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Modelling Small Bodies Gravitational Potential for Autonomous Proximity Operations by Andrea Turconi

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Modelling Small Bodies Gravitational Potential for Autonomous Proximity Operations by Andrea Turconi Modelling Small Bodies Gravitational Potential for Autonomous Proximity Operations by Andrea Turconi Thesis submitted in fulfilment of the requirement for the degree of Doctor of Philosophy Marie-Curie Initial Training Network PITN-GA-2011-289240 AstroNet-II : The Astrodynamics Network Surrey Space Centre Faculty of Engineering and Physical Sciences University of Surrey Guildford, Surrey, GU2 7XH, UK c Andrea Turconi 2017 ii Abstract Maintaining missions in proximity of small bodies involves extensive orbit determination and ground station time due to the current ground-in-the-loop approach. The prospect of having multiple concurrent missions around different targets requires the development of concepts and capabilities for autonomous proximity operations. Developments in on-board navigation by landmark maps paved the way for autonomous guidance at asteroids. The missing elements for achieving this goal are gravity models, simple enough to be easily used by the spacecraft to steer itself around the asteroid, and guidance laws that rely on such inherently simple models. In this research, we identify a class of models that can represent some characteristics of the dynamical environment around small bodies with sufficient accuracy to enable autonomous guidance. We found that sets of three point masses are suitable to represent the rotational equilibrium points generated by the balance of gravity and centrifugal accel- eration in the body-fixed frame. The equilibrium point at the lowest Jacobi energy can be viewed as the energy-gateway to the surface. Information of the location and energy of this point can then be used by a control law to comply with a condition of stability against impact for orbital trajectories. In this thesis, we show an optimisation process for the derivation of three-point mass models from higher order ones and compare the profile of the Zero-Velocity curves between the two models. We define an autonomous guidance law for achieving body fixed hovering in proximity of the asteroid while ensuring that no impact will occur with the small body during the manoeuvre. Finally, we discuss the performance of this approach by comparing it with another autonomous guidance law present in literature and we suggest possible future developments. iii iv Statement of Originality This thesis and the work to which it refers are the results of my own efforts. Any ideas, data, images or text resulting from the work of others (whether published or unpublished) are fully identified as such within the work and attributed to their originator in the text, bibliography or in footnotes. This thesis has not been submitted in whole or in part for any other academic degree or professional qualification. I agree that the University has the right to submit my work to the plagiarism detection service TurnitinUK for originality checks. Whether or not drafts have been so-assessed, the University reserves the right to require an electronic version of the final document (as submitted) for assessment as above. Andrea Turconi v vi Acknowledgements At the end of these years at the Surrey Space Centre, I have a lot of people to thank for making this research effort possible and enjoyable through their support and friendship. First of all, I want to thank my principal supervisor Prof. Phil Palmer who gave me the opportunity to join the Astrodynamics Group at Surrey on such an interesting project within an ERC training network. Phil taught me a lot, encouraging me to always challenge my conclusions and to look at problems from all possible angles; at first for the sheer pleasure of finding interesting patterns in nature and finally to discover what equations and plots really entail. I feel privileged to have had him as supervisor; every chat with him on any topic ended up in exploring new horizons, exactly as we did during the AstroGroup walks among some of the most beautiful landscapes of Dorset and the South-West. Phil couldn’t see this work completed and he is greatly missed. I am grateful for how he helped me to develop my "potential" throughout these years and I will always bring with me his passion for the "good questions". Special thanks go to my second supervisor, Prof. Mark Roberts for his help in rationalising the possible avenues of my research all those times when I had too many ideas on what could be done. His support has been very important in the key stages of this project. Last but not least, I want to thank Dr Roberto Armellin for being my supervisor during the time of writing. His suggestions, coming from a fresh look at the problem, definitely improved the final work. Thanks go to my examiners Prof. James Biggs and Dr Chris Bridges who reviewed this work and provided valuable feedback and to Prof. Guglielmo Aglietti for chairing the viva exam. This research wouldn’t have been possible without the Astronet-II Marie- Curie Initial Training Network and the coordination effort by its Principal Investigators Prof. Gerard Gómez and Prof. Josep Masdemont along with the academics and industry partners throughout the network. Thanks also to