2015. sources affecting the long-term predictions of space debris evolutionary 7. B. Bastida Virgili, “Mega-constellations, small satellites and their impact models”, Acta Astronautica, 113, pp.51-65, 2015. on the space debris environment”, 67th International Astronautical 15. J.C. Dolado-Perez and F. Alby, “Using Satellite Vulnerability Analysis Congress, Guadalajara, Mexico, 26-30th September 2016 to Specify the Minimum Required Detectable Size of an Effective Space 8. J.C. Dolado-Perez, R. Di-Costanzo and B. Revelin, “Introducing MEDEE Surveillance System”, 5th International Association for the Advancement – A New orbital debris evolutionary model”, Proceedings of the Sixth of Space Safety Conference, Versailles, France, 17-19 October 2011. European Conference on Space Debris, Darmstadt, Germany, 22–25 16. H.G. Lewis and H. Timothy, “Implications of Prolonged Solar Minimum April, 2013. Conditions for the Space Debris Population”, Proceedings of the Sixth
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European Conference on Space Debris, Darmstadt, Germany, 22-25 22. P. Krisko, “Proper Implementation of the 1998 NASA Breakup Model”, April 2013. European Space Agency Publication SP-723. Orbital Debris Quarterly News, 15, pp.4-5, April 2011. 17. D. Whitlock, “Modelling the Effect of High Solar Activity on the Orbital 23. Inter-Agency Space Debris Coordination Committee, “Stability of the Debris Environment”, Orbital Debris Quarterly News, 10, pp.4-5, 2006. future LEO environment”, http://www.iadc-online.org/Documents/ 18. B. Bastida Virgili, S. Lemmens, T. Flohrer et al., “Influence of Solar IADC-2012-08,%20Rev%201,%20Stability%20of%20Future%20 Activity on Long Term Propagations”, 65th International Astronautical LEO%20Environment.pdf. (Last Accessed 13 July 2017) Congress, Toronto, Canada, 29 September - 3 October 2014. 24. V. Morand, J.C. Dolado-Perez and D.A. Handschuh, “Analysis of 19. C. Martin, R. Walker and H. Klinkrad, “The Sensitivity of the ESA mitigation guidelines compliance at international level in low earth DELTA model”, Advances in Space Research, 34, pp.969-974, 2004, orbit”, Proceedings of the Seventh International Space Safety Conference, 20. J.C. Dolado and B. Revelin, “The Effect of uncertainties on the Friedrichshafen, Germany, 20–22 October 2014. effectiveness of mitigation and remediation measures”, 66th International 25. H. Krag, S. Lemmens, T. Flohrer and H. Klinkrad, “Global trends in Astronautical Congress, Jerusalem, Israel, 12-16 October 2015. achieving successful end-of-life disposal in LEO and GEO”, Proceedings 21. N.L. Johnson, P.H. Krisko, J.C. Liou and P.D. Anz-Meador, “NASA’s of the Thirteenth International Conference on Space Operations, New Breakup Model of EVOLVE 4.0”, Advances in Space Research, 28, Pasadena, CA., 5–9 May 2014. pp.1377-1384. 2001,
(Received 6 June 2017; Accepted 19 June 2017)
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104 Sensitivity of theJournal Space of Debris the British Environment Interplanetary to Large Society, Constellations Vol. 70, and pp.105-117, Small Satellites 2017
SENSITIVITY OF THE SPACE DEBRIS ENVIRONMENT TO LARGE CONSTELLATIONS AND SMALL SATELLITES
H.G. LEWIS1, J. RADTKE2, A. ROSSI3, J. BECK4, M. OSWALD5, P. ANDERSON6, B. BASTIDA VIRGILI7 AND H. KRAG7* 1. University of Southampton, United Kingdom. 2. Technische Universitaet Braunschweig, Germany. 3. IFAC-CNR, Italy. 4. Belstead Research Limited, United Kingdom. 5. Airbus Defence and Space GmbH, Germany. 6. Clyde Space Limited, United Kingdom. 7. ESA/ESOC Space Debris Office, Germany. Email: [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected] and [email protected]*
Opportunities provided by small satellites in low Earth orbit (LEO) are anticipated to make a significant impact on the space economy through the delivery of important and innovative services. However, with plans by some companies to operate large constellations of small satellites in LEO, and with many small satellite launches forecast in coming decades, there is concern that existing debris mitigation measures will not be sufficient to counteract the impacts of this increased space activity on the LEO environment. Within this context, a team comprising engineers from industry, academia and the European Space Agency have performed an assessment of the potential impact of small satellites and large constellations on the space debris environment. This paper provides an overview of the work undertaken and the results that emerged. Keywords: Space debris, large satellite constellations
1. INTRODUCTION
Low Earth orbit (LEO) is experiencing a renaissance thanks involving a number of European space agencies, was reported to increasing commercialisation of space. Small satellites have in Bastida Virgili et al. [1] and highlighted the importance played a vital role in this revolution and they have a unique of post-mission disposal (PMD) measures on the mitigation ability to bring new products and services to market at short of debris resulting from a 1080-satellite constellation. timescales and for relatively low-cost. This has caused a dramatic Separately, Radtke et al. [2] computed collision probabilities increase in both the number of commercial actors within the and the number of collision avoidance manoeuvres for the space industry and the number of small spacecraft launched. proposed OneWeb constellation, with different assumptions With the expectation that this change will continue into the for the success of the PMD, mission altitude and lifetime. future, especially given plans to operate large constellations of The results underlined the sensitivity to the mission altitude communication satellites in LEO, there is some concern about and the PMD success, with the need for very high PMD the effectiveness and relevance of the existing space debris success rates for mission altitudes that experience little mitigation guidelines. atmospheric drag. Further, Peterson et al. [3] found that some of the proposed large constellations can be expected to Whilst the long-term effects arising from the introduction generate approximately one collision per year in total for the of constellations and small satellites to LEO have been operational satellites and another two collisions per year for investigated in the past (e.g. [1-6]) few studies have been able the disposed satellites. to examine the sensitivity of the space debris environment to more than a limited set of parameters. As such, only a In 2016 and 2017, a team comprising engineers from relatively incomplete understanding of the possible impacts of industry, academia and the European Space Agency performed large constellations and small satellites on the environment has a comprehensive assessment of the potential impact of emerged. In fact, little is known about the measures that might small satellites and large constellations on the space debris be taken by large constellation or small satellite operators to environment. This assessment included: (1) a review of enable to mitigate the effects of their activities on the space historical and proposed future small satellite activities and environment. associated technologies; (2) a large number of long-term projections using three evolutionary codes; and (3) detailed A recent initiative focused on large constellations, analysis of the results of the first two activities, to understand the sensitivity of the debris environment to key satellite and This paper was presented at the ESA 7th European Conference on constellation parameters. Initial results from the projections Space Debris, ESA/ESOC, Darmstadt, Germany, 18-21 April 2017 were presented in Bastida Virgili et al. [6] and more detailed
105 H.G. Lewis, J. Radtke, A. Rossi, J. Beck et al. analyses of particular results are presented in [7-9]. This paper provides an overview of the simulation studies performed during the study and presents the key results and lessons learned.
2. METHODOLOGY
Three evolutionary debris models were used to perform long-term environment projections: the Debris Analysis and Monitoring Architecture to the Geosynchronous Environment (DAMAGE) developed at the University of Southampton, the Long-Term Utility for Collision Analysis (LUCA) developed at Technische Universität Braunschweig, and the Space Debris Mitigation long-term analysis program (SDM) developed at IFAC-CNR.
The analysis was based on comparisons of long-term projections of the orbital object population ≥ 10 cm, under a Fig. 1 Launch rate of small satellites used for simulation studies. variety of small satellite and mega-constellation scenarios, with The medium rate was adopted for the small satellite baseline case. a reference scenario comprising: • Initial population: all objects ≥ 10 cm with perigee < performed. Investigations by Liou [10] and Lidtke et al. [11] 2000 km in orbit on 1 January 2013 have shown that sample sizes of 40-60 MC runs are needed for • Future launch traffic: repeat 2005-2012 cycle reliable estimates (within 10%) of the mean to be made. Projection period: 1 January 2013 to 1 January 2213 Post-mission disposal (PMD) of 90% of spacecraft and For this study, three categories of evaluation metrics were rocket bodies to a 25-year orbit used: (1) metrics based on averages (e.g of the number of objects No explosions or collisions) computed over all MC runs, (2) metrics based No collision avoidance on the statistical variability in MC runs (so-called “criticality norms”) and (3) metrics based on probabilistic assessments of The baseline constellation case, which was the same the MC runs. as reported in Bastida Virgili et al. [1, 6], then included the following in addition to the reference: The sum of the differences between the averages (of the number of objects or the number of collisions) from a test case Walker-delta constellation comprising 1080 satellites in and the reference case, normalised by the standard deviation 20 orbital planes at 1100 km altitude and inclined at 85° and weighted by the time interval, N, gives an indication of the Constellation satellite design lifetime of 5 years, 200 kg criticality [12]: and 1 sq. metre Constellation build-up phase from 1 January 2018 to 1 NN− January 2021 with 20 launches per year and 18 satellites * 11nTEST() in REF () i CC=∑∑i = (1) per launch NNσ () i ii=11= REF Constellation replenishment phase from 1 January 2021 to 1 January 2070 (50 years) with 12 launches where niTEST () is the number of objects or number of collisions per year and 18 satellites per launch. Note that the first in the small satellite/constellation test case at an epoch (year) replenishment launches commenced on 1 January 2023 given by i, niREF () is the number of objects (or collisions) in PMD of 90% of constellation spacecraft to a 400 × 1100 the reference case and σ REF ()i is the standard deviation of the km or “25-year” disposal orbit reference MC runs at the same epoch. Values of Ci and C* (or Immediate de-orbit of rocket bodies “Cnorm” as they are referred to elsewhere in this paper) were evaluated over the number of years in the simulation, or at the The baseline small satellite case incorporated the medium end of the projection period. launch rate scenario, based on models by Lewis et al. [4] and superimposed on the reference case (Fig. 1). A description of The probability based metrics quantify the likelihood the small satellite launch traffic model as implemented in this of there being a difference between the test case (i.e. with a study is provided in Radtke et al. [8]. constellation or small satellites) and a reference case, or the likelihood that the two cases are similar. The aim is to estimate Variations of the constellation and small satellite the probability that the number of objects or collisions at any parameters with respect to the baseline cases provided the epoch and in a MC run drawn at random from the results of set of simulation cases that were investigated. The variations the test case is less than (or equal to) the number of objects or considered for the constellation cases included mission collisions at the same epoch in a MC run drawn at random from lifetime, constellation altitude, number of satellites and the results of the reference case: spares, satellite characteristics and lifetime, and launcher behaviour, amongst others. The variations in the small NN * 11 satellite baseline case included the launch rate, the satellite P=∑∑ Pi = PnTEST()() i< n REF i (2) size/form factor, the launch altitude, and post-mission NNii=11= disposal, amongst others.
Values of Pi and P* (or “P(T 106 Sensitivity of the Space Debris Environment to Large Constellations and Small Satellites years in the simulation, or at the end of the projection period. If 3.2.1 Post-Mission Disposal (PMD) the test case and the reference case are identical then Pi will be 0.5. Constellation PMD was investigated in several cases. In many of the simulations performed, at least one other parameter was 3. RESULTS also varied. 3.1 Reference Case Initially, the PMD success rate was selected from the set {60%, 80%, 90%, 95%, 100%} and two different types of The reference case provided an opportunity to compare the disposal orbit were investigated: (1) a disposal orbit with a results of all three evolutionary models. Figure 2 shows the fixed perigee (400 km) and apogee (1100 km), with a nominal predictions of the number of objects made by DAMAGE, LUCA lifetime of approximately 20-25 years (results shown in Fig. 6), and SDM. For this case, SDM predicted the highest average and (2) a disposal orbit with a nominal residual lifetime of 25 number of objects throughout the projection period, followed (relatively closely) by DAMAGE and then LUCA. The latter Fig. 3 Evolution of the cumulative number of catastrophic model predicts a net decrease, on average, in the number of collisions for the reference case. objects by the end of the projection period, compared with the number at the beginning. Whilst Fig. 2 appears to show that the distribution of the final populations predicted by LUCA are significantly lower than the equivalent distribution predicted by either DAMAGE or SDM, the reality is that there is some overlap due to a number of outliers. The number of catastrophic collisions predicted by each model is shown in Fig. 3. The SDM model predicts a catastrophic collision rate of 0.2/year (R2 = 0.999), on average, whereas LUCA predicts a corresponding rate of 0.14/year (R2 = 0.994). For the first 50 years of the projection, all three models predict catastrophic collisions at a rate of 0.2/year, on average. 3.2 Large Constellations As for the reference case above, the baseline constellation case Fig. 4 Effective number of objects over the projection period for was simulated using all three evolutionary models and the the constellation baseline case. results below provide a comparison (Figs. 4 and 5). These results are consistent with those presented in Bastida Virgili et al. [1]. They show that the impact of the constellation on the orbital object population can be separated into three components: a quick population rise during the constellation build-up and replenishment; a period of population decay as PMD measures reduce the number of constellation satellites; and a long-term, gradual increase in the population due to collisions involving long-lived, failed constellation satellites. The sections below describe the results obtained through the variation of the constellation parameters. They are presented in order of their impact on the space debris environment, as determined using the evaluation metrics outlined above. Fig. 2 Effective number of objects over the projection period for Fig. 5 Evolution of the cumulative number of catastrophic the reference case. collisions for the constellation baseline case. 107 H.G. Lewis, J. Radtke, A. Rossi, J. Beck et al. Reference case (no constellation) Constellations: 60% PMD success Constellations: 100% PMD success Fig. 6 Effect of constellation post-mission disposal success rate on key summary metrics computed by DAMAGE for a 400 × 1100 km disposal orbit. Constellations: 95% PMD success years. The two approaches yielded consistent results, with very 0-Year Residual Lifetime high numbers of objects and catastrophic collisions generated for a PMD success rate of 60%. The number of objects and collisions decreased (following a quadratic fit, 2 R = 1.0 for both number of objects and collisions) as the PMD success rate increased. Whilst high PMD success rates resulted in fewer failed satellites at the constellation altitude, they also led to higher numbers of satellites traversing large parts of the LEO region Fig. 7 Comparison of the spatial distribution of collisions computed by DAMAGE, for PMD corresponding to disposal in disposal orbits and, consequently, a higher proportion of orbits with 25 years residual lifetime. Note the change in scale of collisions involving constellation and background objects. the z (depth) axis between the plots. Indeed, the flux on the International Space Station (ISS) increased five- to ten-fold, compared with the reference case, during the operational lifetime of the constellation. Similar of objects and catastrophic collisions (Fig. 8). For example, a results were reported by Peterson et al. [3]. So, it is not correct 90% PMD success rate with a 25-year residual lifetime resulted to assume that even perfect adherence to PMD guidelines will in the same cumulative number of catastrophic collisions (75) result in no impact on the environment. as an 85% PMD success rate with a 5-year residual lifetime, although there were more objects in LEO at the end of the In spite of the seemingly less-than-optimal outcome for projection period. Whilst the trade-off is biased in favour of the high PMD success rates, it is important to recognise that the PMD success rate, the results do suggest that mission designers discussion here relates to relative differences; in absolute terms may have some flexibility in their approach to PMD, especially there were approximately five times fewer constellation-versus- if high PMD reliability is a challenge. background catastrophic collisions for a 100% PMD success rate, compared with a 60% PMD success rate. Nevertheless, Reference [1] investigated different disposal orbit options if the aim is to remove any impact of a constellation on the and found, in general, that elliptical orbits with short residual background population, measures that address the constellation- lifetimes were desirable. Here, a greater variety of disposal orbit versus-background collisions below the constellation altitude options was investigated using DAMAGE and LUCA. These will be required. High PMD success rates consistently reduce the models predicted a comparable average number of catastrophic number of objects and the number of catastrophic collisions, in collisions for each of the disposal orbits investigated (R2 = absolute terms, while shorter residual lifetimes limit the impact 0.866) and the subsequent criticality norm values for the of the constellation on the background population (Fig. 7). catastrophic collisions were similarly close (R2 = 0.867). The results can also be used to find different combinations The surface charts in Fig. 9 show that the impact of the of the two PMD measures (success rate and residual lifetime) constellation disposal orbit on the LEO environment is not that tend to produce the same outcome, in terms of the number simply a matter of whether the orbit is elliptical or whether the 108 Sensitivity of the Space Debris Environment to Large Constellations and Small Satellites Fig. 8 Effect of constellation PMD success rate and residual Fig. 9 Effect of constellation disposal orbit apogee and perigee lifetime of disposal orbit on the number of objects (top) and the altitudes on the number of objects in orbit at the end of the cumulative number of catastrophic collisions (bottom) in 2213. projection period (top), and on the number of catastrophic collisions (bottom). residual lifetime is short. Indeed, both DAMAGE and LUCA predicted relatively high number of objects and catastrophic PMD success rates were sub-optimal, a large fraction (88%) of collisions for the 300 × 300 km disposal orbits, which had the resulting > 300 catastrophic collisions in the environment the shortest residual lifetime. It is likely that the volume of involved an object from the constellation and 69% of those space at this altitude is insufficient to support the number of collisions (about 180) were self-induced, on average. This satellites using it for disposal. In addition, simply lowering does suggest that the constellation “comes off worse” in this the perigee of the disposal orbit to 300 km or 400 km altitude type of situation and this may be an incentive for constellation without also adjusting the altitude of the apogee (with respect operators to aim for high reliability. to the constellation altitude) did not lead to a reduced impact on the environment, even though the residual lifetimes were Overall, the results from LUCA and DAMAGE for the PMD relatively short and the satellites could be distributed through cases demonstrate the importance of compliance with this debris a large volume of space because of the elliptical orbits. It is mitigation guideline by all space users sharing the LEO region. recommended that constellation operators perform a trade-off The results also highlight the need for constellation operators with respect to the environmental impact and delta-V, on a to build-in a resilient approach to their mission operations and case-by-case basis, with the aim of finding achievable disposal debris mitigation measures, should the background launch orbits that limit impacts on the environment. activity change in a manner that leads to an increased potential for conjunctions with constellation satellites. Given the potential for the disposal orbits of constellation satellites to intersect the orbits of objects in the background 3.2.2 Constellation Launch Vehicle Behaviour population, it was necessary to consider the effects of different PMD behaviour and launch activity in the background The behaviour of the launch vehicles used to orbit the population too. The results from DAMAGE and LUCA constellation satellites represents an important parameter with simulations for a range of background behaviours showed respect to the LEO environment. In Lewis et al. [4], the role of very good agreement with respect to the trends (R2 > 0.9). the launch vehicle upper stages was neglected. Here, we have As expected, when the PMD success rate for the background investigated a range of possible behaviours for these objects – population changed from 90% to 60% the number of objects primarily relating to PMD success rate and the residual lifetime in LEO at the end of the projection period increased by of the disposal orbits the stages are transferred into, but also approximately 10,000 in the DAMAGE results with an considering the payload release altitude and the impact of additional seven catastrophic collisions, on average. There increased background launch activity. was a corresponding decrease in the proportion of catastrophic collisions involving constellation objects (from 47% to 38%) There was significant, detrimental effect on the LEO but no change in the proportion of those collisions that were environment when the launch vehicles deployed their payloads self-induced or involved a background object. In contrast, at the constellation altitude and then did not perform any post- doubling the launch traffic resulted in a greater proportion of mission disposal. In addition to the baseline case, the number constellation-versus-background catastrophic collisions. of objects in LEO at the end of the projection period was > 200,000 and > 500 catastrophic collisions had taken place. In the case where the constellation and the background Nearly 100% of all catastrophic collisions and nearly 100% 109 H.G. Lewis, J. Radtke, A. Rossi, J. Beck et al. of all fragments generated over the projection period were the background explosion rate. The effect, however, appeared to result of a constellation object. In addition, one-third of the be limited to a relatively small increase in the average object catastrophic collisions involved an object from the background population, when the explosion rate increased from two to five population. As with the constellation satellites, implementing per year, with no significant change in the average number of and increasing the PMD success rates for upper stages in catastrophic collisions. The relatively constant values for the this case resulted in substantial benefits to the environment. criticality norms calculated from the DAMAGE results also Limiting the time spent by these objects in the LEO region to suggest little impact on the distribution of outputs from the MC 10 years also provided some benefit. runs. The effect of non-compliant launch vehicles can be mitigated The DAMAGE results also show a direct impact of the if the satellite release occurs at relatively low altitude because background explosions on the constellation traffic: as the the upper stages can be removed by atmospheric drag. In fact, background explosion rate increased, so too did the fraction when satellites were deployed from the launch vehicle at an of catastrophic collisions involving a background object and a altitude of 400 km the impact on the LEO environment was no constellation object. Whilst the effect was small, nevertheless it different to that of the baseline case, in which the launch vehicle demonstrated the interdependence of the two populations. upper stages were assumed to de-orbit immediately (see Fig. 10). Payload releases at altitudes up to approximately 600 km 3.2.4 Constellation Size were seen to have no significant impact on the LEO population or cumulative number of catastrophic collisions. So, a prudent In general, the number of objects and the number of catastrophic approach to the deployment of constellation satellites would be collisions in LEO at the end of the projection period were to release them at low altitudes from where they can perform an proportional to the size of the constellation – i.e. the number of orbital transfer (either impulsive or low-thrust) to the mission satellite members (Fig. 11). For relatively small constellations altitude; any upper stage that subsequently fails to comply with (e.g. a few hundred satellites) the impact on the LEO post-mission disposal guidelines will decay relatively quickly environment was indistinguishable from the reference case (p and have minimal impact on the LEO environment. >> 0.05 in a Wilcoxon test). In fact, there was a probability of more than 25% that the number of objects predicted to be 3.2.3 Background Explosions on-orbit at any point in the projection period was less than the number of objects predicted for the reference case (and also for Another aspect of the background behaviour that was the cumulative number of catastrophic collisions). Increasing investigated in this study was the explosion rate. Again, the size of the constellation beyond approximately 600 DAMAGE and LUCA were used to evaluate the impact of two satellites resulted in the emergence of a significant difference explosion rates, in addition to the no-explosion, baseline case: in the P(T 110 Sensitivity of the Space Debris Environment to Large Constellations and Small Satellites Increasing the constellation size resulted in a non-linear (quadratic; R2 = 1.0) increase in the number of self-induced catastrophic collisions but a linear increase (R2 = 0.993) in the number of constellation-versus-background catastrophic collisions. For the largest constellation studied, the average catastrophic collision rate in the LEO environment was higher than one per year, with 90% of those collisions involving at least one constellation object and generating 70% of all fragments. In general, the use of spare satellites reduced the impact of the constellations on the LEO environment. In addition, the benefits were proportional to the fraction of the constellation satellites that were spares, such that the largest constellation (3000 satellites with 18 spares per plane) saw decreases of 24.2% in the number of objects in the year 2213, and of 33.74% in the number of catastrophic collisions by 2213. Further work is required to evaluate the sensitivity of these benefits to the number/proportion of spare satellites and also to determine the impact of the use of storage orbits above or below the constellation. However, the first pass through this case provided some evidence that the use of spare satellites can be encouraged. 3.2.5 Constellation Satellite Characteristics All three evolutionary models were used to investigate the influence of the mass and area of the constellation satellites on the LEO environment. The DAMAGE simulations covered 14 cases, whilst LUCA and SDM evaluated five and three cases, Fig. 12 Effect of constellation satellite mass and area on the respectively. In general, DAMAGE predicted fewer objects number of objects (top) and cumulative number of catastrophic but more catastrophic collisions by the year 2213 for all three collisions (bottom) in the year 2213, computed by DAMAGE. cases, compared with SDM, but the overall trends, with respect to satellite mass and area, were the same for both models (R2 m to 6 sq. m. led to the involvement of a constellation object in > 0.8). In contrast, the correlation between the results from approximately 80% of all catastrophic collisions, regardless of DAMAGE and LUCA for their five common cases was poorer. the satellite mass. For LUCA, the effect of satellite mass and area on the number of objects and the cumulative number of catastrophic collisions Another constellation satellite characteristic investigated in 2213 was not as pronounced as it was for DAMAGE, a result was the lifetime. In the baseline case, the lifetime of the that was likely due to different implementations of the breakup satellites was fixed at five years. Longer satellite lifetimes model and orbital propagator. led consistently to fewer objects in the LEO environment and fewer catastrophic collisions. In addition, the ability to extend The DAMAGE results indicate that the constellation satellite lifetimes beyond the design life also led consistently to satellite mass and area played two distinct roles in the the same benefits. The change from a 3 year lifetime to a 7 + 3 evolution of the LEO environment (Fig. 12). Firstly, increasing year lifetime (where satellites can continue to operate for up to the cross-sectional area of the satellites from 1 sq. m to 6 sq. three years beyond their nominal design life) led to a reduction m resulted in a significantly higher collision rate, because the in the mean number of objects from 40,720 to 28,921; a change collision probability is proportional to the cross-sectional area. of 29%. A change of 48% was observed for the mean number Due to the high altitude of the constellation, away from all but of catastrophic collisions between these two cases. the slightest effects of atmospheric drag, the increase in area did not translate into faster decay rates, which meant that the 3.2.6 Constellation Mission Lifetime larger, failed satellites were exposed to higher debris fluxes for long periods. In turn, the high collision rates generated a higher DAMAGE and LUCA were consistent in predicting a greater number of fragments that, again, were slow to decay from the impact on the LEO environment from constellations with longer constellation altitude and ultimately enhanced the population. mission lifetimes, compared with constellations with shorter Secondly, increasing the mass of the satellites from 100 kg mission lifetimes, both in terms of the number of objects in the to 400 kg resulted in a higher number of fragments being environment at the end of the projection period and the number generated per collision, because the number of fragments is of catastrophic collisions. Indeed the number of catastrophic proportional to the mass according to the NASA standard collisions and the number of objects at the end of the projection breakup model [13]. However, these fragments did not add period were directly proportional to the mission lifetime. significantly to the collision rates that were observed (bottom panel of Fig. 12). For relatively short mission lifetimes (e.g. < 30 years) there was a relatively high probability (> 30%) that a DAMAGE MC For constellation satellites of 400 kg and 1 sq. m, run from the constellation case would predict a lower number approximately half of all the catastrophic collisions in LEO of objects and catastrophic collisions than a MC run from the involved a constellation object, the same outcome for satellites reference case. For long mission lifetimes (e.g. > 80 years) of 200 kg and 1 sq. m. In contrast, changing the area from 1 sq. DAMAGE predicted that constellation objects were involved 111 H.G. Lewis, J. Radtke, A. Rossi, J. Beck et al. in more than 50% of all catastrophic collisions in LEO, which with one constellation at 1100 km and the other at 1300 km generated more than 40% of all fragments. Consequently, altitude; or (2) three constellations, including the baseline there are clear benefits that arise from limiting the duration of constellation at 1100 km, a 1400-satellite constellation with constellation activities (or from monitoring and re-evaluating 35 planes at 1200 km and inclined at 45°, and a 120-satellite constellation activities at regular intervals throughout the constellation with 12 planes at 1200 km and inclined at 85°. mission). All of the satellites were assumed to be 200 kg in mass and 1 sq. metre in area, and the constellation mission lifetimes were 3.2.7 Constellation Satellite Explosions assumed to be 50 years. The impact of explosions within the constellation was As each constellation adhered to the same post-mission examined by DAMAGE and LUCA. At the highest explosion disposal practice and success rate (90%), the number of failed rate considered (4% of failed constellation satellites) there were satellites left on-orbit after the constellation mission was approximately 45 to 55 explosions within the constellation directly proportional to the number of satellites launched to mission lifetime with each explosion generating 238 fragments maintain the constellation. As such, the number of objects in according to the NASA standard breakup model. the LEO environment for the multiple constellation cases was always higher than it was for the baseline case. In addition, The size of the 2213 population increased by 35% from the growth in the object population that occurred after the 30,816 objects (for no explosions) to 41,503 objects (for the end of the constellation missions was at a higher rate for the highest explosion rate), on average. The effect of the explosions multiple constellation cases than for the baseline case; again, on the number of catastrophic collisions was approximately due to the larger population of failed constellation satellites. half that observed for the number of objects, with only an It is straightforward to conclude, therefore, that increasing the 18% increase in the number of catastrophic collisions for the number of constellations operating in the LEO region will lead worst explosion case, compared with the baseline. In contrast, to proportionally greater impacts on the environment unless the LUCA results suggest very little impact was made by the measures are taken to address the additional traffic. constellation satellite explosions on the average number of objects or on the average number of catastrophic collisions, 3.2.10 Constellation Satellite Failures even for the worst-case explosion rate investigated. For the 4% explosion rate case, the LUCA results show an increase of 10% The satellite failure model in DAMAGE, which is based on in the 2213 population and an increase of less than 0.05% for in a two-Weibull mixture model, was modified to account for the number of catastrophic collisions. enhanced failure probabilities at different phases of the satellite life (early/infant, midlife and end of life). In all cases the overall 3.2.8 Constellation Altitude probability of failure was still set by the post-mission disposal success rate (= 1 – PMD success rate) and the failure model It was apparent that for either disposal scheme (400×1100 was used to determine at what stage of the satellite’s lifetime km disposal orbit, or “25-year” disposal orbit), constellations that the failure occurred (Fig. 13). located at relatively low altitudes tended to result in fewer objects on-orbit by the end of the projection period, almost The impact of the failure model depended on the constellation certainly due to the greater atmospheric drag acting on any “concept of operations”. For satellites using chemical satellites failing before the start of the post-mission disposal propulsion the failure always occurred during the constellation phase. However, the catastrophic collisions involving a operations, regardless of the failure model, because all orbit constellation object were more likely to involve an object transfers were assumed to be instantaneous. This meant that from the background population when the constellation was at failed satellites were consistently at the constellation altitude. lower altitudes (e.g. on average, 60% of catastrophic collisions In contrast, satellites that used electric propulsion failed at one involving a constellation object also involved an object from of three points: during the ascent (i.e. on near-circular orbits the background population when the constellation was located below the constellation altitude), during the constellation at 700 km, whereas only 20% involved two objects from the operations (i.e. on circular orbits at the constellation altitude), constellation). In general, more self-induced collisions in the or during the initial descent towards the final disposal orbit constellation take place when the constellation is at a higher (i.e. on elliptical orbits below the constellation altitude). The altitude than when it is located at a lower altitude. likelihood of failure at any of these points was determined by the failure model used. At a simplistic level, the selection of constellation altitude will be a trade-off between the relative benefits to the In general, the electric propulsion option resulted in fewer environment overall (i.e. aim for a constellation at low altitude) catastrophic collisions at all release altitudes, compared with and the relative impacts on other space users (i.e. aim for a the chemical propulsion option, regardless of the failure constellation at high altitude to avoid these). This trade-off model. The benefits gained from the use of electric propulsion is affected by other factors such as the constellation satellite almost certainly come from the changed concept of operations, mass and area characteristics, which affect the rate of decay which permitted satellites failing during the ascent phase from and collision probability, and the number of satellites needed to low altitude to be removed from the environment through achieve the required coverage. atmospheric drag or, even in a worst case scenario, to be away from the constellation. 3.2.9 Multiple Constellations The results indicated that if failures were more likely to The SDM model was used to investigate the impact of multiple occur near to the beginning or end of life of the constellation constellations on the LEO environment. For these simulation satellites then the number of objects and the number of cases the following parameters were adopted (1) two identical catastrophic collisions was reduced overall, compared with the 1080-satellite constellations, both based on the baseline case, baseline case (which utilised the nominal failure model shown 112 Sensitivity of the Space Debris Environment to Large Constellations and Small Satellites led to fewer objects remaining in the LEO environment at the end of the projection period, and fewer catastrophic collisions. However, the benefits diminished as the separation increased. In the best case (8 km separation) there were 25% fewer catastrophic collisions and 11% fewer objects by 2213, compared with the baseline case. Further work is needed to understand the scope of possible benefits that could be achieved by separating the orbital planes, with simulations needing to incorporate plausible scenarios for achieving such separations that also account for the changing coverage patterns. In the previously reported simulation cases, it was assumed that the constellation satellites were able to perform collision avoidance manoeuvres with 100% success. This assumption was varied here in order to evaluate the criticality of the collision Fig. 13 Satellite failure probabilities for five failure model versions avoidance capabilities for the constellation. The collision in DAMAGE. avoidance success rate was set to one of the following values: 50%, 70%, 90% or 100%. The results indicate that the number of objects in the LEO environment and the number of catastrophic in Fig. 13). Further, the probability-based metrics indicate that collisions was inversely proportional to the collision avoidance early failures led to MC run outputs that were close to those success rate, but the difference between the best case collision produced for the reference case (P(T 113 H.G. Lewis, J. Radtke, A. Rossi, J. Beck et al. Fig. 15 Effective number of objects ≥ 10 cm over the projection period for the small satellites baseline case. Fig. 14 Effect of the removal of failed constellation satellites on the number of objects and the number of catastrophic collisions, computed by DAMAGE. In fact, only 21% of all catastrophic collisions in LEO involved a constellation object when 20% of the failed constellation satellites were removed each year, and only 13% of these were self-induced, constellation-versus- Fig. 16 Cumulative number of catastrophic collisions for the small constellation collisions. The benefits achieved through the satellites baseline case. removal of the constellation satellites remain, in spite of the addition of the failed removal satellites. Indeed, for a 3.3.1 Background Behaviour removal rate of 20% and a success rate of 80%, there was still a 14% decrease in the number of objects by the end of The behaviour of the background population was varied with the projection period, and a 15% decrease in the number of respect to the PMD success rate (30%, 60%, or 90%), the catastrophic collisions. These findings again highlight the disposal orbital lifetime (10 years or 25 years) as well as the benefits that arise from the prevention of a build-up ofa launch rate (standard or double launch rate). These simulations population of failed constellation satellites. In addition, the were only performed using DAMAGE and the results are results suggest that taking action to reduce the population of shown in Fig. 17. failed constellation satellites is better than no action, even if there is some risk. When the background launch rate was doubled, the values of all the metrics effectively doubled. However, increasing 3.3 Small Satellites the post-mission disposal success rate in the background from 60% to 90% led to a decrease in the criticality norms by values The small satellite baseline scenario was investigated using between 31% and 49%, depending on the other parameters. The DAMAGE and LUCA. For both models, the results show a use of disposal orbits with shorter lifetimes provided further clear increase in both the number of objects on orbit and the benefits. cumulative number of catastrophic collisions over time when compared to the reference case (Figs. 15 and 16). Looking Two background explosion rates were also investigated at the DAMAGE results only, over the whole simulation using DAMAGE: two and five explosions per year. The impact time frame, the number of objects increased on average by a of two explosions per year was no significant (both criticality factor of about 2.7. For LUCA, the number objects over time values remained below 1.0 with respect to the small satellite increased by a factor of about 1.6 over the complete simulation baseline case). However, the results from the five explosions time frame per year case demonstrated a statistically significant impact on the long-term evolution of the number of objects. Overall, the The sections below describe the results obtained by varying impact was higher for the number of objects compared with the the small satellite parameters, presented in order of their impact on the cumulative number of collisions. impact on the space debris environment. Only the results from cases investigated using DAMAGE and LUCA are presented. 3.3.2 Small Satellite Release Altitude Further details and results from the other cases are reported in Radtke et al. [8]. The impact of the release altitudes of the small satellites was 114 Sensitivity of the Space Debris Environment to Large Constellations and Small Satellites Fig. 18 Effect of small satellite release altitude on criticality norm metrics computed by DAMAGE and LUCA. Fig. 17 Effect of background launch traffic and disposal behaviour on key summary metrics computed by DAMAGE. investigated using DAMAGE and LUCA. Two variations from the baseline were performed: one, in which small satellites were launched to lower altitudes, and one which they were launched into higher altitudes. For this, the underlying distributions to control the small satellite launch Fig. 19 Effect of small satellite launch rate on number of objects altitudes were varied (see [8] for more details). In addition and catastrophic collisions computed by DAMAGE and LUCA. to the release altitude, the number of dedicated launches was varied in the low and the high release altitude scenario: 80% 3.3.3 Small Satellite Launch Rate of all small satellites were launched using dedicated launchers rather than 50%. To assess the impact of the small satellite launch rate, three variations were performed (Fig. 1): (1) a fixed, low launch rate, The results are shown in Fig. 18 (both criticality norms similar to the rates observed today; (2) a medium increase in correlate with R2 ~ 1.0 between LUCA and DAMAGE). launch rate until a saturation at 270 small satellites per year was Increasing the number of dedicated small satellite launches achieved; and (3) a high increase in launch rate to a saturation had little impact on the derived metrics. On the other hand, of 540 small satellites per year. the release of small satellites into higher orbits led to greater impacts on the environment, in terms of the number of objects The results indicated that the small satellites launch rate and the number of catastrophic collisions. This is especially the directly translated into a proportional increase of all the case for the high altitude variation. The reason for the increase is measured metrics (some shown in Fig. 19). Furthermore, the simply the exponentially increasing lifetime of small satellites increase in both numbers of objects and collisions, as well as at the higher altitudes, the increased collision probabilities the criticality norms, correlate well for both models (R > 0.99). of the small satellites due to their extended lifetimes, and the extended lifetimes of fragment clouds, created during 3.3.4 Other Small Satellite Parameters collisions involving small satellites. The results provide some evidence for measures that limit the release of small satellites Several other parameters were investigated in the context of the at high altitudes, where their lifetimes are higher than the study. These included the size of the small satellites, disposal of recommended 25 years. small satellites (through the application of propulsion), collision 115 H.G. Lewis, J. Radtke, A. Rossi, J. Beck et al. avoidance, and the deployment to swarms and constellations. the satellite lifetimes, thereby reducing the replenishment The results of those investigations are reported in Radtke et launch requirements and by reducing the lifetime of the al. [8]. constellation operations. 3.4 Constellation and Small Satellites Further, the benefit of ADR can be seen in the results, with a reasonable impact if at least 5% of failed satellites are removed. Of particular interest to the community, is the combined impact Over the constellation lifetime, this is of the order of one satellite arising from the deployment of large constellations and an per year, which appears feasible given the number of satellite increasing release of small satellites into the LEO environment. launches. Higher impacts can be observed with higher removal To provide some insight into this future possibility, DAMAGE rates. It is worth noting that similar benefits can be obtained by was used to investigate a number of scenarios featuring the extension of the satellite lifetimes, which has the potential to be baseline constellation and the baseline small satellite launch a cheaper solution, so this also provides an interesting trade-off activity. The scenarios included constellation post-mission for industry. disposal based on fixed 400 × 1100 km orbits and also based on a 25-year residual lifetime. There is some vulnerability to the behaviour of the background population. Clearly, where operators are less As expected, the combined large constellation and small compliant with space debris mitigation guidelines, the existence satellite traffic produced a higher number of objects and a higher of a large number of operational satellites provides an increased number of catastrophic collisions, on average, than the cases risk, even if the constellation operators are diligent. The impact featuring only one of those elements. In general, the baseline of the constellation is increased if the compliance of the small satellite traffic had a greater impact on the environment background population with mitigation guidelines is poor. than the large constellation, but the relative changes arising from the combined case were still significant. Including the These results should provide some reassurance: potential small satellite traffic with the constellation resulted in 63.9% negative impacts of a large constellation can be reduced through more objects and 90.8% more catastrophic collisions in LEO careful design and operation. Clearly, some of the design and by the year 2213 than the constellation alone. The change operation choices will involve important trade-offs (e.g. with with respect to the small satellite traffic alone was 17.6% and respect to coverage, cost, and other satellite characteristics) 46% for the number of objects and the number of catastrophic that will require detailed analysis, but a key finding is that the collisions, respectively. impact on the environment can be addressed. 4. DISCUSSION 4.2 Small Satellites 4.1 Large Constellations The most sensitive parameter in the simulations is the behaviour of the background population. Therefore, the measures which Consistently with previous studies, the most influential can be taken to mitigate against the impact of small satellite aspect on the future space debris environment is the post numbers are vulnerable to the behaviour of the general satellite mission disposal of spacecraft and rocket bodies. The impact population. of compliance below 90% for the constellation has the most substantial impact on the environment regardless of the metric Of the scenarios where the background behaviour is used. There is substantial benefit in maximising the reliability/ good, it is clear that the key aspects affecting the impact of success of post mission disposal. small satellites are the number of satellites, the altitudes of deployment and the size of the satellites. Where there are In some cases, the use of electric propulsion can be more dedicated launches operating to deploy satellites at lower efficient than having satellites delivered directly to the target altitudes, especially where these are within the 25-year orbit. Importantly, it increases the robustness of the system lifetime domain, a reduced impact on the environment can be to failures and to post mission disposal failures. It is clearly observed. This consolidates the concern that unmanoeuvrable evident in the data that a low deployment altitude effectively small satellites deployed at higher, more populous, altitudes raises the compliance with post mission disposal requirements can remain a source of collision risks. It is noticeable in the by having both rocket body PMD failures and dead-on-arrival results reported in [8] that this effect can be mitigated against (DOA) failures naturally compliant with PMD guidelines. where the small satellites have a collision avoidance capability, At the same time, satellites that use electric propulsion will and this capability would be recommended for small satellite require larger solar arrays to meet the relatively high power missions at higher altitudes. requirements of those systems, which will increase the cross- sectional area exposed to impacts and could have a negative The trend towards increasing small satellite sizes is expected impact on the environment. Ultimately, there is a trade off with to have a significant impact on the environment according to the the collision area. results (reported in [8]). Again, collision avoidance capability has some mitigating impact. Where this propulsive system is The number of satellites has a significant effect. It seems also able to provide a de-orbit capability, increased benefit is possible for constellations consisting of up to 1500 satellites to observed. This suggests that the guidelines for the de-orbit of have a minimal effect on the environment. In order to achieve small satellites should be similar to other satellites if deployed this, an appropriate altitude must be selected, and the satellites at sufficiently high altitude. themselves must be relatively small. The characteristics of the satellites themselves, particularly the collision (projected) area, 5. CONCLUSIONS have a high sensitivity demonstrating that an influence on the environment should be considered at the satellite design stage. Most opportunities for risk reduction come from measures that Further environmental benefits can be observed from increasing limit exposure of the orbital object population to constellation 116 Sensitivity of the Space Debris Environment to Large Constellations and Small Satellites and small satellite traffic. Importantly, this is not simply a case to communicate responsibilities widely. However, there is a of launching to altitudes that are sparsely populated. Further, trade-off: imposing restrictions on small satellite missions only one of these measures is represented in existing space could forfeit many of the advantages offered by them. In debris mitigation guidelines: post-mission disposal. particular, the cost impact could be severe and affect the commercial viability of missions. Given the innate complexity involved in constellation design and operation, and the relatively low number of Nevertheless, the simulation results suggest that it is operators, it may be better to address the risks posed by large important to have regulation of the small satellite population in constellations on a case-by-case basis. In contrast, there are order to mitigate the effects on the environment. The existing fewer opportunities overall to mitigate the impacts of small space debris mitigation guidelines already provide the basis; satellites. For the most part, this is due to the constraints on but evidence of the past decade has shown that satellites have the design of CubeSats. Without the ability to perform post- a patchy record of compliance, at best [14]. Enforcement, mission disposal, there is currently no overlap with existing perhaps, will provide a more robust way to mitigate the impacts space debris mitigation guidelines; compliance with the so- of small satellites on the environment. called “25-year rule” is typically achieved through launch to low altitudes but this can’t always be achieved. In addition, ACKNOWLEDGEMENTS the small satellite community is large and made up of a diverse set of actors, which makes it difficult to develop a The authors gratefully acknowledge the support of the case-by-case assessment approach. Consequently, there is iSolutions team at the University of Southampton and the use perhaps a need to consider additional space debris mitigation of the Iridis High-Performance Computing facility. The work guidelines for small satellites and CubeSats given the need was funded through the ESA General Studies Programme. REFERENCES 1. B. Bastida Virgili, J.C. Dolado, H. Lewis, J. Radtke, H. Krag, B. Revelin, 8. J. Radtke, E. Stoll, H.G. Lewis and B. Bastida Virgili, “The impact of the C. Cazaux, Colombo, R. Crowther M. Metz, “Risk to space sustainability increase in small satellite launch traffic on the long-term evolution of the from large constellations of satellites”, Acta Astronautica, 126, pp.154- space debris environment”, 7th European Conference on Space Debris, 162, 2016. Darmstadt, Germany, 18-21 April 2017. 2. J. Radtke, C. Kebschull E. and Stoll, “Interactions of the space debris 9. A. Rossi, E.M. Alessi, G.B. Valsecchi, H.G. Lewis, J. Radtke, C. environment with mega constellations – using the example of the Bombardelli and B. Bastida Virgili, “A quantitative evaluation of OneWeb constellation”, Acta Astronautica, 131, pp.55-68, 2017. the environmental impact of the mega constellations”, 7th European 3. G.E. Peterson, A.B. Jenkin, M.E. Sorge and J.P. McVey, “Implications Conference on Space Debris, Darmstadt, Germany, 18-21 April 2017. of proposed small satellite constellations on space traffic management 10. J.-C. Liou, “A statistical analysis of the future debris environment”, Acta and long-term growth in near-earth environment”, 67th International Astronautica, 62, pp.264-271, 2008. Astronautical Congress, Guadalajara, Mexico, 26-30 September 2016. 11. A. Lidtke, H.G. Lewis and R. Armellin, “Statistical analysis of the 4. H.G. Lewis, B.S. Schwarz, S.G. George and P.H. Stokes, “An assessment inherent variability in the results of evolutionary debris models”, of cubesat collision risk”, 65th International Astronautical Congress, Advances in Space Research, 59, pp.1698-1714, 2017. Toronto, Canada, 29 September-3 October 2014. 12. A. Rossi, H.G. Lewis, A. White and B. Bastida Virgili, “Analysis of 5. B. Bastida Virgili and H. Krag, “Small satellites and the future space the consequences of fragmentations in low and geostationary orbits”, debris environment”, 30th ISTS, Kobe-Hyogo, Japan, 4-10 July 2015. Advances in Space Research, 57, pp.1-12. 6. B. Bastida Virgili, H. Krag, H. Lewis, J. Radtke and A. Rossi, “Mega- 13. N.L. Johnson, P.H. Krisko, J.-C. Liou and P.D. Anz-Meador, “NASA’s constellations, small satellites and their impact on the space debris New Breakup Model of EVOLVE 4.0”, Advances in Space Research, 28, environment”, 67th International Astronautical Congress, Guadalajara, pp.1377-1384, 2001. Mexico, 26-30 September 2016. 14. S. Frey, S. Lemmens, B. Bastida Virgili, T. Flohrer and V. Gass, “Impact 7. H.G. Lewis, J. Radtke, J. Beck, B. Bastida Virgili and H. Krag, “Self- of end-of-life manoeuvres on the residente populations in protected induced collision risk analysis for large constellations”, 7th European regions”, 67th International Astronautical Congress, Guadalajara, Conference on Space Debris, Darmstadt, Germany, 18-21 April 2017. Mexico, 26-30 September 2016. (Received 30 June 2017; Accepted 13 July 2017) * * * 117 StefanJournal Frey of theand British Stijn Lemmens Interplanetary Society, Vol. 70, pp.118-124, 2017 STATUS OF THE SPACE ENVIRONMENT: CURRENT LEVEL OF ADHERENCE TO THE SPACE DEBRIS MITIGATION STEFAN FREY1 AND STIJN LEMMENS2 European Space Agency, European Space Operations Centre, Robert-Bosch-Str. 5, 64293 Darmstadt, Germany. Email: [email protected] and [email protected] To counter an ever increasing number of man-made objects orbiting Earth which are endangering current and future space missions, the Space Debris Mitigation (SDM) guidelines, issued by the Inter-Agency Space Debris Coordination Committee (IADC), were first published in 2002. These guidelines were a model for various international and national standardisation and regulation activities on SDM. One part of the research conducted at the Space Debris Office at the European Space Operations Centre (ESOC) is to study and monitor the level of implementation of these guidelines. This report summarises the status of the near Earth space environment by illustrating the number of objects orbiting Earth. The current and historical environment is assessed, with a focus on the interference of the IADC protected regions, the Low Earth Orbit (LEO) and the Geostationary Orbit (GEO). It includes an estimate of the evolution of the collision risk of payloads and rocket bodies with space debris, computed with ESA’s Meteoroid and Space Debris Terrestrial Environment Reference (MASTER) tool. And it illustrates the current level of adherence to the SDM guidelines in terms of end-of-life operations and the release of mission related objects. Keywords: Space Debris, Mitigation Guidelines, IADC 1. INTRODUCTION The space debris mitigation guidelines, published by the Inter- the degree of implementation of end-of-life (EOL) Agency Space Debris Coordination Commitee (IADC) in 2002 manoeuvres in order to clear the protected regions; and revised in 2007, were introduced to reverse the trend of the number of released mission related objects (MROs). the ever increasing number of space debris, to mitigate the risk of collisions and to preserve the space environment for future Not being discussed in this report are the parts of the mitigation generations [1]. In particular, two regions are protected by the guidelines concerning the prevention of on-orbit collisions and guidelines; the Low Earth Orbit (LEO) and the Geostationary fragmentations during and after normal operations. Orbit (GEO), subsequently referred to as LEOIADC and GEOIADC (see Table 1 for the definitions of those regions). Now, 15 years 2. CURRENT AND HISTORICAL STATUS later, sufficient time has passed for the guidelines to propagate OF THE SPACE ENVIRONMENT into national and international standards [2] and to be applied to recent space missions. It is of interest to see whether trends 2.1 Numbers can be found indicating a broadening implementation of the guidelines. This reports shows some of the results produced The number of observable objects orbiting Earth as of the by the Space Debris Office of the European Space Agency reference epoch 1 January 2017 is almost 18500 (see Table 3). (ESA) on quantifying the level of adherence to the mitigation Each object counted was observed at least once in 2016, and guidelines. is assumed to not have re-entered before the reference epoch. Almost two thirds of these objects reside in LEO and nearly Herein, the historical and current environment in terms of 5% in GEO. Additionally, objects on orbits crossing into the numbers and collision risk is presented. At each reference epoch protected regions increase the traffic further (see Table 4); 394 (1 January), every observed orbiting object was counted and a objects cross both, LEOIADC and GEOIADC and 2629 objects state was obtained from the Database and Information System penetrate into LEOIADC only. A total of 2637 objects intersect Characterising Objects in Space (DISCOS) [3]. The collision with (and reside in) GEOIADC. Table 4 also gives an idea of how risk is subsequently calculated using the Meteoroid and Space long on average the crossing objects spend in the protected Debris Terrestrial Environment Reference (MASTER) tool [4]. regions; the equivalent number of objects is calculated More than 50,000 MASTER runs were performed in a highly from summing up the dwell time fraction over all objects automatic and distributed system. The results are presented per interfering the region. The dwell time fraction is defined as the object type (see Table 2) and orbital class (see Table 1). total time an object spends in the protected region per orbit, divided by its orbital period. E.g. the 394+2629=3023 objects Then, two components addressed by the mitigation crossing LEOIADC add an equivalent of 12638-12230=408 guidelines are discussed: additional objects to the protected region. Thus each LEOIADC crosser dwells on average 13.5% of its orbital period within LEOIADC. Note that the velocities of these crossers are typically This paper was presented at the ESA 7th European Conference on considerably higher at their respective perigees, compared to Space Debris, ESA/ESOC, Darmstadt, Germany, 18-21 April 2017 the objects fully residing in LEOIADC. 118 Status of the Space Environment: Current Level of Adherence to the Space Debris Mitigation TABLE 1: Orbit Classifications, with Semi-Major Axis a, Eccentricity e, Inclination i, Perigee Height hp, Apogee Height ha and Declination δ. The Units are km and Degrees. Orbit Description Definition ∈ LEO Low Earth Orbit hp/a [0, 2000] ∈ ∈ GEO Geostationary Orbit hp/a [35586, 35986] i [0, 25] EGO Extended Geostationary Orbit a ∈ [37948, 46380] e ∈ [0, 0.25] i ∈ [0, 25] ∈ ∈ ∈ GTO GEO Transfer Orbit hp [0, 2000] ha [31570, 40002] i [0, 90] ∈ ∈ NSO Navigation Satellites Orbit hp/a [18100, 24300] i [50, 70] ∈ MEO Medium Earth Orbit hp/a [2000, 31570] ∈ ∈ LMO LEO-MEO Crossing Orbits hp [0, 2000] ha [2000, 31570] ∈ ∈ MGO MEO-GEO Crossing Orbits hp [2000, 31570] ha [31570, 40002] ∈ HEO Highly Eccentric Earth Orbit hp [0, 31570] ha > 40002 ∈ LEOIADC IADC LEO Protected Region hp/a [0, 2000] ∈ ∈ GEOIADC IADC GEO Protected Region hp/a [35586, 35986] δ [-15, 15] TABLE 2: Object Types. Type Description PL Payload PM Payload Mission Related Object PD Payload Debris RB Rocket Body RM Rocket Mission Related Object RD Rocket Debris UI Unidentified TABLE 3: Number Observed Objects in Geocentric Orbit as of 1 January 2017. PL PM PD RB RM RD UI Total LEO 2300 113 5959 822 490 2474 72 12230 GEO 708 3 4 67 0 0 30 812 EGO 401 37 1 181 0 35 845 1500 GTO 60 10 10 217 49 214 312 872 NSO 230 1 0 70 2 0 0 303 MEO 52 53 8 16 2 5 37 173 LMO 90 47 130 207 221 590 307 1592 MGO 66 2 82 158 4 10 184 506 HEO 24 1 19 42 0 48 300 434 Other 30 3 0 4 0 0 26 63 Total 3961 270 6213 1784 768 3376 2113 18485 TABLE 4: Number Observed Objects in Geocentric Orbit Penetrating into the Protected Regions, in Absolute (abs) and Equivalent (eqv) Terms, as of 1 January 2017. PL PM PD RB RM RD UI Total both (abs) 19 1 20 73 15 122 144 12230 LEOIADC (abs) 2464 171 6118 1277 760 3326 743 812 LEOIADC (eqv) 2335 124 6050 871 528 2611 119 1500 GEOIADC (abs) 864 37 41 281 15 148 1251 872 GEOIADC (eqv) 762 11 5 103 1 9 124 303 none (abs) 652 63 74 299 8 24 263 173 119 Stefan Frey and Stijn Lemmens Figures 1 and 2 show the evolution of the number of the collision risk is greatly underestimated, as collisions with observable objects orbiting Earth, per object type and orbital particles smaller than 10 cm are ignored (most of which would classification respectively. The two steep increases after 2007 result in non-catastrophic collisions [7]). At the same time it and 2009, are due to the Chinese anti-satellite (ASAT) test [5] is slightly overestimated, as the capability of manoeuvring to and the Iridium 33/Kosmos 2251 collision [6]. The number avoid a probable collision is ignored. However only about a of UIs is expected to rise dramatically with improved sensor third of all PLs - ignoring human spaceflight - reaching EOL capabilities. between the years 2000-2015 proved to have orbit control capability [8]. And the capability of manoeuvring alone does 2.2 Virtual Collisions not protect against a collision; conjunctions also need to be predicted and appropriate measures taken in order to prevent Using the MASTER tool allowed to estimate the space debris a collision. The trend in Fig. 3 shows that the likelihood of flux each of the PLs and RBs counted above receives over the collision is on the rise. The steep increase at the reference epoch course of one complete orbit. Only particles sized between 1 January 2007 is due to the ASAT test of 11 January 2007. The 0.1-100 m in reference diameter were taken into account, MASTER tool is population based, and for each calculation as they generally correspond to the objects involved in so chooses the population which is closest to the reference epoch. called catastrophic collisions, i.e. having an impact energy In this case, the population from 1 February 2007 is - rather above 40 J/g. Multiplied with the cross sectional area of the than the one from November 2006 - closer to the reference object, and the time-frame of one year results in the number epoch of the majority of the selected states. Thus the estimate of virtual collisions each object experiences in one year, under includes the short-term future. the assumption of a non-perturbed orbit. The virtual is added because these are not real collisions, but merely estimated ones, LEO is by far at greatest risk to see a collision, with 0.15 which give a measure of the collision risk for each object. virtual collisions in one year, or one virtual collision of a PL or RB with an object larger than 10 cm in 7 years. The Table 5 shows the summed number of virtual collisions following discussion is thus focused on LEO only. Within 10 for PLs and RBs separately in each orbital class. Note that years (after the rise induced by the ASAT test), the number of Fig. 1 Evolution of the number observed objects in geocentric orbit by object type. Fig. 2 Evolution of the number observed objects in geocentric orbit by orbital class. 120 Status of the Space Environment: Current Level of Adherence to the Space Debris Mitigation TABLE 5: Cumulative Number of Virtual Collisions of PLs and RBs with Debris (sized 0.1-100 m) per Year as of 1 January 2017, According to the MASTER Tool. PL RB Total LEO 6.8 × 10−2 8.2 × 10−2 1.5 × 10−1 GEO 3.1 × 10−4 1.6 × 10−5 3.2 × 10−4 EGO 3.9 × 10−5 1.0 × 10−5 4.9 × 10−5 GTO 9.8 × 10−5 6.2 × 10−4 7.1 × 10−4 NSO 5.4 × 10−6 5.3 × 10−6 1.1 × 10−5 MEO 1.8 × 10−5 4.8 × 10−6 2.2 × 10−5 LMO 5.1 × 10−4 1.2 × 10−3 1.7 × 10−3 MGO 1.2 × 10−6 9.2 × 10−6 1.0 × 10−5 HEO 7.8 × 10−6 3.8 × 10−5 4.6 × 10−5 Other 1.6 × 10−6 6.4 × 10−10 1.6 × 10−6 Total 6.9 × 10−2 8.4 × 10−2 1.5 × 10−1 Fig. 3 Evolution of number objects (sized 0.1-100 m) colliding with PLs and RBs on-orbit per year, according to the MASTER tool. Note that the increase in collision risk due to the ASAT test is evident already as of 1 January 2007, due to the way the tool chooses the resident populations. virtual collisions per year rose by 51.5%, while the number of shall be limited to 25 years or less. Objects in geosynchronous PLs and RBs orbiting only rose by 33.7%, translating into a orbits, where no atmospheric drag acts to clean the region, 14.3% increase of collision risk on average for each PL and RB. shall relocate into an orbit that remains outside GEOIADC for the Within 20 years, the number of virtual collisions rose by 206%, foreseeable future (refer to [1] for a more technical description). while at the same time the number of PLs and RBs increased Vessels related to human spaceflight are not taken into account by 65.9%, meaning the individual collision risk increased on for the synthesis of the results, as they tend to skew the results average by 84.6%, i.e. almost doubled. positively in terms of count and mass due to their objectives. Objects reaching EOL are binned into four different categories, Integrating the trend of the virtual collisions in LEO of the depending on whether they performed an EOL manoeuvre and past 60 years results in 1.03 virtual collisions for PLs and 1.45 their respective orbits pre- and post-EOL manoeuvre: for RBs. More than half being accumulated within the past 10 years (0.56 for PLs and 0.72 for RBs respectively). So far, four no attempt: no manoeuvre was performed despite collisions between catalogued objects have been reported in residing in a non-compliant orbit; LEO [9]. insufficient attempt: the object performed a manoeuvre that failed to reach in a compliant orbit; 3. END-OF-LIFE OPERATIONS successful attempt: the performed manoeuvre put the object into a compliant orbit (includes objects that The mitigation guidelines state that an object reaching the end performed a manoeuvre even residing in an already of operational mission should perform a manoeuvre to clear compliant orbit pre-manoeuvre); dense orbital regions by reducing its remaining orbital lifetime, naturally compliant: without performing a manoeuvre, preferably to zero. In LEOIADC, the post-mission orbital lifetime the object is compliant due to an orbital lifetime 121 Stefan Frey and Stijn Lemmens limited to less than 25 years by atmospheric drag (only as successful attempt and naturally compliant). The following applicable in LEOIADC). paragraph only takes into account LEOIADC objects reaching EOL in the last 10 years of analysis, i.e. 2006-2015 for PLs and In-depth description of the methodology used to determine 2007-2016 for RBs. GEOIADC objects are discussed in the next the EOL of LEO objects can be found in [10]. For a more paragraph. 49.9% of all PLs are naturally compliant and did not detailed summary of the results given here for GEO objects, perform an EOL manoeuvre. Of the other half (taking it as 100%), please refer to [11]. only 6.7% successfully implemented a manoeuvre complying with the guidelines. Another 10.4% tried to do so but failed to Figures 4 to 6 show the relative evolution of those categories comply with the 25-years rule. As for the remaining 82.9% (or for PLs (relative count and mass) and RBs (only relative count 41.5% of all PLs), no attempt to comply with the guidelines as the mass trend is qualitatively the same) in LEOIADC reaching was performed. In absolute terms, 53.3% are compliant. The EOL. The pluses in the figures show a 10-year moving average last two years could suggest an improvement in behaviour, of the compliant objects (i.e. the sum of the objects categorised but looking at the evolution of the compliant mass (Fig. 5), it Figure 4. Evolution of compliance of PLs (not related to human spaceflight) in LEOIADC. Pluses show the 10-year moving average of compliant objects (i.e. the naturally compliant ones and the ones performing a successful EOL manoeuvre). Fig. 5 Evolution of compliant mass of PLs (not related to human spaceflight) in LEOIADC. Fig. 6 Evolution of compliance of RBs in LEOIADC. 122 Status of the Space Environment: Current Level of Adherence to the Space Debris Mitigation becomes evident that the count figure is skewed by a change in the PL launch trend. The steep increase in naturally compliant category for the years 2014 and 2015 is due to the large numbers of cubesats introduced in the previous years mostly into orbits low enough, or with area-to-mass ratios high enough, to decay within 25 years. In terms of mass, 60.3% are compliant in the same time-range, consistently sloping downward in the 10- year moving average. RBs more successfully clear LEOIADC. Again, about half (49.4%) of the RBs are in orbits which are naturally compliant and no EOL manoeuvre was performed. Of the other half (taking it as 100%), 43.9% implemented a successful and another 13.6% an insufficient manoeuvre. The remaining 42.6%, or 21.5% of all RBs, (the parts do not sum to unity due to rounding errors) did not attempt to adhere to the guidelines. In absolute terms, 71.6% are compliant. The share of RBs actively clearing LEOIADC is on the rise, but mostly at the expense of already naturally compliant RBs. The relative Fig. 8 Release of PL MROs. number of non-compliant RBs remains almost constant around 29%. Figure 7 shows the compliance trend for PLs in GEOIADC. The following discussion only considers the ones residing in GEOIADC and reaching EOL between 2007-2016. 66.1% successfully raised their orbits high enough above GEOIADC. Another 23.2% tried to do so, but failed, leaving only 10.7% or 1 in 9 PLs that did not attempt a clearance manoeuvre. The share of objects successfully implementing an EOL manoeuvre is - leaving out the year 2015 as an outlier - on the rise but seems to saturate at around 75%. Note that on average, only 16.8 PLs reached EOL each year in this period, making the figures prone to large variances. 4. RELEASE OF MISSION RELATED OBJECTS Fig. 9 Release of RB MROs. The mitigation guidelines state that no debris, such as camera covers and de-spin weights, should be released during normal operations for both PLs and RBs. Figures 8 and 9 show the 5. CONCLUSIONS evolution of released mission related objects in number and mass for PLs and RBs respectively. The number of released MROs The historical and current status of the space environment was from PLs decreased drastically towards the end of the cold war presented in terms of numbers and collision risk. It was shown down to and remaining at 5.6 per year (or 0.661 tons) averaged that the likelihood of a collision of a PL or RB with an object over the past 10 years. RBs however continue to release MROs larger than 10 cm is increasing faster than the total number of PLs at significant levels; over the past 10 years, they released on and RBs. Currently one such collision is predicted to occur every average 35.4 objects (or 10.741 tons) per year. The numbers 7 years, but the frequency is likely to increase in the near future. presented here are to be interpreted as a lower limit only. From orbit dynamics alone it is difficult to distinguish between the Furthermore, the current level of adherence to the space intentional and non-intentional release of space debris. debris mitigation guidelines was presented. To summarise: Fig. 7 Evolution of compliance of PLs in GEOIADC. Pluses show the 10- year moving average of compliant objects (i.e. the ones performing a successful EOL manoeuvre). 123 Stefan Frey and Stijn Lemmens • 53.3% of the PLs and 60.3% of the PL mass reaching the number of released PL MROs reached low levels EOL in LEOIADC between 2006-2015 are compliant. already before the year 2000, but continues to be In terms of mass, this share is constantly sloping significant for RBs. downward; • 71.6% of the RBs reaching EOL in LEOIADC between The level of adherence 15 years after the introduction of the 2007-2016 are compliant, a fraction virtually unchanged mitigation guidelines is sobering, the only exception being the for 8 years in a row despite an increased EOL manoeuvre clearance of PLs in GEOIADC. The environment around Earth, activity; especially in LEOIADC is continuing to get more hostile almost • 66.1% of the PLs reaching EOL in GEOIADC between every year. The goal of the mitigation guidelines - to preserve 2007-2016 are compliant, tendency rising but possibly the Earth environment for future generations - is still beyond saturating; reach. REFERENCES 1. Inter-Agency Space Debris Coordination Committee, “IADC Space 7. P.H. Krisko, “The predicted growth of the low- Earth orbit space debris Debris Mitigation Guidelines”, 2007. environment - an assessment of future risk for spacecraft”, Proceedings 2. International Standards Organisation, “Space systems - space debris of the Institution of Mechanical Engineers, 2007 mitigation”, ISO 24113:2011, 2011 8. S. Frey, H. Krag, M. Metz, S. Lemmens and B. Bastida Virgili, “Achieving 3. T. Flohrer, S. Lemmens, B. Bastida Virgili, et al., “DISCOS - Current Successful End-Of-Life Disposal in LEO”, Proceedings of the 10th IAA Status and Future Developments”, Proceedings of the 6th European Symposium on Small Satellites for Earth Observation, 2015 Conference on Space Debris, SP-723, 2013 9. C. Pardini and L. Anselmo, “Review of past on-orbit collisions among 4. S. Flegel, J. Gelhaus, M. Möckel, et al., “Maintenance of the ESA catalogued objects and examination of the catastrophic fragmentation MASTER-Model”, Final Report of ESA contract 21705/D/HK, 2010 concept”, Acta Astronautica, 100, pp.30–39, 2014. 5. National Aeronautics and Space Administration, “Chinese anti-satellite 10. S. Lemmens and H. Krag, “Two-line-elements based manoeuvre test creates most severe orbital debris cloud in history”, Orbital Debris detection methods for satellites in low earth orbit”, Journal of Guidance, Quarterly News, 11, pp.2-3, 2007 Control, and Dynamics, 37, pp.860–868, 2014. 6. National Aeronautics and Space Administration, “Satellite collision 11. ESA Space Debris Office, “Classification of geosynchronous objects”, leaves significant debris clouds”, Orbital Debris Quarterly News, 13, Issue 19, 6 April 2017. pp.1-2, 2009 (Received & Accepted 19 June 2017) * * * 124 Journal of the BritishFast Interplanetary Re-Entry Deorbitation Society, Vol.with 70, Acceptable pp.125-133, Risk Level2017 FAST RE-ENTRY DEORBITATION WITH ACCEPTABLE RISK LEVEL ELISABET CID BOROBIA1, CLAIRE FRÉMEAUX2 AND JEAN-FRANÇOIS GOESTER3 CNES, 18 avenue Edouard Belin, 31401 Toulouse Cedex 9, France. Email: [email protected], [email protected] and [email protected] One important action, needed to limit the space debris population increase in the low Earth orbit region, is to deorbit all space systems after the mission lifetime. This can generally be done either by controlled direct re-entry or by moving to an orbit which will ensure a natural decay of the space object within a limited time span, as short as possible. Direct controlled re-entry is, of course, the most efficient way to proceed with regard to lifetime reduction and human casualty risk control. However, it is demanding in terms of means and requires a well dimensioned propulsion subsystem to perform the last re-entry burst. In particular, controlled re-entry is not feasible with low thrust propulsion. Uncontrolled re-entry is less efficient, leaving the space objects uncontrolled during years before effective re-entry, but is simpler to achieve. However, the risk towards human population at the time re-entry occurs should be limited and several national or agency regulatory texts require the human casualty risk to be lower than 10-4. Between these two routes, fast re-entry deorbitation appears as an attractive solution: manoeuvres are performed until the satellite is left very close to its effective re-entry, human casualty may be limited, and this method could also be available with low thrust propulsion. This paper will analyse several key elements regarding final orbit, casualty risk and manoeuvre strategy implementation in order to progress towards operational feasibility of fast re-entry deorbitation. The first part will introduce fast re-entry deorbitation concept, constraints and principles. A second part will address the final decay phase: casualty risk and target re-entry orbit choice. The third part will discuss manoeuvre strategies to reach this target orbit with chemical or electrical propulsion. Keywords: Space debris, fast re-entry deorbitation 1. INTRODUCTION 1.1 Concept For an uncontrolled re-entry, the effective casualty area at the time the re-entry occurs may be everywhere on the globe, inside a latitude bandwidth determined by the satellite inclination. Fast re-entry deorbitation is a good improvement to debris mitigation regarding two aspects: It drastically reduces the total residual lifetime and, thus, the risk of explosion or collision which creates new debris before effective re-entry. It may reduce the casualty risk to an acceptable value, by limiting the length of the possible on-ground casualty Fig. 1 Fast re-entry deorbitation ground track length. area and targeting favourable geographic conditions (see example in Fig. 1). atmospheric density model, 1.2 Constraints Solar activity level. We will call “ground track” the estimated area where debris are These elements are not well known and vary with time. likely to reach the ground: it is not really a ground track as it It appears very difficult to predict with good precision the corresponds to a set of possible re-entry points. possible impact zone of an object which is due to re-enter soon. Therefore, the duration of natural decay at the end of Several elements with uncertainties contribute to this pseudo deorbitation must be as short as possible in order to reduce the ground track, among which: final ground track length: typically one day or so. • ballistic coefficient of intact object, Before natural decay, the satellite will execute manoeuvres surviving fragments and their aerodynamic in order to reduce its altitude. At the beginning, manoeuvre will characteristics, not be a problem but, with the altitude decreasing, the satellite This paper was presented at the ESA 7th European Conference on will have difficulty to maintain its nominal attitude control Space Debris, ESA/ESOC, Darmstadt, Germany, 18-21 April 2017 capability due to the increase of aerodynamic forces and 125 Elisabet Cid Borobia, Claire Frémeaux and Jean-François Goester torques: this limit in altitude depends on the satellite geometry and inertia. It may typically happen below 250 km. For electric propulsion there is another important constraint regarding the electrical power budget: long thrusts will discharge the battery and some amount of time will have to be devoted to battery charge. Available thrust time will, thus, be limited. This limit will depend on various parameters such as: local time, inclination, eccentricity, apogee/perigee orientation, eclipse duration, season, Solar panel orientation during thrusts or altitude. Fig. 2 Elliptic deorbitation. 1.3 Main Principles The deorbitation will consist in a variety of tangential negative manoeuvres that will decrease the altitude until reaching a final re-entry orbit. This final orbit must ensure a rapid decay ending in a targeted zone on Earth that will guarantee a low casualty risk. If a circular orbit is kept during the descent, the satellite will be on a quasi-circular orbit when manoeuvres are stopped before decaying naturally. The decay time starting from a 250 or 300 km circular orbit is one week to a few weeks (for a 1 ton /10 m2 satellite), which is too long to ensure a short ground track length. Therefore it is necessary to adopt an elliptical descent strategy rather than a pseudo circular one: this strategy may allow continuing manoeuvres at apogee, even if perigee is very low (see Fig. 2). This will be possible as long as attitude stability can be maintained at these very low altitudes, which may need a Fig. 3 Re-entry duration depending on perigee argument (ω) and dedicated attitude pointing in order to minimize the atmospheric solar activity. torque. Nominal attitude control must be reacquired after each perigee pass and before next apogee manoeuvre. the North hemisphere are more prone to a faster descent than 2. TARGET RE-ENTRY ORBIT the orbits with South perigee arguments, as shown in Fig. 3. The possible impact zone is also smaller for the cases with the Once the satellite is in the re-entry orbit, the manoeuvres are argument of perigee in the North than the ones in the South. no longer possible. Thus, this re-entry phase should be as short However, the best position is to be as close as possible to the as possible in order to reduce the uncertainties and reduce the Equator, where the Earth potential term J2 produces minimum impact zone. decay duration. 2.1 Influence of Some Parameters This difference between the North and the South hemisphere is independent from the season because all the tests performed Let us examine several elements that impact the re-entry in both equinoxes and solstices offered this exactly same duration. behaviour. Indeed, the difference between North and South is only due to Earth potential and independent from the Sun 2.1.1 Altitude position. Of course the altitude is a major element that impacts re-entry 2.1.4 Low Impacting Parameters duration: lower the altitude, faster the re-entry. Some of the input parameters have small or negligible effect. 2.1.2 Solar Activity 2.1.4.1 Season Depending on the solar activity, the satellite decays faster or slower. A faster decay takes place when the solar activity is Some dates are slightly more favourable because the high, which also reduces the possible impact zone dimension. atmospheric density around the Earth depends on the season. Thus, high solar activity is favourable to improve the final re- Figure 4 shows the atmospheric density at equator for very low entry, as it can be seen in Fig. 3. altitude (130 km) given by MSIS2000 model where a re-entry in the months of September-October is faster. 2.1.3 Perigee Argument 2.1.4.2 Local Hour The position of the initial perigee argument in the final re- entry orbit has a huge impact in the duration of this phase The mean local hour (angle between the Sun direction and the and in the impact zone dimension. Indeed, due to the Earth orbital plane) have a small effect during the re-entry orbit (Fig. potential term J3, re-entry orbits with arguments of perigee in 5). 126 Fast Re-Entry Deorbitation with Acceptable Risk Level The second part consists in continuing the propagation starting from these regularly spaced points and splitting the satellite into fragments. At this point the satellite is no longer considered as a single object but as a group of independent debris. The survival debris are propagated down to the Earth where total casualty risk is computed for each debris trajectory. Finally, global casualty risk is obtained by summing casualty risks for each trajectory weighted with its probability. 2.2.2 Perigee Argument Impact In the current revision of ELECTRA, the RF mode runs with a fixed solar activity model. The following hypotheses have been taken, corresponding to a typical Pleiades-like observation satellite: 1 ton and 8.5 m2, local time at ascending node: 22h30, • final re-entry orbit altitude: 130 km / 350 km, Fig. 4 Density depending on the local hour and day of the year. • ballistic coefficient: 52 kg/m2, with dispersion : ±10% uniform. 2.2.3 Perigee Argument Impact The first results confirm a different behaviour depending on the initial perigee argument, as presented in paragraph 2.1.3. The minimum impact zone length is around 3 orbits for a perigee near equator, higher for a perigee near the poles. Moreover, a perigee in South hemisphere will lead to a greater impact zone length than a perigee in the North hemisphere (see Fig. 6). Fig. 5 Negligible differences in the impact zone length depending on the local hour. 2.2 Casualty Risk The use of a fast re-entry deorbitation is mainly justified if there is a reduction of the risk compared to an uncontrolled re-entry. Thus, the gain in terms of risk must be demonstrated. Fig. 6 Length of the impact zone, in terms of orbital revolutions, depending on the re-entry perigee argument position. 2.2.1 ELECTRA Final Re-Entry Orbit Mode 2.2.4 Longitude Phasing Impact The ELECTRA program computes the casualty risk at ground. It has four modes: The risk of the ground track impact zone varies depending Risk at launch (RL) on Earth’s phasing. Indeed, the most populated zones present Risk for controlled re-entry (RC) greater risks, than, for example, the oceans. Thus, the • Risk for final re-entry orbit (RF) positioning/phasing with the Earth has a huge impact. The risk Random risk (RA) also depends on the number of fragments and their casualty area; the bigger the object, the higher the risk. The third mode was used to compute casualty risk and ground track length. The risk has been computed with the method described in §2.2.1 for several orbits with different perigee arguments and The principle is to consider a dispersion on ballistic for two sets of survival debris: 15 or 6 debris, including or not coefficient, which represents the uncertainty on atmospheric structure panels. Nowadays, as there is a certain concern about density model, solar activity and effective attitude during the ground risk, satellites are more prone to be designed with re-entry. In this mode, numerous points are provided for the materials that favour their burning during the re-entry. Then, intact vehicle before fragmentation, which are geographically the case of 15 debris represents the worst possible case where regularly spaced to fit with the population grid spacing, in the structural panels are not burned, and the 6 debris case order not to miss a small but populated area. Each point has its represents an improved design or more favourable scenario associated probability of occurrence. where these panels are burned. 127 Elisabet Cid Borobia, Claire Frémeaux and Jean-François Goester For each case, the risk has, then, been re-estimated with longitude translations representing different Earth phasing possibilities with initial orbit: the best Earth phasing gives the minimum risk value for a given initial orbit. These minimum risk values are shown in Fig. 7 for different perigee arguments. In all cases, the minimum risk is below the random risk (uncontrolled re-entry). Thus, a reduction of the impact length and an adequate Earth phasing can reduce the risk provided by an uncontrolled re-entry. It can be seen that for the 15 debris case, only perigee arguments in North hemisphere allow to find a longitude phasing with risks below the specified limit risk (10-4), being compliant with the FSOA (French Space Operation Act). For the 6 debris case, a favourable longitude phasing is easier to find whatever the perigee argument is. Indeed, the risk level is one order of magnitude lower than with 15 debris case: this shows the extreme importance of Fig. 8 The maximum uniform distribution risk, taking into minimizing the number and surface of survival debris. It account the worst longitudinal positions of the impact zone. is also important to improve our knowledge and predictive capability regarding satellite fragmentation and surviving entry, its trajectory would be known and could perfectly debris: for the same satellite, different tools (eg NASA DAS, match one of the bad phasing possibilities, producing even ESA DRAMA or CNES DEBRISK) may give different sets a higher risk. of survival debris, which has a non-negligible impact on final risk estimation. Nevertheless, in this example all the maximum risks are higher than the 10-4 FSOA limit, even in the favourable case of The maximum risk may also be evaluated (Fig. 8): it 6 debris. It means that the phasing with the Earth is mandatory corresponds to the worst possible Earth phasing in longitude. in order to obtain an acceptable risk. The risk value is, then, higher than the uncontrolled re- entry. One could tend to believe that in some cases the Thus, the safest re-entry orbit should come from the good uncontrolled re-entry is better, but it is not really the case. perigee argument and good date/longitude phasing to target In fact, the results are worse due to the definition of this a chosen Earth zone, in order to minimize the risk and be risk itself. As in the fast re-entry deorbitation the ground compliant with the FSOA. track length is finite (length of several orbits), when it is badly placed and touches very populated areas, the risk is The previous risks were determined through a uniform risk increased. The random re-entry evaluates all the zones of distribution. However, it is also possible to use a Gaussian the Earth from a minimum to maximum latitude, smoothing distribution which reduces the risks. Figure 9 shows how, when the higher risks. A few days before an un-controlled re- using a Gaussian distribution, the risk is acceptable regardless Fig. 9 Risk comparison between a uniform distribution and a Fig. 7 The minimum uniform distribution risk, taking into Gaussian distribution. account the best longitudinal positions of the impact zone. 128 Fast Re-Entry Deorbitation with Acceptable Risk Level of the perigee argument value. The choice of the distribution The deorbitation can be performed through two different type depends on the confidence in the ballistic coefficient strategies: one that penalizes the duration and the other one that dispersions. A Gaussian distribution is acceptable if there is a penalizes the consumed mass. good confidence in the mean ballistic coefficient. On the other hand, if this is not the case, a uniform distribution would be 3.1.3 Elliptical Strategy more appropriate. This strategy performs only decelerating apogee manoeuvers 3. DEORBITATION STRATEGY that lower the perigee. On the other hand, the apogee decreases naturally due to a higher drag force near the This section addresses the manoeuvring phase which brings the perigee. The chemical engine is powerful, so the frequency satellite to the re-entry orbit. of manoeuvres becomes an important parameter. Indeed, if the manoeuvers are too frequent, the perigee will reach the These studies are done considering a typical observation target altitude too early, with an apogee still too high. A valid satellite with Pleiades-like characteristics: see Table 1. deorbitation strategy should find the perfect frequency of apogee manoeuvers to reach the target re-entry orbit: right TABLE 1: Reference Satellite apogee and perigee altitude at right date. For Pleiades satellite Characteristics: ~ Pleiades. case, the right frequency is one manoeuver every two days, as Orbit altitude 700 km shown in Fig. 10. Eccentricity and ω Frozen, North Pole Local hour 22.5 h Mass 1000 kg Surface 10 m2 3.1 Chemical Propulsion The following studies present some results reproducing a case with chemical propulsion. Table 2 shows the propulsion characteristics of Pleiades satellite. TABLE 2: Pleiades Propulsion System Characteristics. “Isp” is the Specific Impulse. DeltaV/man 2.5 m/s Thrust 1N · 4 engines Manoeuvre duration 10 min Isp 210 s 3.1.1 Direct Re-Entry Fig. 10 Elliptic deorbitation strategy with chemical propulsion. Ha and hp are apogee and perigee altitude. With chemical propulsion, it is possible to perform a controlled direct re-entry, which is the best way to ensure security and This strategy allows saving fuel because natural drag force comply with international and national regulations. However at perigee is used to decrease apogee instead of the propulsion direct re-entry is very demanding: 180 m/s are needed to re- system, but it requires a lot of time: four months. enter from the mission orbit. 3.1.4 Circular Strategy On the other hand, it is also possible to deorbit the satellite through a lot of small manoeuvres executed to decrease its It is possible to add, to the previous strategy, perigee manoeuvers altitude down to 250 km for example, and then perform one which lower the apogee. final large thrust to re-enter. This final thrust would require around 90 m/s, which means 6 hours thrust with 4N propulsion A theoretical example is shown in Fig. 11 with apogee and capacity. This is of course not realistic. Direct re-entry needs perigee manoeuvres performed at each orbit (in a real case the a powerful and dedicated propulsion subsystem with a high frequency would certainly be lower, or there would be regular thrust capacity (> 100 N) in order to be able to do this final re- interruption which would enable a correct orbit determination). entry manoeuvre rapidly enough (10 to 15 minutes). When the altitude is too low, perigee manoeuvre are stopped and apogee manoeuvre continue until target perigee altitude is 3.1.2 Fast Re-Entry Deorbitation reached. Fast re-entry deorbitation allows to perform operations with This strategy enables a higher frequency of manoeuvres and a standard propulsion subsystem, and to save the consequent an important reduction of the duration but the fuel consumption hydrazine mass needed for the final re-entry thrusts. increases. 129 Elisabet Cid Borobia, Claire Frémeaux and Jean-François Goester Fig. 11 Circular deorbitation strategy with chemical propulsion. TABLE 3: Typical Electrical Propulsion System Characteristics. Thrust 82 mN Manoeuvre duration 20 minutes max. Fig. 12 Simulation with and without duration reduction due to 10 minutes min. eclipses. The shadowed part shows the points where the apogee is in eclipse. Isp 1400 s Then, the surface changes principally the final perigee altitude, 3.2 Electrical Propulsion being possible to obtain it lower when the surface is smaller. The electrical engines provide smaller thrusts at higher specific As a conclusion, the deorbitation becomes more difficult impulse. Thus, the strategy is completely different from when the satellites are huge in terms of mass or with large the one using chemical engines. In this study, the Pleiades surfaces. satellite is also used as reference but with electrical propulsion characteristics (Table 3). 3.2.1.2 Batteries Charging 3.2.1 Basic Strategy - Main Influence Parameters The electrical propulsion needs a lot of energy and depends on the batteries charging. Thus, the duration of the manoeuvers The simpler re-entry strategy is applied: one maximum apogee cannot always be maximum: it depends on the battery charging manoeuvre at each revolution to lower the perigee. An example time available (outside eclipses). of result can be seen in Fig. 12: indeed this leads to long operations (around 100 days). Simple hypotheses were taken into account to show the impact, supposing that the batteries charging is possible during It is important to evaluate the effect of different the manoeuvres when they are illuminated: parameters. Manoeuvers done at each apogee pass. 3.2.1.1 Mass and Surface Manoeuvre duration is maximum when it takes place outside the eclipse. Mass and surface have a different influence. Manoeuvre duration is reduced when it takes place totally or partly inside the eclipse. The satellite mass impacts on the manoeuvre efficiency during all deorbitation. A small mass is favourable because the Figure 12 shows the difference between using constant manoeuvres are more effective, the perigee decreases faster, duration manoeuvres and eclipse dependant durations. and the total duration is reduced. Logically, the strategy with constant manoeuvres duration is more efficient, reducing the whole deorbitation duration. The satellite surface has an impact only when the drag force Moreover, the perigee reduction rate is constant, as each is more important, so, in the lowest altitudes near the end of manoeuver produces the exactly same perigee reduction. deorbitation. The satellites with a higher surface cause more drag and, thus, the apogee decreases faster: altitude limit for On the other hand, in the case of variable manoeuvre duration, apogee manoeuvre may be reached before perigee has reached the perigee reduction rate is not constant. The duration depends a low enough altitude. On the other hand, the satellites with on the apogee position in relation to eclipses, with an apsis smaller surface cause less drag, the apogee decreases slower, axis rotation of ~100 days period; it becomes more difficult to incrementing the available duration for lowering the perigee. predict the total duration and the final perigee altitude. 130 Fast Re-Entry Deorbitation with Acceptable Risk Level In the previous simulations the starting date, local hour or perigee argument did not have any important impact. Nevertheless, the position of the eclipses changes depending on these input parameters and so does the deorbitation simulation, the final result becoming very dependent from the input characteristics. The orbits with mean local hours at 6h or 18h are exempt of eclipses, thus, they can use the maximum duration of the manoeuvers all the time. There is another problem associated to the batteries charging. When the perigee is lower than a certain altitude (typically 250 Fig. 13 Shadowing effect difference between summer and winter km), the satellite loses its attitude performance and may not (in black). Target ending zone (in green). be able to orient solar panels to charge the battery. Then, the manoeuvers duration is even more reduced because of this prove the validity of these strategies during the whole year, lack of charging time. This is another constraint which adds simulations are performed in this worst case: ending close complexity to the deorbitation and degrades the final perigee to Summer solstice, the feasibility for any other date being altitude. automatically demonstrated. 3.2.1.3 Solar Activity It is possible that using different satellites or different threshold altitudes, the strategy could only be performed The solar activity has an impact in the final characteristics on ending at the winter solstice, imposing a huge constraint in the the re-entry orbit: deorbitation strategy. A higher solar activity implies a faster apogee reduction. 3.2.2.2 Setting the Initial Perigee Argument Then, the available duration to reduce the perigee is smaller and the final perigee altitude remains higher. LEO orbits are nearly circular. The frozen eccentricity often A lower solar activity decreases slower the apogee and, used for stability reason is around 10-3, perigee oriented thus, there is more time to apply apogee manoeuvers that towards North direction. Apogee manoeuvres will increase lower the perigee. Moreover, the apogee manoeuvres eccentricity and the apsis axis will rotate with a period close are more effective, improving the perigee descending to 100 days. rate. So, surprisingly, in this phase a low solar activity will be favourable, allowing reaching a lower perigee To reach the desired perigee argument at the end of deorbitation, altitude. it is necessary to initialise the perigee argument to the appropriate value at the beginning of operations, taking into account the During the manoeuvring phases, a low solar activity expected rotation of the apsis axis during the operations. improves the results. However, once the satellite is in the re- entry orbit, the high solar activity is the one that improves them. For cost reason, it will be possible neither to maintain the perigee argument in a constant position during operations nor 3.2.2 Strategies Depending on Solar Activity to move the apsis axis to a desired value at the end of operations when eccentricity is higher. It would neither be appropriate As it was explained in the previous section, there are lots of to wait until achieving naturally the target perigee argument parameters that influence the deorbitation. In this section, three because the waiting orbit at low altitudes is very expensive due solutions are presented for three different cases: low, medium to high drag force and should only be used in order to phase the and high solar activity. satellite with the Earth. The duration of the manoeuvres is variable, as it is shown Thus, the positioning of the perigee argument should be in §3.2.1.2. Moreover, the duration is even more reduced when set as soon as possible: dedicated manoeuvre will ensure the the perigee attitude is no longer controllable. appropriate setting of apsis axis. This will induce an extra cost, except in the ideal case where the desired initial perigee The requirements of the final re-entry orbit are: argument is the same as station-keeping one. Orbit 350x130 km. The argument of the perigee must be set in the North 3.2.2.3 Initial Apogee Raising hemisphere. • In order to maximize the manoeuvre duration in the final Once the perigee argument is well positioned, the deorbitation phase which is the most critical, the apogee cannot end manoeuvers start. The simpler strategy is to perform tangential in eclipse. As it is an orbit with local hour 22.5h, the braking manoeuvers at apogee to lower the perigee. argument of the perigee should finish close to 0º. Unfortunately, this solution is not always sufficient: it may 3.2.2.1 Final Perigee Argument Constraint happen that when the satellite reaches the minimum apogee altitude, the perigee altitude is still too high. This problem With the last two constraints the position of the perigee occurs when there is not enough time to decrease the perigee argument is very limited. It should be set close to the eclipsed because the apogee has decreased too fast (the higher the solar Equator but only in the North hemisphere part. For an orbit activity, the more common this problem is). with local hour 22.5h, ending during the Summer solstice gives the worst condition because the eclipse is much positioned in Different solutions can be envisaged: maintain the apogee the South hemisphere, as it is shown in Fig. 13. In order to during operations, increase the initial apogee and leave it evolve 131 Elisabet Cid Borobia, Claire Frémeaux and Jean-François Goester naturally afterwards, or increase the initial apogee and maintain Table 4. In order to end with the same conditions, the cases it afterwards. All these solutions slow down the reduction of with higher solar activity need to increase the initial apogee the apogee altitude and give more time to achieve the desired causing a longer duration and a higher consumption. The perigee lowering. perigee argument change is also different in each case because it depends on the deorbitation duration. Maintaining the apogee altitude requires perigee manoeuvres during deorbitation. The available batteries charging time is 3.3 Comparison Between the Strategies shared between perigee and apogee manoeuvres, so, the apogee manoeuvre frequency is reduced when both manoeuvres Figure 15 shows a summary between the different strategies. are performed simultaneously, and the cost and duration of The chemical propulsion implies the highest consumption; operations increases significantly. These are the reasons of why however, it can lead to a reduction of the duration (9 days this method has been discarded. instead of 159!). Moreover, the chemical propulsion has another very important advantage: the duration of the manoeuvres is Then, the best solution is to perform only perigee manoeuvers independent of the eclipses. Thus, the chemical propulsion is at the beginning of the strategy to reach the target apogee easier to simulate and to foresee. Its velocity increment is also altitude and then continue with only apogee manoeuvers higher, so, in case of manoeuvre avoidance it would also offer to lower the perigee. Of course the drawback here is that an better performance. Nevertheless, it has a main disadvantage initial apogee altitude, which depends on predicted drag force of needing a huge mass and the necessary volume to contain it. and solar activity level, should be assumed. The effective drag Figure 15 also shows how the elliptical chemical strategy does force may be different during deorbitation and it will have to be not offer a significant advantage with respect to the electrical compensated during operations. strategies: its duration remains long and its consumption is 3.2.2.4 Results for Several Solar Activity Levels Fig. 15 Summary of the durations and consumption between the different electrical and chemical strategies. The two chemical The results of these simulations are shown in Fig. 14 and options are outlined in black. Fig. 14 Perigee and apogee altitudes during deorbitation depending on the solar activity. TABLE 4: Main Characteristics of the Deorbitation Strategies When Re-Entering During Summer Solstice. Low solar activity Medium solar activity High solar activity (F10.7=65, Ap=0) (F10.7=140, Ap=15) (F10.7=200, Ap=30) Duration (days) 148 159 177 Consumption (kg) 12 14 15 ha final (km) 350 350 350 hp final (kg) 130 130 130 ω initial (deg) 90138 90160 90177 ω final (deg) 0 0 0 deltaV (m/s) 164 186 208 ha max (km) 710 800 888 132 Fast Re-Entry Deorbitation with Acceptable Risk Level much bigger. The circular chemical strategy is more interesting all quantitative results are of course dependant of the satellite with a huge improvement in duration. and orbit characteristics. However, the influence of several parameters has been studied, leading to some useful elements: On the other hand, electrical propulsion is less effective in term of duration: it lasts around 150 days, but very efficient in Final perigee argument is better in North hemisphere term of consumption with only 15 kg compared to more than and should be close to the Equator: it is necessary to 100 kg with chemical propulsion. The results are better when anticipate perigee argument rotation at the beginning of the solar activity is lower. operations. The perigee of the re-entry orbit should be low enough 4. CONCLUSION to assure an acceptable value of casualty risk. The perigee is lowered through apogee manoeuvers, thus, Fast re-entry deorbitation seems feasible and represents a the altitude of the apogee should be high enough to good alternative to the uncontrolled re-entries when a totally perform these manoeuvres until achieving the targeted controlled re-entry is not feasible. With a good phasing of final perigee. In case of high or medium level of solar perigee argument and longitude phasing, it is possible to reduce activity, it requires an initial raising of the apogee. the casualty risk to an acceptable value. Longitude phasing with Earth is important: a good control of the operations duration is needed to preserve The deorbitation manoeuvres could be performed using perigee and apogee altitude decrease rate. chemical or electrical propulsion. Chemical propulsion allows short operations but needs a lot of fuel. Electrical propulsion Several elements have not been studied, among which allows saving mass but means long operations, even with very the sensitivity of satellite, its orbit characteristics and the frequent manoeuvres. It also requires high battery capacity and manoeuvring phase real time control to achieve the four charging capacity. important rendez-vous: perigee orientation, perigee altitude, apogee altitude and longitude phasing, taking into account The results presented in this study where based on a variation of the solar activity, manoeuvre performance... particular LEO satellite with its mass and geometry; on a Management of degraded cases such as collision avoidance or Sun-Synchronous orbit with an ascending node in eclipse: safe mode recovery also needs to be studied. REFERENCES 1. S.A. Gaudel, C.Hourtolle, J.F. Goester and M. Ottavian, De-orbit désorbitation à poussées faibles, CNES internship report, 2013. strategies with low-thrust propulsion, Springer International, 2015. 4. B. Hassan and C. Hourtolle, Maneuvering strategies for semi-controlled 2. C. Hourtolle, S. Delattre, J.F. Goester and E. De Pasquale, “Studies about reentries applied to low Earth orbits, CNES internship report, 2015. a shallow re-entry for ATV-5”, 25th International Symposium on Space 5. G. Colas and A. Gaudel-Vacaresse, Computation of risks during Flight Dynamics ISSFD, Munich, Germany, 19-23 October 2015. uncontrolled atmospheric re-entries on final orbit, CNES internship 3. M. Ottaviani, J.F. Goester and A. Gaudel-Vacaresse, Stratégies de report, 2014. (Received 22 June 2017; Accepted 13 July 2017) * * * 133 S.Journal Peters, of W. the Eidel, British R. Förstner Interplanetary and H. Society,Fiedler Vol. 70, pp.134-142, 2017 ARCHITECTURE AND FIRST ACHIEVEMENTS OF A SIMULATION FOR THE APPROACH OF AN UNCOOPERATIVE TARGET S. PETERS1*, W. EIDEL1†, R. FÖRSTNER1‡ AND H. FIEDLER2 1. Institute of Space Technology & Space Applications, Universität der Bundeswehr München, DE 85577 Neubiberg, Germany. 2. German Space Operations Center (GSOC), DLR Oberpfaffenhofen, DE 82234 Weßling, Germany. Email: [email protected]*, [email protected]†, [email protected]‡ and [email protected] With space debris becoming more and more a concern for satellite operators, efforts need to be initiated to sustain a safe space environment and stop the permanent increase of debris. One of many is the active removal of large objects - 5 to 15 per year. The present paper introduces a concept based on a kit-chaser system: A chaser satellite will attach kits to multiple targets. The kit-target set-up will de-orbit controlled, while the chaser proceeds with capturing targets to equip them with a kit. For testing purposes, a simulation is derived for this concept. The paper presents the multiple modules the simulation is built on. The approach starts at a distance of about 11 m in close vicinity. The method of capture is a robotic arm. Future developments can focus on various modules to be added and/or existing ones to be adjusted to further requirements or specifications. The implementation of self-awareness for the chaser to react to unexpected situations or failures without the need for a signal from the ground-station. Keywords: Uncooperative target, simulation, approach 1. SPACE DEBRIS In the past decades, space debris has become a growing concern when successfully implementing those measurements, an for satellite operators. To sustain the current environment increase in the number of debris objects is conceivable from the around Earth, mitigation measurements such as an improved simulations. Only the constant removal of 5 to 15 large objects observation or implementation of post-mission disposal have of highly frequented orbits per year will have an influence on taken place and are further developed. Regarding long-term the long term stabilization of the LEO space environment [3]. sustainability, a repeated active debris removal of 5 to 15 large objects per year - objects that have a mass of at least one ton - The approach presented within this paper addresses the has to be included to stabilize the orbits. An otherwise starting removal of at least 5 large objects to be removed controlled cascade effect would prohibit the use of the affected orbits and within one year. With rendezvous and docking with an with that limit missions in space. uncooperative object never having been performed, a wide range of challenges have to be met. The object of choice will While the prediction for debris trajectories and manoeuvre, not send any data on its altitude or motion, it will not have a how to avoid them, have improved, still about 3 collision pre-designed point of contact for e.g., grabbing, and there will avoidance manoeuvres (CAM) per satellite and year have to be be no way of communication with it. Close vicinity may lead performed. CAM can only be performed in case of a warning. If to the point where a command from a ground station could be the approaching object however was not tracked - for example sent too late, with the possible result of a collision of the two due to its size - no command will be given and a collision may objects. decommission the satellite. Another feared scenario is the collision of two large objects that both cannot manoeuvre. An Having those considerations in mind, the Autonomous incident of two rocket bodies of the SL-16 type, for example, Debris Removal Satellite - #A (ADReS-A) is conceptualized. could double the number of the known debris in low Earth orbit ADReS-A targets multiple SL-8 rocket bodies to provide them (LEO). They have been observed to have missed each other by with a de-orbit kit for controlled re-entry. The concept aims to a few milli-arc-seconds [1]. Especially with the latter scenario improve the self-awareness of a chaser satellite with the ability in mind, the active removal of debris is inevitable. to react to failures while in close vicinity. Sufficient testing is required as the influence on objects in space is limited. Thus, a Additional mitigation measurements are already simulation based on the demands of ADReS-A shall support the implemented. These measurements include post-mission concept. As the simulation is derived from the mission concept, disposal, limiting of mission-related debris, limiting of potential an introduction to the concept of ADReS-A is given at first. explosions by e.g., releasing left-over propellant, limiting the probability of accidental collisions or avoiding an intentional 2. MISSION CONCEPT destruction and other harmful activities [2]. However, even The idea behind ADReS-A was presented in much more detail This paper was presented at the ESA 7th European Conference on in previous work, and can be found for example in Reference Space Debris, ESA/ESOC, Darmstadt, Germany, 18-21 April 2017 [4] or [5]. A summary of the concept is given in the following. 134 Architecture and First Achievements of a Simulation for the Approach of an Uncooperative Target 2.1 Mission Architecture analysis that covered heritage, complexity, re-usability, and similar aspects. The largest advantage of a robotic arm is its As mentioned in Section 1, large objects are targeted. ADR legacy and possible use for on-orbit servicing, a promising field has to be performed for many years and should therefore be as of business development in space which again makes financing effective and efficient as possible. It will hardly be cost wise of such mission more likely. favourable to launch only one removal chaser per mission. Hence, ADReS-A consists of a main chaser and multiple de- The chaser has a second, linear, arm to carry and attach orbit kits. While the chaser - ADReS-A - incorporates most of the de-orbit kit. The kit will be attached to the target’s nozzle, the complexity regarding docking and manoeuvring techniques, using a clamp mechanism for a stable connection. The nozzles the kits are designed simpler. They will de-orbit together physical parameters promise the most robust connection. The with the target and be lost during the re-entry. Their task is to satellite design can be found in more detail in Reference [5]. perform the de-orbit in a controlled way to an uninhabited area. ADReS-A needs the maximum of flexibility and will therefore 3. SIMULATION carry one kit at a time to the designated target, while the other kits wait in a parking orbit somewhat lower than the target’s When developing a simulation, certain considerations have to orbit. Other concepts to be found in the literature concentrate be taken into account. What shall be shown by the simulation? mainly on the removal of one object or the technology behind What modules have to be included to reach that goal? Which it, rather than addressing the whole problem of long-term functionalities shall form the basis of the simulation? Which sustainability of the space environment. The simulation derived level of detail is meant to be provided by the simulation? What follows this example, but is based on a concept for multiple simplifications compared to reality are acceptable? etc. The removal. Figure 1 gives a preliminary mission time line of the following section reasons the decisions made for the simulation concept. regarding the approach of ADReS-A. After the frame is presented, the multiple modules included and displayed in Fig. 2 2.2 Target are presented. The level of detail and simplifications accepted are explained within their description. Efficiency is one of the main goals of ADReS-A. Astudy performed in 2013 by the author analysed the available data 3.1 Frame for Simulation of about 17.000 objects of the SatCat [6] according to collision probability and hazardousness of such. As predicted, large The motivation for creating a simulation for the docking objects were the most influential objects. Further on, the study process derives from the need to test various strategies before analysed those objects according to their vicinity - taking into realizing such a mission. Active debris removal has never been consideration that one chaser has to travel between multiple performed in space. Ideas on what challenges to overcome and objects while consuming as little propellant as possible. SL-8 which difficult events may occur can be derived from missions rocket bodies (SL-8 R/Bs) turned out to gather in at least that cover the very close approach or rendezvous procedures. three different orbits - two around 74 degrees inclination at an Docking has been performed manually on the International altitude of 1500 to 1600 km and 700 to 800 km, respectively, Space Station, and some behaviours may be derived from there. and one at an inclination of about 82 degrees at an altitude of However, an uncooperative target never designed to be handled in 900 to 1000 km. No other objects of a similar type were found space will bring up various occurrences that cannot be foreseen. to be as close to each other as the SL-8 R/Bs. Hence, the orbit A simulation may help to understand and thus prepare for some concentrating most of the rocket bodies (the latter one), was of them. The simulation of ADReS-A is built from modules, as chosen as mission orbit with SL-8 R/Bs as targets. can be seen in Fig. 2. This object-oriented programming allows us to vary parameters without changing the whole process, and 2.3 Satellite Design to add and delete modules. These features will be of advantage once the simulation is further developed. Based on the target selection and the mission architecture, a chaser satellite (ADReS-A) and de-orbit kits are designed. For As shown in Fig. 1, the simulation of ADReS-A will cover removal technology, a robotic arm resulted from a weighing the part of the close approach once in reach of 11 m distance Fig. 1 Mission time line for ADReS-A. The simulation covers the part from close approach (< 11 m) and mating. 135 S. Peters, W. Eidel, R. Förstner and H. Fiedler Fig. 2 Architecture for the simulation of ADReS-A. along the direction of flight up to the actual rendezvous & J2-term, the gravity-gradient, solar radiation pressure, Earth’s docking of the two systems. At this distance, the camera in use magnetic field or the objects aerodynamic drag are considered. is able to track the detailed motion of the target, needed for a safe approach [7]. Calculated are the approach to a moving 3.2.2 Target Parameter docking point and multiple abort trajectories in case of a failure or contradictory data that cannot be solved. As mentioned in Section 2.2, SL-8 R/Bs are targeted. The simulation needs input about their size, mass and inertia torque The level of detail is quite low at this point of the which are derived from the CAD-design. development. However, due to the modular-setup, changes can be implemented if necessary or required. With the rocket bodies being of Soviet Union origin, actual CAD-data is hard to find. The design shown in Fig. 3 is based 3.2 Operational Specifications on References [9] and [10]. Another vague data is their mass. Their dry mass is known to be about 1.4 t. However, they did The simulation requires the input of at least 43 parameters. 6 not deflate unused propellant as is proposed nowadays. An of them cover the satellite’s and target’s relative position (x, y, additional weight of 200 kg (about 14%) was thus added for the z-direction), 6 cover their relative velocity ()vvvxyz,, and an calculations. Especially with left-over propellant, the chance for additional 6 give statements about the objects angular velocity sloshing is high, however, the rocket bodies’ inertia torque was (wwwwwwSx,,;,, Sy Sz Tx Ty Tz ) . 6 more address the objects derived from an assumed homogenous distribution of the mass. orientation (given in quaternions), 3 parameters describe each objects dimension (2 x radius, 4 x length from each centre of 3.2.3 Spacecraft & Kit Parameter mass forward and backward). Moreover, the inertia torques have to be assigned (3 parameters each). For now, two parameters With the spacecraft and de-orbit-kit CAD-design, the data about define possible optimization implementations. The available mass, size and inertia torque are extracted. Sloshing will not be maximal thrust, momentum and allowed time for the trajectory considered at this point. The satellites mass is about 1.1 t (wet), have to be assigned, as well the position of the docking the mass of one kit is about 500 kg (wet). The kit will be carried points. Additional information can be adapted concerning any inside the body of ADReS-A. Figure 3 shows the object’s CAD weighing of the optimization parameters, a safety area to avoid models. A simplification for the simulation transfers the models a collision at any time, or any area limitations the chaser is not into a cylindrical shape. allowed to enter when approaching the target. 3.3 Specifications 3.2.1 Environmental Parameter Operational specifications address the special needs of the In accordance with Section 2.2, an orbit of 970 km altitude mission during the approach. One specification, which is not with an inclination of 82.9 degrees is aimed for. The parking part of the simulation but needs to be considered beforehand, is orbit will be about 30 km below the target’s orbit. An analysis the illumination of the target by the sun. To calculate the correct performed concerning the radiation and electrostatic charges motion rate, the camera needs about 130 min [7]. However, it [8] revealed a usual exposure. Especially with the mission does not work adequate by shadow or darkness, neither when lasting one year, no extraordinary precaution is planned. facing the Sun directly nor when her reflection on the surface of the target is too bright. Thus, the time of one orbit revolution The simulation is based on the relative dynamics of the two of about 90 min is limited to nearly 52 min observation systems (target & chaser + kit). As the two objects are really time. The proof of fully charged batteries for a maximum in close and show similar mass and size, perturbations will act operation time, enough propellant or antenna pointing are other very similar to them. Therefore, no perturbations such as the specifications that need to be handled outside the simulation. 136 Architecture and First Achievements of a Simulation for the Approach of an Uncooperative Target Fig. 3 Involved objects for the mission (not scaled). Left: SL-8 R/B; Middle: Kit; Right: ADReS-A. Operational specifications that influence the simulation pointing out of orbit (like the x-axis in the CW-equations) and directly are, for example, the exact time when a manoeuvre ξ completes the orthogonal tripod (while the corresponding can take place so sensitive sensors are not harmed by light or y-axis in the CW-equations points into the direction of flight). shadow. The battery status will need to be supervised as well as the functionality of the subsystems. Complete system of equations according to Eidel [11] 3.4 Dynamics ()()01 ξξEid = + e ξ (1) While the whole mission requires absolute and relative ()1 ηηEid =()0 + e η (2) navigation, the simulation is based on relative dynamics and rigid body dynamics. ()()01 ζζEid = + e ζ (3) 3.4.1 Coordinate Systems The first part reflects the CW-equations: To describe the motion of the two (three) involved objects, ()0 ' '' ' ξ=2 ζ cos τ + 6 ζ + 4 ξ sin τ − 3 ξ + 2 ζτξ +− 2 ζ multiple coordinate systems are in use. The local-vertical, 0()() 00 0 0 00 local-horizontal (LVLH) system, cf. Alfriend [12], describes (4) the relative position of the objects. Two additional coordinate systems are body-fixed and centred in the target and spacecraft ()0 η= ηcos τη + ' sin τ (5) & kit models. The coordinate systems are required to describe 00 the objects orientation in space. The quaternions in use solve the problem of singularity of the also commonly used Euler ζ()0 =−+ ζ ξ'' τζ + τ + ζ + ξ ' angles. The implementation of the Euler Equations allow for ()300 2 cos 0 sin 2() 2 00 (6) the two docking points - one belonging to ADReS-A, the other to the SL-8 R/ - to rotate within the simulation and describe the rigid body dynamics. In an unrotated state, the axis of the body- and the second part defines the relative dynamics more fixed system align with the ones used in the LVLH-system. precisely: 3.4.2 Relative Dynamics ξ()1 = ζξ +'' θ −− ξ ζ θ τ 4()() 500 cos 0 0 2 0 sin 0 sin Relative dynamic calculations can be adequately used for any −+2 2ζ'' cos θξ sin θ cos τ distance smaller than 100 m. As the simulation aims to provide 0 00 0 a tool for the analysis and verification of different strategies, it 33'' +()3ζ00 + 2 ξ sin() 2 τθ ++ 0 ζo cos() 2 τθ +0 is obvious to use rather analytic equations for the approach than 22 numerical. The Hill’s equations or Clohessy-Wiltshire (CW) (7) −ζ + ξ'' τθ +−− ξ ζ τθ + equations provide a suitable approximation for the numerical 7() 200 sin () 0() 02 0 cos() 0 approach, derived for near-circular orbits. The SL-8 R/Bs orbits −ζ + ξ'' θ −− ξ ζ θτ have an eccentricity of about 0.003, the use of CW-equations 3()() 500 cos 0 00sin 0 is thus considered suitable. The following figures give an idea ''71 about their accuracy if adapted to the discussed ADR-mission. +3ξζ00 + sin θξζ 000 ++ cos θ0 22 For the simulation of ADReS-A, efforts for a more precise analytic approach were made. The Eidel-equations are derived ()1 η= ηcos θηθ − 2' sin cos τ for small elliptical orbits with eccentricities smaller than 0.1. ( 0 000) They add an additional term to the CW-equations, as can be ' +−ηsin θη cos θ sin τ seen in Equations 1 to 3. In consistence, they use the LVLH- ( 0 00 0) coordinate system with the origin of ordinates within the 1 (8) +η0cos() 2 τθ +− 00 2cos θ satellite. In contrast, the axes are pointing in different directions 2 - η is parallel to the vector of the angular momentum (similar ζ 1 ' to the z-axis in the CW-equations), is defined as the +η0sin() 2 τθ ++ 00 3sin θ extension of the connection of the centre of Earth to the satellite 2 137 S. Peters, W. Eidel, R. Förstner and H. Fiedler For now, the CW-equations are applied to the simulation ζ()1 =−+ ζξ'' θ −− ξ ζ θ τ 2()() 500 cos 0 0 2 0 sin 0 cos as they are much simpler and deviate from the numerical calculations by only 0.6%. With all the simplifications −+ζ'' θξ θ τ 20 cos 00 sin 0 sin implemented at the moment, the high precision calculations by Eidel would not make much of a difference. Once a higher −ζ + ξ'' τθ ++ ζ τθ + ()300 2 cos()() 2 00 sin 2 0 (9) accuracy is required, they will be a very good choice to be ''implemented for a better analytic analysis. −3() 2ζ00 + ξτ sin() τθ ++ 0() 13 ζ 0 + 4 ξ 0 cos θ 0 ' 3.5 Optimizer +−()3ζξ00 2 sin θ 0 For the optimal path planning, the work of Michael et al. [13] τ ω ⋅ In the equations, is the nominated time variable 0 t was applied. The addressed optimization problem in his work with was solved using the software package OCPID-DAE1, cf. Gerdts [14]. Here, a robust sequential quadratic programming µ = (SQP) method is combined with a gradient calculation using w0 3 (10) 2 sensitive implicit differential equations (DAE). The package ()ae()1− “is suitable for optimal control problems subject to differential algebraic equations of index one” [13]. Here, µ is the gravitational parameter, a the semi-major While the package allows for the optimization of more than axis and e the eccentricity of the orbit. θ0 represents the true anomaly at the time t = 0 . The initial conditions are given by one subject, the presented work focuses on a minimum energy consumption. This allows for a cost limitation as the required ''energy is directly proportional to the propellant and thus to ξ()()()()()0= ξη00 ; 0 = ηζ ; 0 = ζ 0 ; ξ '0 = ξη 0 ; '0 = η 0 weight and costs of the mission. Other subjects of optimization ' and ζζ'() 0 = 0 could be time or a combination of the two. Further work will The whole derivation was performed by Dr. Eidel [11]. analyse the mission accordingly. As displayed in Fig. 2, the required input is a combination of the mission parameters To get a better understanding of how much influence the and the relative dynamics. The output of the optimizer is the Eidel-equations have on the accuracy of the simulation, the approach trajectory, which is then further processed for failure following figures compare the numerical calculations with the implementation CW-equations and the Eidel-equations. 3.6 Visualization In Figs. 4 and 5, the accuracy of the different approaches compared to each other is displayed. A higher dependency of 3.6.1 Objects the different variables can be derived for the Eidel-equations. Additionally, the Eidel-equations show a 100 x higher precision The involved objects are modelled and exists as 3D CAD for the position and velocity derivation after 3 orbits in both versions as shown in Section 3.2.3. For a faster calculation, they cases e.g., in case no relative velocity is involved and a relative are simplified as cylinders. The spacecraft and kit together form velocity of 0.01 m/s in every direction at the same distance is a cylinder of 2.35 m in diameter and 3 m in length. A rocket assumed. body cylinder has a length of 6.6 m and a diameter of 2.4 m. The Fig.4 Exact position and velocity of the two systems with no relative velocity and a 11 m distance in the direction of flight. Derivation resulting by using the analytic approach of Clohessy-Wiltshire and Eidel are given in the middle and right hand graphics. The x-axis counts the orbits taken. 138 Architecture and First Achievements of a Simulation for the Approach of an Uncooperative Target Fig. 5 Exact position and velocity of the two systems with a relative velocity of 0.01 m/s in every direction and a 11 m distance in the direction of flight. Derivation resulting by using the analytic approach of Clohessy-Wiltshire and Eidel are given in the middle and right hand graphics. The x-axis counts the orbits taken. detailed design can be implemented for visualization or more the manoeuvre, the spacecraft will choose from its memory detailed calculations if required. The mass and initial torque of the abort trajectory next to come. It will not take the closest the CAD model is mirrored as designed. trajectory, as this might be the one just passed and a turnaround is simply not realistic. 3.6.2 Berthing 3.6.4 Environment The design of ADReS-A includes a robotic arm. Time for the grabbing manoeuvre and thus final attachment has to be provided The visualization of the environment mirror the parameter after the chaser has reached its intended position. A berthing included. Sun and Earth pose possible perturbations, and are box not exceeding the arm’s limitations shall give the required thus displayed. flexibility for the final attach. As seen from Section 3.4.2, drift will affect the two objects, attitude control will be required to 3.7 Game → Autonomy limit the effect. During the grabbing, however, such action may be harmful. The box gives an area, in which the chaser can drift When considering the active removal of an object never designed without the attitude control adjusting. Time limitations for the for such, events of unforeseen failures or misleading sensor- final docking can be derived using the equations presented. The data will occur more often than during established spacecraft simulation ends with the two docking points mating. It has to be missions. The proven handling in case of a failure is the switch mentioned that the mating point presents two points within the into safe-mode, with the spacecraft expecting further instruction berthing box with the final approach performed by the robotic from ground. For ADR, the approaching spacecraft has no time arm - a manoeuvre out of the scope of this work. to wait for a ground-station recover signal as the very close vicinity and possible drift may result in a collision. Hence, 3.6.3 Trajectories on-board processing, fault management and self-awareness of the spacecraft are the key technologies that need to be pushed The approach trajectory is derived from the formerly listed forward. One step towards that is the on-going development of modules. It describes the trajectory most propellant-saving and on-board processor capabilities. Even though a few years behind ends with the two docking points mating. Any considerations Earth’s PC-development, the progress looks promising [15]. about the stabilization of a potentially tumbling target is not part of the simulation and therefore not part of the discussion. 3.7.1 Failure Implementation Data derived from the simulations give information about the relative distance, relative velocity and required thrust for the For now, the autonomy should rather be called automation and time of the approach. is limited to deciding, which abort trajectory has to be taken after a failure occurs during the approach. The request is to take The abort trajectory is calculated with the same equations the next abort trajectory in line, aiming to react as soon and used for the approach trajectory. As a result, depending on the as efficient as possible, as propellant is one of the restricted number of abort trajectories chosen and the safety parameter resources on board a spacecraft. Failures are implemented implemented, the time for calculation is multiplied (for a randomly for now and are addressed further in Section 4. direct approach 685 s of processing time is required). Hence, those trajectories need to be calculated beforehand to react 3.8 Output in time as the total approach will take about 8 min. Once the whole approach has been initiated and a failure occurs during Figure 6 gives an idea of the graphical representation of the 139 S. Peters, W. Eidel, R. Förstner and H. Fiedler Fig. 6 Approach trajectory (cyan) and potential abort trajectories (magenta). The yellow line marks the path of the two docking points that meet eventually. trajectories that could be followed. The origin of ordinates is 3.9 Considerable Future Developments positioned within the target (LVLH-system), the tripods show the position of the docking points. Two yellow lines, that 3.9.1 Exchange of Modules eventually meet, show the path of those points during approach. It can be seen that the target is tumbling in this specific The modules of the simulations will be further specialized. simulation. Additionally, the pre-calculated abort trajectories Investigations will concentrate of an improvement of the are displayed in magenta. For some of them, the initial starting existing modules and the implementation of missing ones as point seems to be the best choice concerning fuel consumption. indicated in Table 1. Especially the failure handling module While the chaser proceeds further on its approaching trajectory, will be improved in the next steps. Once the simulation fulfils the algorithm made from a mixture of fuel optimization and the requirements set, different strategies for a safe approach safety requirements, chooses the second safe point within this will be tested as well as different failure scenarios. Those setup on the x-axis, this time in front of the target. scenarios will include minor failures, which should not lead to an abort, major failures, which should lead in any case to 3.8.1 Propellant Consumption an abort, and failures that have to be classified according to the situation. The required thrust for a successful approach is displayed in Fig. 7. The steps mirror the 50 intervals calculated as the 3.9.2 Validation thrust will be given in multiple impulses. The closer the chaser gets, the fewer thrust is induced - the reduction of the relative To proof a newly developed tool, it needs to be validated velocity to a minimum for staying within the berthing box and against existing models. In case of the presented simulation, performing the actual grabbing is required. a transformation into GMAT [16] is momentarily in progress. As the simulation is based on commonly used equations, little The consumption each trajectory would require is displayed deviation is expected. A simple scenario of the approach will be in Fig. 8. Dependent on the safety requirements (e.g., the safety tested to note the deviations. In case both setups processed with parameter Cerr ), the value at each point varies. A successful the different tools are coherent, it can be assumed, that more approach takes about 2.67 kg hydrazine, displayed by the complicated ones mirror the environment in the same way. vertical line in the figure. Here, eight abort trajectories and the approach trajectory have been calculated e.g., the approach 4. FAILURE SCENARIOS trajectory has been divided into eight, at each point (0/8, 1/8, 2/8, ..., 8/8) an abort was derived. With the total manoeuvre Further development of the simulation aims to switch requiring about eight minutes, an abort trajectory is available between failures that definitely result in an abort, failures every 60 sec. that derive from contradictory sensor-data and can be solved Fig. 7 Chronological sequence of the thrust during the approach. 140 Architecture and First Achievements of a Simulation for the Approach of an Uncooperative Target Fig. 8 Fuel consumption for different abort trajectories and different safety requirements. The straight line gives the consumption of the approach, the Cerr parameters mirror the different safety demands for the abort. TABLE 1: Overview Modules of the Simulation Frame. mission and some subsystems. Further on, the system needs to verify, if the specific requirements of the involved subsystems Simplified Adjustable and components will not be violated by the intended solution Environment no perturbations some effort of the original failure. An optimization process guided by the autonomy concept shall protect the spacecraft. Target Body Cylinder ü Chaser Body Cylinder ü The displayed approach is a very simplified version of the Sloshing homogenous some effort actual decision process. The more parts are included, the more requirements have to be met. Moreover, those requirements Orbit Circular ü → Eidel will change over time. The modular setup of the presented Optimization energy and/or time simulation tool will allow for changes that address complexity and situation specific constraints. Optimizer OCPID-DAE1 ü Failure implem. random some effort 4.1 Autonomy Concept without abort and failures, were the momentary capabilities Various autonomy concepts have been tested on low level for of the chaser decide for or against an abort. Together with an space application. Wander [17] gives an overview of those increased autonomy and decision making processes within, concepts, resulting in the idea to find the solution in ground- failures will be handled according to their level of impact to based applications. Unfortunately the formerly considered the system. COSA system [8] was not developed further, documentation is difficult to find. Therefore, the decision has been made to test Preliminary considerations concerning a failure scenario the developed system on a lower level with one of the Wanders’ need to involve the multiple subsystems and according presented concepts. components, the failure would affect. Redundancy of some parts such as the cameras to determine the targets motion are As described within this paper, the autonomy module can be essential. It is assumed, that such failure will be detected and replaced within the simulation. In case, a high level autonomy treated with the replacement of the faulty component. system is available, testing should include the platform developed. Critical aspects during the approach can either be internal (e.g., a comportment fails) of external (e.g., an obstacle is in the TABLE 2: Failure Scenario: Solar Array Fails. desired flight path). Moreover, a deviation between systematic Involved or mechanical failures can be made. Figure 9 gives the approach Subsystem Impact Component to failed power requirements. In this case, the approach is ready to be started, but the system recognizes insufficient power Power Solar array other arrays need to cover supply and stops the berthing attempt. As this is a symptom, loss the search for the failed component is essential to overcome the buffer covers loss problem. Battery increased recharge time Finding the failure may not lead to a solution of the problem. Data Handling OBC recalculation to protect In case the failed part is unable to be replaced by a redundant other sensors one, the influence a change of the mission has on the other Mission time may take longer systems needs to be considered. In the displayed version, the a failed solar array could for example change the mission approach extra recharge time time line if a decision is made to use the other arrays to cover the loss and thus to extend the recharge time of the batteries. alignment provide more sunlight for Table 2 gives some examples a failed solar array has on the other solar arrays 141 S. Peters, W. Eidel, R. Förstner and H. Fiedler Fig. 9 First level of failure scenario approach to determine faulty part and react accordingly. 5. SUMMARY ACKNOWLEDGMENTS The paper describes a mission concept for the active removal The presented work is supported by Munich Aerospace and of SL-8 rocket bodies with the intention to slow down the Helmholtz Association. The project Sicherheit im Orbit, the growth of space debris in low Earth orbit. A simulation guiding theme for this work, is a cooperation between DLR environment to test different strategies for the part of close and Universität der Bundeswehr München. Additionally, the vicinity to the target has been derived. It is described in its authors would like to thank Johannes Michael for his support momentary detail, including considerations that have been on the simulation implementation. Acknowledgments also go investigated. First results and the visualization are shown in to the students of the Universität der Bundeswehr München the end. that supported this work with their theses. REFERENCES 1. D. McKnight, “Debris Remediation Examined via an Operational Success html. (Last Accessed 12 October 2016) Framework”, 4th Workshop on Space Debris Modeling and Remediation, 10. H. Cowardin et al.. “Optical Signature Analysis of Tumbling Rocket Paris, France, 6-8 June 2016. 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Wander and R. Förstner, “Innovative Fault Detection, Isolation and Space Debris Removal”, 64th International Astronautic Congress, Recovery Strategies on-board Spacecraft: State of the Art and Research Beijing, China, 23-27 September 2013, Paper No. IAC-13-A6.5.3. Challenges”, http://www.dglr.de/publikationen/2013/281268.pdf. (Last 9. Modelict-Konctruktor, http://www.mkonline.ru/2000-07/2000-07-14. Accessed 15 June 2017) (Received 7 June 2017; Accepted 14 June 2017) 142 Journal of the British InterplanetaryE.Deorbit – ESA’s Society, Active Vol. Debris 70, pp.143-151, Removal Mission 2017 E.DEORBIT – ESA’S ACTIVE DEBRIS REMOVAL MISSION ROBIN BIESBROEK1, LUISA INNOCENTI2, ANDREW WOLAHAN1* AND SARA MORALES SERRANO1** 1. ESTEC, Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands. 2. ESA/HQ, Rue Mario Nikis 8-10, 75015 Paris, France. Email: [email protected], [email protected], [email protected]* and [email protected]** More than 23000 objects larger than 10 cm are regularly tracked and LEO represents the most congested zone. Even if all space launches were halted tomorrow, the amount of debris would continue increasing. The most effective way to stabilise debris population is to remove the large non-functional objects from the most populated orbits which are the source of small debris. The term used to remove a large object from orbit is Active Debris Removal (ADR). However, capturing and deorbiting an uncooperative object is extremely challenging; such a mission has never been performed and requires a number of key technology advancements. Keywords: Space debris, active debris removal 1. INTRODUCTION TO E.DEORBIT 1.1 Scope of E.deorbit ESA wants to pave the way for future ADR missions by removing a single large ESA-owned space debris from the protected Low Earth Orbit (LEO) zone in the 2021-2023 timeframe. The motivation for this project is that by now over 17,000 objects around Earth can be tracked from ground, and less than 1,000 of these objects are actual active satellites. Looking closely at Fig. 1, a dense area close to Earth is the near polar region of orbits with altitudes between 600 km and 800 km. Several independent studies have shown that space debris Fig. 1 Overview of space debris in the year 2013. with the largest probability of collision are the large objects located in dense areas, and it is generally considered that the growth of space debris can only be stabilized if give of those large objects are removed per year from these orbits. 1.2 What E.deorbit Needs to do The e.deorbit mission objective is to “Remove a single large ESA-owned space debris from the LEO protected zone”. From this objective, six different ‘use cases’ are defining all the main tasks the e.deorbit needs to fulfil in order to achieve the mission objective: Fig. 2 e.deorbit use cases. 1. Launch into space 2. Perform LEOP and commissioning Ad 2: After launch, deployment of the solar panels (in case 3. Transfer and phase to target orbit of deployable panels) will be done, initial contact with ground 4. Rendezvous with target will be made and housekeeping data will be sent to Earth. 5. Capture target Testing and calibration of the GNC (guidance, navigation and 6. De-orbit target control) sensors and all critical equipment will be done during Figure 2 gives an overview of the use cases. this phase. Ad 1: The launch into space is foreseen to be done by ESA’s Ad 3: Since e.deorbit will need to have a large propulsion smallest launcher VEGA, using the ‘VEGA-C upgrade’. system for the de-orbit use case, it is more optimal to have VEGA insert e.deorbit into a low altitude initial orbit (e.g. 300 This paper was presented at the ESA 7th European Conference on km) and then use e.deorbit’s own propulsion system to transfer Space Debris, ESA/ESOC, Darmstadt, Germany, 18-21 April 2017 to the target orbit. The target’s orbit (as described in section 3.1 143 Robin Biesbroek, Luisa Innocenti, Andrew Wolahan and Sara Morales Serrano is estimated to be 760 km high). Based on position estimates part of ESA’s Directorate of Operations (D/OPS). The objective of the target by ground tracking, the orbit of e.deorbit will be of Clean Space is guaranteeing the future of space activities phased with that of the target, until the target can be picked up by protecting the environment. With the Clean Space initiative, by the GNC sensors. ESA will devote increasing attention to the environmental impacts of its activities, both on Earth and in space [1]. Figure Ad 4: Based on the GNC sensors, E.deorbit can now calculate 3 shows the branches of Clean Space. the relative position with respect to the target, and it will then perform several hops to get close to the target, until a hold point E.deorbit falls under the branch ‘Active Debris Removal’. is achieved from which an inspection of the target can take The budget allocated to this branch was up to 20 M€ for place and the attitude and motion of the target is determined. the 2012 to 2016 timeframe, and 41 M€ for the 2017-2019 timeframe. This allocation is for the system design studies and Ad 5: When a ‘go ahead’ is received from ground, the related technology developments. Within ESA, the technical capture shall take place. This is done by means of a robot arm implementation of e.deorbit is assigned to the Systems, Software (i.e. synchronize the motion of e.deorbit with the target, and and In-Orbit Demonstration department of the Technical and capture the target at its launched interface ring). Since the target Quality management directorate. is likely to be rotating, the rotation needs to be stopped, by initiating a de-tumbling mode on e.deorbit, now with the target 2.2 PLANNING attached via a robot arm. The global plan of e.deorbit is shown in Fig. 4. Ad 6: Once the correct attitude is obtained to initiate the de- orbit burns, the de-orbit phase will start. In order to minimize As every ESA mission, the Ministerial Council (MC) gravity losses, the de-orbit burn could be split into several firings meetings dictate the plan. The next MC is expected to take of the main thrusters. The re-entry will burn up both target and place by end 2019. By this time, the Preliminary Design Review e.deorbit during the aerothermal dynamics forces when the (PDR) should have completed so that a dossier for a project atmosphere is entered. Several re-entry zones are identified in implementation can be prepared as proposal for the MC. the Pacific (North and South) and Indian Ocean, since some parts of the target could survive the re-entry and impact the water. Since 2012, several assessment studies have been performed (‘e.deorbit CDF study’, ‘Service Oriented Approach towards 1.3 Organization of this Paper ADR’, ‘ADR with AVUM’, and the e.deorbit phase A & b1 studies, all described in section 3.3). E.deorbit is, at time of Four questions will be answered in the next four chapters: what writing this paper, finalizing the Invitation to Tender (ITT) for the boundaries of e.deorbit? How is e.deorbit executed? How the Consolidation Phase: a bridging phase between phases B1 can we enable success? And what do we see when we re-assess and B2, which will start on 1 July 2017 and is planned to run e.deorbit on a regular basis? for half a year. 2. BOUNDARIES OF E.DEORBIT For the 2017-2019 period (between the MC 2017 and MC 2019), A Maturation Phase is proposed. This consists of a phase This chapter shows the organization, planning and stakeholders B2 system study, a robot arm technology development study, of e.deorbit, which all define the boundaries in which this a GNC technology development study and a net technology project can move. development study. The total budget sums up to 41 M€. The Maturation Phase ensures that all system and sub-system 2.1 Clean Space designs have reach TRL 6 by 2019. The system study is to start first with a work package to consolidate requirements E.deorbit is a mission requested by ESA’s Clean Space Office, for the technology developments. Then, all three technology Fig. 3 Clean Space and its branches. 144 E.Deorbit – ESA’s Active Debris Removal Mission Fig. 4 e.deorbit timeline. developments start while the system study consolidates the sponsoring and participating to the detailed design phase. system design. When the technology developments finish, Several technology development studies are also run within the they feed back their findings into the system study for a final GSTP programme with additional subscriptions from the UK iteration on system level. More information on the technology and Spain. The current Consolidation Phase is subscribed by development studies can be found in section 5.1. Germany, Poland, Portugal and Canada. Pending financial subscriptions, this Maturation Phase Active stakeholders are therefore the European delegations, can start end 2017 leading to the Preliminary Design Review European industry itself. Within ESA, several directorates are (PDR) in end 2019, and the start of the phase C/D phase and stakeholders due their involvement in the system studies, such the Engineering Model in 2020. Following extensive testing, as the mission analysis team, operations team and space debris the creation of the Structural and Thermal Model as well as the team at ESOC, Germany, as well as the TEC support team and Flight Model can commence in 2022. The Acceptance Review communications office, and the General Studies Programme is planned for end 2023 however as is normal in this early stage team, all at ESTEC, The Netherlands, plus the Clean Space of the project, a 10% margin is set on the schedule, giving a team at ESOC, Germany. launch date in mid 2024, a year after the objective to capture ENVISAT by 2023. When the mission is launched, several stakeholders are active such as the Arianespace launcher provider, satellite 2.3 Stakeholders operators and ITU (International Telecommunications Union). Until the phase A the system design studies, as well as most Stakeholders such as media and other national agencies are technology development studies, were performed within ESA’s affected and influencing the mission however it should not be General Studies Programme. This typically implied that there forgotten that other space missions (both current and future) are were no restrictions on the countries of the bidding companies. influenced by e.deorbit as well because a potential candidate Starting the detailed design phase (B1), a switch to the General for generating many space debris objects in case of collision, is Support Technology Programme (GSTP) was implemented now safely removed from orbit. meaning that the funding is received from member states that subscribe to this activity, and bidding companies can only be Finally, several studies are executed within Europe for from the participating countries. By early 2015, subscriptions future space tugs; tugs that enable LEO to GEO transfer, LEO were received from Germany, Belgium, Poland, Italy, to beyond GEO transfer, in-orbit servicing and ADR. Many Portugal, Sweden and Canada, and these are now the countries technologies developed within the e.deorbit project are directly 145 Robin Biesbroek, Luisa Innocenti, Andrew Wolahan and Sara Morales Serrano applicable to future space tugs, and as such planned space tugs stakeholders will benefit from the execution of the e.deorbit project and its technology developments. 3. EXECUTING E.DEORBIT We will now go more in debt concerning how the e.deorbit contracts are executed and what are the main drivers for the design. 3.1 Target Requirement Selecting a target space debris for the mission is not an easy task. While no nation can claim that space debris exists exclusively Fig. 5 Impression of ENVISAT; made using STK. in its territory, a launching state that puts an object into space has and keeps jurisdiction over that object, even if it turns into 3.2 E.deorbit Driving Requirements space debris. A target debris can therefore only be removed with the consent of the launching state(s) that put the debris object The main driving requirements can be linked to the elements into orbit. Moreover, the launching states are liable for any acting on e.deorbit, called ‘actors’. Calling e.deorbit the ‘space damage caused on Earth from the re-entry, or any collision in element’, the main actors can be identified as: case fault can be established. This means that if e.deorbit has a malfunction and causes either a collision in space or a damage on Launch element Earth, there may be major implications on the liability. For this Ground element reason, an ESA-owned target is proposed as ESA is a launching Target element state. Furthermore, the object shall be in the (near) polar orbit Environment element region at an altitude between 600 km and 800 km, since this is a crowded orbit with space objects as shown in section 1.1. Note that several other actors can be defined (e.g. GSP for positioning, standards, safety, ESA team, production team, etc.) For the requirements phase (i.e. phase 0 to phase B1), but only the actors linked to critical aspects of the technical ENVISAT was chosen as target, for the following reasons: design are shown here. The environment element here is both space and Earth, as the space environment will act on e.deorbit 1. It is one of the few ESA-owned debris in LEO during its mission, and the Earth’s atmosphere will act on 2. It has a heavy mass, roughly 8 tonnes e.deorbit during the re-entry. From the actors, an e.deorbit 3. It is located in a crowded near polar orbit (Sun context diagram can be made showing the most important Synchronous Orbit at 800 km). Predicted altitude for influences from and on e.deorbit, see Fig. 6. 2023 is 760 km. The following technical design drivers are identified: ENVISAT was launched on 1 March 2002 and its mission ended on 9 May 2012. Figure 5 shows an impression of a Launch environment: the selection of a small launcher possible attitude by 2023. such as VEGA-C poses a strong constraint on the maximum e.deorbit wet mass. A study performed by the university of Braunschweig [2] TM/TC (telemetry, tele-commands): when in the created a priority list for removal based on orbit, mass and size vicinity of the target, the communication link can suffer and not only was ENVISAT on top of this list, it also showed from interference by the target, and e.g. a live video-link that ENVISAT’s mass and size are similar to most other objects during capture may not be possible. within the list (e.g. Zenith-2 stage 2). For this reason, ENVISAT Capture: the capture mechanism has a low TRL marks an excellent opportunity to serve as a benchmark target (Technology Readiness Level). E.deorbit will need for future debris removal missions. After submission of the to get very close to a tumbling target and initiate a preliminary project plan, ESA confirmed the use of ENVISAT synchronized motion with the target in order to not as target for the phase B2 study. collide with it. There are several challenges to be overcome related to Fig. 6 E.deorbit context diagram. this particular target choice, which could be a good test for future targets. As can be seen in Fig. 5, the solar panel rotation mechanism is locked in such a position, that it complicates access to the launcher adapter ring (which is situated at the bottom of the model in the picture). Moreover, several observation campaigns have shown that ENVISAT is in a tumbling motion, and the current models do not conclude on the possible attitudes by 2024. Some models even predict rotations of up to 5 degrees per second, and therefore e.deorbit must be designed with these tumbling rates in mind. Finally, ENVISAT was still designed before the digital era, and finding details within the design is often complicated. This is enforced by the fact that many of the engineers who worked on the design of ENVISAT have retired by now. 146 E.Deorbit – ESA’s Active Debris Removal Mission Tumbling motion: when the target is captured its AVUM PRE tumbling motion needs to be damped. De-tumbling Propulsion AVUM may pose high torques on the robot arm’s joints, and AVUM Runtime Proximity the attitude and control system needs to quickly adapt to Standard Extension Module newly calculated centre of mass of the stack (e.deorbit plus target connected). Forces: when any force is applied to the target, it must be ensured that no new debris is created (e.g. by parts braking off). This is in particular true for forces through points like the gripper on the robot arm, even if the foreseen contact point is confined to a small area. Relative sensors data: image recognition of the target is likely to be needed, which could require heavy processing on board the spacecraft. Push de-orbit: When doing the de-orbit burns by polling the target (robot arm capture), the system must calculate the centre of gravity and ensure that the thrust force is aiming at the centre of gravity, in order to avoid a spin- Fig. 7 Using VEGA’s upper stage as e.deorbit platform. up of the stack. Heat will have a positive effect on the space element as the upper stage of VEGA could serve as a satellite platform itself, it will burn up the target and e.deorbit. However some on to which the capture and GNC equipment would be mounted parts of the target may survive the aerothermal dynamic as an ‘AVUM proximity module’, see Fig. 7. The motivation was forces. also that the VEGA upper stage already had a large bi-propellant Thrust: e.deorbit must ensure thrusting through the total propulsion system on board. The study concluded in December stack centre of gravity in order not to start a rotating 2013 and an internal ESA review was executed in March 2014. motion. The proposal was put forward to continue studying this option Finally, the re-entry has strong safety requirements, via ESA’s GSTP programme, however so far no support was requiring complex planning including contingency found. cases, and additional redundancy on board e.deorbit. In 2014 e.deorbit’s phase A started. After a competitive 3.3 Performed System Studies for E.deorbit bidding process, three companies were awarded a phase A contract, namely Airbus, Kayser-Threde and Thales Alenia Since 2012, several system studies have been executed both Space. Each contractor was asked to study three system options: internally as externally (i.e. via contracts awarded by ESA). a de-orbit mission with a rigid capture method, a de-orbit mission with a flexible capture method, and a re-orbit mission. In 2012 an internal assessment study was carried out by Two internal reviews were held, namely a Mission Baseline ESA’s Concurrent Design Facility (CDF) [3]. The study Review and Mission Design Review, before going to the focused on two capture techniques which were identified as Preliminary Requirements Review (PRR) in September 2014. most suitable for capturing non-cooperative targets, based The PRR consisted of a technical panel and a review board. on previous in-house studies. The first option was based on a The review board, after evaluating the findings of the technical capture using a clamping mechanism that embraces the target panel, recommended discontinuing both the harpoon and the (like tentacles) and achieves a firm grip on the target. However re-orbit options for later phases. It also proposed to further it was shown that the accuracy with which the target could be study the development plan, consolidate mission requirements captured was not enough for the attitude system to guarantee and the touching mechanisms design before proceeding with a de-orbit force going through the centre of gravity of the phase B1. Figure 8 shows the configurations for the rigid and new stack, and a robot arm would be required to accurately flexible de-orbit missions proposed by the contractors [8,9, place e.deorbit on the target. The second option was based on 10]. a net capture, where two net canisters were put into the design (one redundant), and the de-orbit burns are executed by a bi- Following the recommendations of the PRR board, an propellant system. The study showed that the VEGA launcher extension of the phase A was offered to the contractors with could be suitable to launch e.deorbit. the objective to 1) apply Model Based Systems Engineering (MBSE) in order to improve requirements generation and Following the CDF study, three contracts were awarded tracking, 2) update the technology development plans, and 3) after a competitive bid, to Airbus, Kayer-threde, and SSTL, improve the gripper or clamping mechanisms modelling. This with the aim to investigate a service oriented approach towards extension came in handy, as it took a few months to issue the the implementation of e.deorbit, and to derive a business invitation to tender for the phase B1, and therefore the extension plan for future ADR missions [4, 5, 6]. The study showed allowed to bridge the waiting time for the next design phase. the strong need of national and international agency sponsor Before the end of phase A, Arianespace released a new user at least one ADR mission, in order to lower implementation manual of the VEGA launcher, showing a strong decrease in cost for future missions. The results of these studies were predicted launch mass performance. The project team decided, presented to the Technology Advisory Working Group at ESA after discussion with ESA’s launcher department, to assume HQ, Paris 2014. that by 2024 the upgraded VEGA-C would be available, and select this as baseline launcher. The year 2013 ended with a conceptual design study of e.deorbit performed by ELV [7]. Since VEGA was considered as Meanwhile at ESA, the e.deorbit study manager, system launcher for e.deorbit, the objective of this study was to assess if engineers and risk engineers sat together to define the tasks of 147 Robin Biesbroek, Luisa Innocenti, Andrew Wolahan and Sara Morales Serrano Fig. 8 Phase A rigid (top) and flexible (bottom) design configurations. the detailed design phase, with the goal to link all identified Fig. 9 Airbus DS phase B1 design [12]. risks from the phase A to tasks in the phase B1. At the end of phase A five main risks were identified: Propellant Tanks 1. Risk of collision between e.deorbit and the target 2. Risk of casualty on ground WaBS TRIDAR 3. Risk of an unsuccessful capture 4. Risk of generating more debris 5. Risk of schedule slippage For each of these five risks, several performance indicators were identified and for each performance indicator a task Deployed Arm was created to help mitigating the risk. For example, extra GPS Receivers simulations were asked to model the rendezvous and capture and Switch phases. On top of this, a typical detailed design of a satellite PCDU using one capture option (to be proposed by the contractor) Gyros S-band was to be performed in order to perform a cost estimate and transponders achieve requirements mature enough for an SRR. The request to continue MBSE during phase B1, as well as the application Fig. 10 OHB systems phase B1 design [13]. of concurrent engineering and the use of collaborative design tools, accessible to both ESA and the contractors, enforced proposed by ESA’s member states, or science team to ESA. In this. The low TRL of the capture technique and GNC software contrast to this, e.deorbit came from a group of engineers within means extra monitoring of the total mission costs, including ESA who had studied sustainability options for space missions, developments, and for the first time a cost ceiling was given at and the mission was proposed to higher management within 150 M€ for the phase B2/C/D/E contract, excluding margins ESA who responded positively and together with other ideas and launcher costs. to protect the environment, ESA member states were asked in the previous Ministerial Council to support the Clean Space In May 2015, the invitation to tender for the phase B1 initiative. So how did this mission study become so successful? was issued by ESA after receiving sufficient subscriptions by The answer lies in teamwork, taking and aiming for decisions, member states (as described in section 2.3) and ESA received and the cultural influence. several proposals. The phase ended in 2016 with the SRR that continued into early 2017. The SRR board noted, among others, 4.1 Teamwork the uncertainties concerning robot arm cost and development plan, and also proposed to lower the tumbling velocity A strong success aspect is teamwork. At ESA a ‘project like’ requirement. Figures 9 and 10 show the phase B1 designs by support is pursued during the phase A and B1 studies. The team Airbus DS and OHB systems respectively. consists of the study manager, two systems engineers, cost engineer, risk engineer, Assembly Integration and Verification At time of writing this paper, ESA is publishing the ITT for engineer, GNC, robotics, mechanisms, and space debris. the Consolidation Phase. Furthermore a strong link is held with the Clean Space manager, Clean Space system engineer, and direct higher management 4. ENABLING SUCCESS within ESA’s TEC directorate. The team members were mostly present from the beginning i.e. active in space sustainability While typical ESA mission ideas are collected at ESA by studies even before Clean Space was created. means of a call for ideas to the scientific or telecommunication community for example, e.deorbit was never a mission The industry team consists of prime contractors and sub- 148 E.Deorbit – ESA’s Active Debris Removal Mission contractors. During the phase B1, the Airbus team consisted indicated having no interest in ‘new missions’ for MC 2016, of ADS ST (Germany), QinetiQ (Belgium), DLR (Germany), and in fact some new mission that were proposed such as AIM SENER (Poland), GMV Poland, GMV Portugal and MDA and SAOCOM-CS, were not given a go-ahead during MC (Canada). The OHB team consisted of OHB-Systems 2016. The Maturation Phase was to continue in GSTP (which (Germany), OHB-Sweden, TAS-I (Italy), MDA (Canada), was over-subscribed after the MC 2016) and since e.deorbit Deimos Space (Spain) and CBK-PAN (Poland). ESA was not proposed as a project, it could not be stopped. recommended frequent contact with industry, not only with the primes but also involving the sub-contractors. Videoconference Unfortunately, with contract sizes and funding requests tools and desktop tools such as Webex were used on a weekly going up (e.g. 41 M€ for the Maturation Phase compared to 1.6 basis. Some contractors voluntarily continued the use of M€ for the phase B1) it becomes harder to obtain the funding concurrent engineering within their team using concurrent / subscriptions. At time of writing this paper, while enough sessions instead of co-location meetings. The PRR and SRR funding was found for the Consolidation Phase, not enough reviews were also held in ESA’s Concurrent Design Facility. funding has yet been found for the phase B2 system study An e.deorbit symposium was held in 2014 and a Clean Space of the Maturation Phase, and the project risks being ended Industry Days workshop with dedicated e.deorbit sessions was prematurely in 2017. held in 2016. 4.3 Culture 4.2 Decisions The e.deorbit mission is studied in a time where the culture puts Several decisions have played and will play a major role in the more and more a focus on environment and its protection. While success of e.deorbit. A first decision was to take a transparent the majority still needs to realize that the Earth environment approach, i.e. inform industry and member states on a frequent includes space until the Earth’s sphere of influence, there is basis on the current plans and the current achievements. The still a high amount of involvement, which becomes evident Clean Space team noted a positive reaction by industry as to the high coverage of e.deorbit videos and press releases on industry was often proposing to discuss at ESA results of the the Internet. Furthermore, when it is in the news that a space company’s own internal studies and ideas. Another decision debris object is about to enter the atmosphere, there is a high was not to narrow down system options, in particular related amount of phone calls and emails received at ESA’s debris to the capture technique, too quickly. The phase A contained office. Movies such as Warner Bros’ movie “Gravity” certainly a mandatory set of three system options. The first phase A aid to the realization of the general public about the hazards of review (Mission Baseline Review) was to select for each of having debris in space. The e.deorbit mission and in particular the three system options the capture technique, out of many the net tests and videos have received much attention on the options considered. While industry was asked to perform a ESA website. And both on-line newspapers as well as paper trade-off between the three system options, it was decided to versions of newspapers often copied press releases. continue technology development studies for net, harpoon and rigid capture options, until the Ministerial Council of 2016. The 5. RE-ASSESSMENT OF E.DEORBIT reason is that the final decision on the capture technique may not only be based on system engineering, but on the preference While the progress of e.deorbit can be considered successful, it by participating member states, i.e. sponsors. Before PRR, a is good to stand still and re-assess the current situation and the Mission Design Review was held to check if the design was projection on the future. How much did we mature really? What mature enough for the PRR. could be required if we did not or are not maturing enough? What can we conclude from the current strategy? It was also decided that the robot arm capture solution would rely on a strong heritage of the German DEOS mission, which 5.1 Maturity aimed at performing a capture using a robot arm in the 2017- 2018 timeframe. For the phase B1 ITT, industry was asked to As mentioned before, e.deorbit is supported by a wide range write proposals with their own preferred capture technology, of technology development studies. The strategy is to continue based on heritage within the companies. The winning bids these developments for net, harpoon and rigid options until the all chose the robot arm plus clamping mechanism option as a next MC decides with which capture method to continue. baseline. The following technology development studies were pursued Finally, it was decided to switch to an ‘optional programme’ in the 2014–2015 timeframe: already early in the design phase. While the phase A was under Net studies GSP funding and therefore only dependent on ESA internal • Net debris capture and parabolic flights; this study funding, it was decided to propose phase B1 to B2 under GSTP studied the motion of net deployment, tested it in funding, meaning that already the phase B1 would only take parabolic flights and modelled it in simulators. place if ESA member states would actually subscribe and Bounced. Mathematical modelling of high elastic sponsor it. This entailed the risk of having no funding for the tethers. detailed design study, but was done on purpose to test interest Elastic tethers; this study performs tests on elasticity of before describing the mission for the MC in 2016. tethers of several materials, and the impact of the space environment. Before the MC of 2016, the ESA decided not to propose Harpoon characterization, bread-boarding and testing; e.deorbit as a mission requesting funding for an implementation this study creates test harpoons suitable for e.deorbit, phase. This was a large decision with both negative and positive and tests the harpoons for different impact conditions. consequences. The negative consequence is a delay in launch date of at least two years, as now the decision to start the project Robotics is moved to the MC of 2019. However, several countries had Clamping mechanism; trade-off of clamping 149 Robin Biesbroek, Luisa Innocenti, Andrew Wolahan and Sara Morales Serrano mechanisms suitable of capturing the target without a GNC Maturation Phase: LIDAR, multi-spectral robot arm. engineering models, image processing hardware, Robotics and GNC set-up; at ESTEC a set-up is created consolidation of GNC algorithms for ADR, validation within the robotics laboratory that allows testing of using a flat-sat set-up. GNC algorithms and sensors. Some of the technologies could reach high TRL by doing GNC And Debris Attitude an In-Orbit Demonstration (IOD). There has been much debate De-tumbling solutions; a study on GNC algorithm and within the e.deorbit team about the necessity of IOD or not [11]. solutions to de-tumble e.deorbit with the target attached One could argue that many tests can be performed on ground via a clamping mechanism. (robotics, GNC sensors). The net behaviour cannot be tested on Advanced GNC solutions for ADR; this study developed ground however a sounding rocket flight is foreseen to test the first control algorithms to stabilize e.deorbit with a target capture, and the tether dynamics could be tested in parabolic attached via a tether. flights or free-flying equipment on board the International Space Image recognition and processing. Mathematical Station. Moreover, an IOD may cause a delay in the e.deorbit modelling on image recognition. schedule, as well as increased overall cost. On the other hand GNC synchronized motion with robot arm. This activity there is the phenomenon of ‘fear mitigation’; managers are studied GNC algorithms for a synchronized motion with more likely to sign for an expensive mission to remove a large robot arm. debris, if it has been proven in space that a small debris can Debris attitude motion and measurements and be removed. A small debris would pose no harm on ground, in modelling. In this activity observation campaigns are case of a malfunction. organized to determine attitudes of debris objects. ENVISAT is one of the objects to be studied. Based on Since e.deorbit is to prove ADR technologies in space, it was the attitude motion, models will be developed to predict decided not to pursue an IOD as well. However several cubesat future debris attitudes. missions have been proposed to test e.g. image processing algorithms. One proposal is called ‘e.Inspector’ which is to The studies were executed with the aim to reach TRL 4 of the inspect ENVISAT visually, and will also allow to determine the technologies. Most studies were executed within ESA’s GSP tumbling rate and axes. programme or Technology Research Programme, allowing only internal approval within the need of member states 5.2 Strategy contributions. Note that no robot arm technology developments were proposed. Instead it was assumed that these technologies Looking back on the decisions made (see section 4.2) and the would benefit from the heritage of the DEOS mission, as work done, it can be concluded that until today the e.deorbit described in section 4.2. studies are on track to prepare a proposed for the implementation phase of e.deorbit the next MC in 2019. The launch date For the 2016-2017 timeframe the following activities are however was shifted by two years due to the insertion of the proposed: Maturation Phase and the postponement of decision to go for Net/Harpoon an implementation, from 2016 to 2019. Net Maturation Phase: deployment prototype (launcher, spool and net) and sounding rocket test; this will allow Some countries were not represented in the phase B1 of testing of a net deployment in space. e.deorbit. In particular countries like France, Spain, and the • Net control algorithms test; possibly using free floating UK, who did participate to the phase A, were not supporting spheres with the ISS. phase B1. This underlines the comment made by ESA’s new Director General at the Paris air show of 2015 on the difficulty in Robotics getting member states to pay for ‘waste removal’. It is typically Clamping mechanisms bread-boarding. The study will far more interesting to give contribution to an interplanetary take the most promising clamping mechanism option probe for example. Much work need to be done to convince of the phase B1 into account and create a breadboard the missing member states to contribute to the noble cause of version for testing purposes. e.deorbit. Robot arm gripper pre-development: design and prototype/demonstrate via functional test a robotic end- As of today, none of the member-states containing prime effector gripper breadboard. This contract has been contractors (e.g. France, Germany, Italy) have indicated interest awarded. to take the leading role for the Maturation Phase. More interest Robotics Maturation Phase: Engineering models of the was shown however in the robotics, GNC and net Maturation clamping mechanism, gripper, robotic arm including Phase studies. ESA will continue to lobby for the Maturation its joints; visual servoing camera, analysis of contact Phase until late 2017. dynamics and hardware validation. GNC & Avionics 6. CONCLUSIONS Hipnos & Comrade: advanced avionics, processing and collaborate control; these studies will focus on E.deorbit is a challenging mission that requires new the mission vehicle management, processing power developments as capturing a uncooperative space debris using a and avionics link between GNC and robotics. These spacecraft, and then de-orbiting it, has never been done before. contracts have been awarded. It allows Europe to take the lead in ADR technologies. Breadboard of multi-spectral camera for relative navigation. E.deorbit started ‘from scratch’ as no ESA programme GNC design and performance validation for ADR with was requesting it, yet due to a motivated team of both ESA, rigid capture industry and delegations, and the push of the Clean Space 150 E.Deorbit – ESA’s Active Debris Removal Mission Initiative, the study matured to a phase B1 level and will are reluctant to take the lead in such an endeavour. now start the Consolidation Phase to consolidate simulations and requirements in order to be ready to start phase B2. Much attention in the media is received (internet journals and Continuation to the phase B2 Maturation Phase phase however TV shows) and an e.deorbit and Clean Space workshops were will require strong motivation by the member states to finance held with a high attendance of European industry, showing a waste management, and the current status is that member states high interest of many companies. REFERENCES 1. ESA, Clean Space, www.esa.int/cleanspace. (Last Accessed 18 July 7. S. Galluci, Active Debris Removal by Adaptation of the VEGA Upper 2017) Stage – Project Executive Summary, ED-NT-1-C -0005-SYS-1-1, ELV, 2. C. Wiedemann, S. Flegel, M. Möckel, J. Gelhaus, V. Braun, C. Kebschull, 29 November 2013. J. Kreisel, M. Metz and P. Vörsmann, “Cost estimation of Active Debris 8. Airbus Defense and Space, E.deorbit phase A Final Report, EDEORBIT- Removal”, 63rd International Astronautical Congress, 1-5 October 2012, ASD-RP-0009, 11 September 2014. Naples, Italy. Paper No. IAC-12.A6.5.3. 9. Thales Alenia Space, E.deorbit phase A Final Report, e.deorbit-TAS-TN- 3. CDF Study Report, “e.deorbit”, CDF-135(C), ESA. FR-0005-0005419345, 15 September 2014. 4. A. Pisseloup, I. Retat, T. Salmon, F. Ducerf, M. Simnacher, O. Colaïtis, 10. Kayser-Threde, E.deorbit phase A Final Report, EDE-KT-RP-0006, 15 R. da Costa, A. Oliveira, P. Voigt, C. Bardot, J. Reed and C. Cougnet, October 2014. Service Approach towards the procurement/development of an Active 11. ESA, To IOD or not to IOD, that is the question, Debris Removal mission – executive summary, Airbus Defense and http://www.esa.int/Our_Activities/Space_Engineering_Technology/ Space, 2014. CDF/To_IOD_or_not_to_IOD_that_is_the_question. (Last Accessed 18 5. L. Richter, Future ADR missions – Executive summary, Kayser-Threde, July 2017) 17 January 2014. 12. Airbus DS, Edeorbit Final Report Phase B1, EDEB1-RIBRE- 6. C. Saunders, Service Approach towards the procurement/development RP-0020-1.0_Final_Report, ESA, 2016. of an Active Debris Removal mission – executive summary, SSTL, 13. OHB Systems, E.deorbit Final Report Phase B1, ESA, 2016. December 2013. (Received 26 June 2017; Accepted 13 July 2017) * * * 151 A.Journal Masson, of theC. Haskamp,British Interplanetary I. Ahrns et al. Society, Vol. 70, pp.152-159, 2017 AIRBUS DS VISION BASED NAVIGATION SOLUTIONS TESTED ON LIRIS EXPERIMENT DATA A. MASSON1*, C. HASKAMP2, I. AHRNS2**, R. BROCHARD1, P. DUTEIS1, K. KANANI1 AND R. DELAGE1 1. Airbus Defence and Space, 31 rue des cosmonautes, 31402 Toulouse Cedex, France. 2. Airbus Defence and Space, Airbus-Allee 1, 28199 Bremen, Germany. Email:[email protected]* and [email protected]** The LIRIS Demonstrator is an experiment of vision based navigation sensors implemented on ATV-5 George Lemaître and activated during the approach phase with the International Space Station (ISS). Studies of non-cooperative rendezvous stress the need for a GNC based on image processing using Lidar sensors and cameras. During the ATV-5 approach, two infra-red cameras, one monochrome visible camera and one scan LiDAR have recorded images during both a dedicated ISS fly-under and the Rendezvous with the ISS ending with docking. This flight database was completed with a reference trajectory processed from telemetry issued from ATV nominal navigation and with information on LIRIS sensors such as position, orientation, calibration laws. Airbus Defence and Space (ADS) has been working for many years on vision-based navigation solutions including target detection, target tracking and navigation filtering. Our image processing solutions are tested on LIRIS flight data to assess their performances on real images and are compared with the reference trajectory to make a post-flight analysis. The experiment covered the full range of rendezvous distances, the ISS starting as a point-like object in images, growing in the field of view and finally having it fully resolved in the sensor. The image processing modules (detection and tracking) use an a priori 3D model of the ISS, and mainly rely on target edges processing, when the resolution is sufficient. They feed a navigation filter with LoS measurements at long range, and both position and attitude measurements at short range. The navigation filter then fuses these inputs together with star tracker and IMU measurements to refine it knowledge on the ISS. In this paper, the main features of the LIRIS demonstration and sensors are presented. The ADS vision based navigation solution (Image Processing + Navigation) is described. The test campaign results on LIRIS data are provided and a discussion on on- board real time implementation is proposed. Keywords: LIRIS, navigation, rendezvous 1. INTRODUCTION The LIRIS Demonstrator is an experiment of vision based paper we will present the results of the post-flight analysis of navigation sensors implemented on ATV-5 George Lemaître by the cameras images and the scanning LIDAR data with specific Airbus Defence and Space for European Space Agency (ESA), emphasis on the relative pose-estimation providing a full six and activated during the approach phase with the International degree-of-freedom relative measurement. Space Station (ISS) [1]. LIRIS demonstration was co-funded by Airbus DS, including in particular, all the post flight analysis The LIRIS flight database collects all the data coming presented in this paper. Studies of non-cooperative rendezvous from the sensors, with time synchronized and associated with stress the need for a GNC based on image processing using a reference trajectory processed from telemetry issued from LIDAR sensors and cameras. ATV navigation [2]. This database contains also information on the sensors, like position, orientation and calibration laws. The LIRIS data is split over two phases. The ISS fly-under Beside the cameras in visible and LWIR spectrum, the LIRIS-2 is from about 70 to 8.8 km and the rendezvous with ISS is experiment concentrated on the acquisition of scanning LIDAR from 3.5 to 0km. The navigation sensors are composed of data (i.e. a relatively dense 3D point cloud of relative 3D point two infra-red cameras, one monochrome visible camera and a measurements between the scanning LIDAR and the ISS as a scanning LIDAR. LIRIS is separated in two experiments: the target object). LIRIS-1 experiment proposed by SODERN which concerns the use of infra-red (IR) and visible (VIS) camera designed In this paper, the main features of the LIRIS demonstration especially for non-cooperative rendezvous in space, and the and sensors are presented. The Airbus Defence and Space Vision LIRIS-2 experiment proposed by JenaOptronik and composed Based Navigation solutions are described. The exploitation of of a LIDAR Optical Head associated to an electronic which LIRIS flight data is provided and preliminary performance as is interfaced with ATV and a recorder. This sensor provided well as benchmarking on a LEON4 processor board will be full 3D scans of the approaching ISS between relative distances given. of 30m down to docking and relative position measurements starting at approximately 2.5km relative distances. In this 2. LIRIS FLIGHT DATA This paper was presented at the ESA 7th European Conference on The ATV-5 Georges Lemaître ascent flight took place from Space Debris, ESA/ESOC, Darmstadt, Germany, 18-21 April 2017 injection by Ariane 5 on July 29th 2014 until docking to the 152 Airbus DS Vision Based Navigation Solutions Tested on LIRIS Experiment Data ISS on August 12th 2014. For the fly under, dedicated flight limited time was available for the extrinsic calibration of the phase for Liris demonstration performed 4 days before the sensors. All sensors (i.e. the cameras and the scanning LIDAR) rendezvous, the ATV was positioned in Earth pointing mode have been extrinsically calibrated with respect to a common by a slew manoeuver, and ATV front cone with LIRIS sensors calibration target consisting of the nominal ATV docking is pointed toward the ISS. The ATV rendezvous with ISS is target-pattern consisting of seven retro-reflective corner-cubes. composed of 2 phases, a far and a close rendezvous. The far Measurements of these corner-cubes have then been used to rendezvous is from 30km to 250m performed with relative GPS estimate the alignment of the LIRIS sensors w.r.t. the main ATV between ATV and ISS. The close rendezvous is from 250m to space-craft. Due to time constraints and facility constraints in docking and use a videometer to measure the ISS position and the integration room, it was not possible to have the target attitude. placed at varying locations in the field of view of the scanning LIDAR. Therefore a rather small target in one of the corners of 2.1 Camera and LIRIS-1 Experiment the field-of view of the scanner had to be used. As discussed later in this paper, this type of extrinsic sensor calibration The LIRIS-1 experiment proposed by SODERN combines did not provide sufficiently high alignment accuracy. Further two camera technologies: thermal infra-red and monochrome calibration efforts were undertaken by Jena-Optronik in order visible camera. The 2 IR cameras are redundant to mitigate the to remove distortion effects of the point-cloud and in order to risk related to single event upsets and the VIS camera is used to provide accurate range measurements. compare IR and LIDAR images especially for the localisation of some ISS enlightened elements excepted during eclipse The orientation matrixes are obtained following the phases. Another advantage for the VIS camera is to present a exploitation of a specific calibration test. The accuracy was better image quality with a higher image resolution of 1360 × estimated to be 0.5 deg for cameras and 1 deg for LIDAR 1024 pixels compared to the 640x480 pixels for the IR camera. but additional margins shall be considered for unknown All cameras have a recording cadence of 1 Hz with a total field- uncertainties, therefore an extrinsic calibration was estimated of-view of 58.6° × 45.7° for IR cameras and 57.5° × 44.9° for from fly-under images as a bias correction. the VIS camera. The LIRIS-1 experiment is activated from 70km to 9km during the ISS fly-under and from 3.5km until 1.4 Data Quality docking during the rendezvous. After receiving the scan data for the post-flight analysis, a first 2.2 Scanning LIDAR and LIRIS-2 Experiment comparison between the geometry of the target model (here the ISS and especially the Russian service-module) based on the This scanning LIDAR was developed and integrated to the reference-data provided by the ATV’s onboard docking-sensors ATV-5 for the LIRIS-2 experiment by Jena-Optronik GmbH. (i.e. the videometer (VDM) provided by SODERN [3] and the This scanner was an prototype of the next-generation scanning telegoniometer (TGM) [4] sensor provided by Jena-Optronik. LIDAR for the relative measurement of non-cooperative Both measurements are based on tracking a set of retro- targets. However, due to safety limitations in the context of reflective corner-cubes attached to the Russian service-module approaching a manned space-craft, the scanning LIDAR was of the ISS. These measurements were taken as reference-data not operated at its highest power-level and thus only provided for comparison, well knowing that these measurements are not data at a reasonable density for 6 DoF navigation in the last 30m. really ground-truth but the best information on the relative state Furthermore, the field-of-view of the scanning LIDAR which is between ATV-5 and the ISS available at that time. foreseen to be ranging between 1° × 1° and 40° × 40° degrees maximum was only controlled by a pre-defined timeline. A first glance at the data showed that especially for the last Connected to this pre-defined field-of-view control also the 30m relative distance the quality is quite good concerning scanning frequency and the scan-density varied according to a density and false measurements. In principle, the 3D-point pre-defined scanning scheme. In the LIRIS-2 experiment, the cloud provided by the 3D-LIDAR fit very well with the model LIDAR was switched on at a relative distance of approximately of the ISS. Only at some portions of the target, the scanning 2.5 km. Because of the power level constraints the LIDAR only LIDAR provided wrong range measurements which tend to be provided a set of single measurements associated to ISS retro too far away. These wrong measurements were mainly on some reflectors (sufficient to allow range assessment) and no dense specific parts showing particular reflective material of the ISS at 3D-scan. This changed from distances of 30m and downwards. that time (since then, the sensor has been made robust to those Also the scan duration changed with relative distances and effects). Additionally, this test showed the first discrepancies varied between 120s for distances larger 300m, 16s for ranges between the scan data and the matching of the model based on between 100m and 300m, 4s for ranges between 100m and the reference data. A range-dependent bias has been observed 30m, 1 Hz between 10m and 30m, and finally 3 Hz for ranges that could be well explained by an error suspicion on the sensor below 10m. According to this also the absolute number of scans alignment. varied with relative distance. 2.5 Bias Correction Using Flight Data 2.3 Intrinsic Calibration on Sensors Because of these observations, the full calibration process has Each camera has its own distortion calibration law estimated on- been revisited and new efforts have been undertaken to improve ground by SODERN and provided in the LIRIS database. The the quality of the sensor alignment. After all a new improved distortion is modelled with a 3rd order polynomial transforming alignment information has been provided by Jena-Optronik coordinates in the detector frame to tangent coordinates in the by matching the scan-data to the ISS model and comparison camera frame. with the reference data. This comparison provided at the end an alignment-information that seems to be much better than the During assembly, integration and testing (AIT) of the result of the extrinsic calibration during time constrained AIT scanning LIDAR in Kourou on the ATV-5 spacecraft, only very in Kourou. 153 A. Masson, C. Haskamp, I. Ahrns et al. 3. IMAGE PROCESSING FOR VISION minimization of the reprojection error [6]. MBT outputs the BASED NAVIGATION attitude and position of ISS in the camera frame. It works as follow. Salient edges from the ISS 3D model are extracted and Airbus Defence and Space (ADS) has been working for many projected on the camera image plane. A solver iterates then to years on vision-based navigation solutions including target find the best pose for which projected 3D model edges best detection, target tracking and navigation filtering. Our image match the image contours. The rest of the tracking sequence processing solutions are tested on LIRIS flight data to assess is made by a loop in which IP-tracking outputs are used to their performances on real images and are compared with initialize the tracking for the next iteration until the end of the the reference trajectory to make a post-flight analysis. The sequence. Figure 1 represents images from cameras and the experiment covered the full range of rendezvous distances, the MBT 2D-projection associated. ISS starting as a point-like object in images, growing in the field of view and finally having it fully resolved in the sensor. The IP algorithms are robust to occlusion, background and target rotation. For the LIRIS-1 experiment, the goal is to have 3.1 Camera-Based Pose-Estimation an independent tracking working with image data only. MBT starts working when ISS has a minimum size in image around The image processing (IP) is composed of detection and 60-100 pixels which corresponds to an approximated distance tracking modules working together in an automatic process of 800 m from the camera. loop [5]. As inputs, calibration data and an a priori 3D model of the ISS are used. They feed a navigation filter with LoS 3.2 3D-LIDAR-Based Position-Estimation measurements at long range, and both position and attitude measurements at short range. For larger distances a relative position measurement between the approaching space-craft and the target space-craft is During the close-range rendezvous approach, when the ISS sufficient for the guidance and control (G&C) to bring the have a sufficient resolution, the IP detection module, based approaching space-craft closer to the target. Therefore, on gradient orientation, is activated. It is used to initialize the at larger distances a simple processing of the received model-based tracking (MBT) which part relies on a non-linear measurements that just computes the geometrical center of Fig. 1 IR1, IR2 and VIS camera image with MBT 2D-projection in colour (respectively red, green and blue). The ISS docking point is at a distance of 20 m from the ATV. 154 Airbus DS Vision Based Navigation Solutions Tested on LIRIS Experiment Data all 3D-point measurements is sufficiently accurate to estimate a relative position. The processing is very simple and just applies centroid estimation. The simple centroid estimation of course does not reflect the systematic deviation between the centroid of scanned 3D-points on the surface of the target space-craft and the actual reference system of the target space-craft. This difference normally results in a bias mainly along the boresight- direction. This bias has been estimated in simulations and taken as a constant corrective value. Using this very simple approach, relative position errors in the order of +/- 10m at 2.5km down to +/- 5m at 300m relative distances have been obtained. 3.3 3D-LIDAR-Based Pose-Estimation The above mentioned method for the scanning-LIDAR based estimation of relative position just by centroid estimation the single measurements is of course not accurate enough for the last meters of the approach. Here, very accurate measurements in the order of centimeters are required. Furthermore, these measurements have to be precisely known with respect to a well-known reference system attached to the target space- craft. Therefore, another method is required that is based on the matching of a 3D model of the target space-craft and the acquired 3D point cloud. For the LIRIS 2 experiment, a tracking-algorithm [7] based on the family of iterative-closest point algorithm (ICP) [8, 9] has been applied. 3.3.1 Target Modelling In order to match the 3D scan points with an expectation of the target space-craft one needs to have a good model of the target geometry. For this purpose, Airbus DS generated several versions of the target model that mainly differ in the level of complexity. The starting model had a total number of 2.8 mio. points and 4.6 mio. polygons. From this a smaller model of 13350 points and 13800 polygons has been made and this model has even been further reduced to 2800 points and 2600 polygons. All models have been compared to the 3D scans of the scanning LIDAR but also to the camera images. Finally one Fig. 2 View of the larger model from simulated scanning LIDAR had to admit that it was not possible to perfectly model the perspective (top) and overlay of target model and acquired scan: Point colours represent the distances between the closest patches target for different reasons. First, not all the details of the of the target model (bottom). target were available for the project team, second, some parts were no longer as built and provided differences due to possible damages. Examples for this observation are shown in Beside the usage of point-to-patch comparison, the final Fig. 2. performance of these type of algorithms is achieved by using specific weighting functions for the distances between points The yellow points indicate points with larger discrepancies and surfaces, specific outlier rejection, as well as highly between scan and model. The next model shows the most optimized distance computation between points and surfaces important discrepancies. For instance, the Urthe-Cast camera which applies as much as possible pre-computations in order to could not be modelled and is missing in our model and thus save computing time on the on-board computer. represented by yellow scan points. Figure 3 shows the view from the camera in the visible spectrum for comparison. 4. RESULT ANALYSIS 3.3.2 Algorithmic Principles For the result analysis, we focused on rendezvous sequence. The IP-tracking camera position and attitude estimation are The matching of the target geometry with the point cloud of the presented without filtering or aiding from the navigation. scan is performed by using the ICP algorithm. Here, we apply The full 6DOF LIDAR-pose-estimation has been applied an ICP variant that matches scan points to the closest points on for close range rendezvous. For larger distances, the scan the model surface. The distances are calculated by computing parameters were not optimally chosen for the pose-estimation the distance between a scan point and the closest point on a and especially the scan density and scan frequency was not small triangular patch that models the target surface. sufficient. 155 A. Masson, C. Haskamp, I. Ahrns et al. 4.2 Middle Range Pose-Estimation Concerning the middle range rendezvous, the ISS appeared with a sufficient resolution after 800 m of distance for cameras and the LIDAR scan data are enough separated down to 300m to ICP algorithms. Figure 4 shows the position estimation with camera and LIDAR along the line of sight direction (X-axis) and lateral directions (Y-axis and Z-axis) comparing to the ground truth reference corrected by LIDAR data. 4.3 Close Range Pose-Estimation Down to a distance of 30m, the ISS images are more detailed Fig. 3 Camera image highlighting the areas of bad modelling of and the model-based tracking is much robust in that conditions. the target. At the end, we can notice that some difference persists when we compare the sensors pose estimations. The extrinsic calibration of sensors can be one on the cause but not only because we 4.1 Ground Truth Correction Using LIDAR Data notice differences in sensor quality when we compare infrared and visible cameras on many properties (resolution, sensor The relative position estimation based 3D-LIDAR scan-points size, variation of PSF…). Other causes are possible to explain has been performed for distances between 2.5km and 30m. differences like the influence of the pairing of position and Due to larger scan times at larger distances, the sampling is attitude or the existence of a local minimum in the MBT not homogeneous. Between 2.5km and 300m, only 11 scans treatment. Figures 5 & 6 show the Camera and LIDAR position have been acquired, at smaller distances, the number of scans and attitude estimation for close range rendezvous increased. A bias obtained from simulations has been subtracted from the centroid computations. The finally achieved accuracy Figure 7 shows the matching between the LIDAR-scan is below 10m-15m for distances up to 2.5km. At lower distances points and the target model. The false color representation of the error decreases down to 5m (e.g. at 300m relative distance). the scan points indicates distances between the model and the Fig. 4 Camera and LIDAR Position estimation for middle-range rendezvous. 156 Airbus DS Vision Based Navigation Solutions Tested on LIRIS Experiment Data Fig. 5 Camera and LIDAR Position estimation for close-range Fig. 6 Camera and LIDAR attitude estimation for close-range rendezvous. rendezvous. Angles are represented in Euler convention. scan points. The yellow points represent the points with largest estimation has been implemented on a state-of-the art LEON4 distances mostly showing not modelled parts of the ISS. The processor which has 4 cores. For the tests, an evaluation board relative distances for the different figures range from 27m, by Gaisler Aeroflex has been used. The algorithm has been 10m, 5m down to 0m (docking). implemented for one single core of the LEON4. For the test purposes, the model of the target has been compiled into the 4.3.1 CPU Load of 3D-LIDAR-Based Pose-Estimation software and also a typical point cloud from the LIRIS data set has been compiled into the source-code, i.e. no real interfacing The LIDAR-based pose-estimation is computationally e.g. via a space-wire interface has been done yet. expensive - at least for a typical on-board computer for space- crafts. In order to test the feasibility of the algorithm on recently Based on this setup, the LIDAR-based pose-estimation could developed on-board computers, the LIDAR-based pose- be run at a frame rate of approximately 3 Hz. This is in good 157 A. Masson, C. Haskamp, I. Ahrns et al. Fig. 7 Overlays of scan and model for several ranges. accordance to the maximum scan frequency of the LIDAR LiDAR and VIS, probably due to their lower resolution, blur in itself which provides reasonable spatial resolution distributed image at close distance and extrinsic calibration errors, but they over a field of view of 40° × 40° also at approximately 3 Hz. provided data during eclipse on the contrary to VIS. Although these tests are not finished yet and real interfaces are still missing, the results are very promising and indicate that LIRIS experiments have provided a unique set of data to such kind of algorithm might be hosted on a single core of a increase validation and maturation of camera and LiDAR based LEON4 processor. navigation solutions. It makes us confident in their ability to be used as rendezvous sensors for future rendezvous missions, 5. CONCLUSION with uncollaborative or collaborative targets. LIRIS has also provided a useful feedback for future missions and experiments The LIRIS Demonstrator was a successful project for non- which should pay a special attention on sensor calibration and cooperative rendezvous in space. It enabled to acquire many target 3D model reliability. Finally, LIRIS should be considered data with LIDAR and cameras, and thus to confront IP as a first step in rendezvous in-orbit demonstration, and more algorithms to real space conditions. It enabled also to assess in-orbit experiments still need to be performed to complete IP robustness and performances, even if this assessment is by present study and to improve visions based navigation nature bounded by reference trajectory accuracy and at short performance assessment. distance by the fact that the sensors have different objects in their field of view (parallax effects). Quantitative performance ACKNOWLEDGMENTS assessment of IP solutions has thus to be taken carefully. The Authors would like to acknowledge ESA and Airbus For far and middle range rendezvous, the position and Defence and Space for LIRIS experiment funding and attitude estimation from camera tracking are correct, the LIDAR successful implementation. They gratefully acknowledge algorithms have lower performance for position estimation, the contribution of Florian Kolb and Michael Windmüller of mainly due to the few number of available scans. For close JenaOptronik, Laurent Majewski of Sodern and Alain Donnard range rendezvous, the accuracy of pose estimation of all and Ulysse Southivong of Airbus Safran Launchers (formerly sensors increases. Many details can be resolved on sensors and Airbus Defence and Space from 2014 till 2016) for the LIRIS the LIDAR scan mode was optimized to upgrade the resolution. data preparation, and Olivier Mongrard and Michael Gansmann Infrared cameras provide less accurate pose estimation than of ESA for all the exchanges easing the exploitation. 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(Received 7 July 2017; Accepted 13 July 2017) * * * 159 inbox 160 Spaceflight Vol 58 March 2016 Diary Notices commercially viable as space technology improves. These include space tugs; space tourism; BIS Lectures and Meetings satellite refuelling; debris removal; debris exploitation; manufacturing in orbit; real-time video from space; space mining; etc. Dangerous Worlds We also anticipate animated discussion on “The Norms of Behaviour in Space”, which are becoming increasingly important as we move towards the era of mega-constellation, the 7 September 2017, 7 pm need for Space Traffic Control, and hence the requirement for significantly enhanced space situation awareness. Speaker: Elizabeth Tasker, Japan Aerospace Exploration Agency RISpace brings together industry, agency, government, financiers, academia and end users. Venue: BIS, 27/29 South Lambeth Road, London, SW8 1SZ We thought the planets of our Solar System were weird worlds, until we began to see the lands 4th BIS Belgium Annual Space Symposium harboured by our neighbouring stars. Huge Jupiters snuggle so close to their star that years last days. Worlds like Star Wars Tatooine begin their nights with dual sunsets, while rogue planets 28 October 2017, 2 pm float in perpetual darkness with no Sun at all. Other planets are split lands with hemispheres of Venue: Armand Pien Observatory, Gezusters Lovelingstraat 1, 9000 Ghent, Belgium eternal day and night, while still more drown in global oceans or seas of lava and tar. Let’s visit worlds more extreme than anything in fiction and ask if any could be called home. BIS Belgium has organised its 4th symposium at a new venue in Ghent. There will be three presentations: Skylark - Britain’s First Space Rocket Elisaveta Orlova - Policy Vacuums on Discovery of Extraterrestrial Life: Causes and Implications 5 October 2017, 7.30 pm Bart Hendrickx - Planetary Exploration Update about planetary missions currently underway and the ones that will be launched in the future Venue: Bath Royal Literary and Scientific Institution, 16 Queens Square, Bath, BA1 Philip Corneille – Spacefarers’ wristwatches 1961-2021 2HN More detailed info about the presentations can be found at www.bis-space.com/belgium/ A joint event by the William Herschel Society and the BIS South West Branch In 1957 ‘Skylark’ was Britain’s first rocket to reach space, and became the basis of the country’s Call for Papers first space programme and the birth of British space science and technology. Over the next Symposium on Space Elevators 48 years, hundreds were fired from Australia and around the world, launching into space thousands of scientific instruments that made pioneering observations of the Earth, Sun, stars 7 November 2017 and galaxies. This activity produced some of the earliest UV and X-ray astronomical images obtained, a little-known result this talk will emphasise. The space elevator has captured the imagination of scientists and writers for decades. The transition to low-cost, low-energy access to space via a smooth, gentle ride on an elevator has been compared to the transition from the horse-drawn carriage to the railways. The necessary Space Day 2017 strong, light-weight material remains elusive, but progress has been made in a number of areas, particularly understanding the minimum requirements and a better grasp of the dy- 7 October 2017, 11 am - 4.30 pm namics. A good summary is found in JBIS, 69, no.6-7, June-July 2016. Venue: The Hive, Sawmill Walk, The Butts, Worcester, WR1 3PD Speakers are invited to submit presentation proposals for talks of up to 40 minutes duration on topics related to space elevators. The scope may include marketing, finance, management, The West Midlands Branch of the BIS has been running this event for several years now and history (past and future) and science fiction, as well as scientific and technological topics such last year’s event was our largest so far with 22 exhibitors, two talks, two children’s shows, a as materials research, climbers, power transmission, simulation and space debris. Presentations build-a-model-spaceship competition and last but not least Rocket Motor static firings! The will also be considered on associated technologies: these may include other techniques for 2017 event, currently in the early planning stage, will be a similar event. establishing fixed infrastructure such as the orbital ring and versions of the launch loop. Please send details of your proposed presentation to [email protected] before end-July 2017. Call for Papers Proposal acceptance will be by mid-September 2017. UN Space Treaty Symposium 10 October 2017 West Midlands Branch Talks The British Interplanetary Society is holding a one day symposium to celebrate the 50th 18 November 2017, 1.45 pm anniversary of the UN Space Treaty which has been the foundation of space law for half a Venue: The Gardeners Arms, Vines Lane, Droitwich, WR9 8LU century. The Society invites proposed papers as contributions to this symposium on two themes: Theme 1 - The history of the UN Space Treaty and its contribution to the exploration The West Midlands Branch is continuing its varied series of talks and lectures at the Gardeners and exploitation of space. Theme 2 - The future of the UN Space Treaty and how it may need to Arms. Our speakers for the afternoon are: Mark Yates – Apollo Era Artefacts and Gerry Webb change to reflect the changes in space activity such as the growth in non-government activity. – The Fermi Paradox. Speakers are asked to send details of their papers via the BIS, un_space_treaty_symposium@ For further details please visit the BIS Website or the BIS WM Facebook page. Come and join us bis-space.com, to Mark Hempsell and Jerry Stone, coordinators of the symposium. for what will be an interesting and entertaining afternoon. 15th Reinventing Space Conference The Fermi Paradox 24-26 October 2017 28 November 2017 Venue: Strathclyde University, Technology & Innovation Centre, 99 George Street, Venue: BIS, 27/29 South Lambeth Road, London, SW8 1SZ Glasgow, G1 1RD The British Interplanetary Society will host a one day symposium to discuss the problems posed by the Fermi Paradox. The format will be similar to the sold out and well received symposium Website: http://rispace.org/ on ‘Future Histories and Forecasting’ held on the 25th January this year, with 10-12 speakers, The focus of the 2017 conference will be on the novel applications that are becoming refreshment breaks and lunch supplied. More details coming soon, including draft programme. Readers are reminded that these Notices contain only a reduced description of the event. Full details can be found online: www.bis-space.com/whats-on JBIS Journal of the British Interplanetary Society jbis.org.uk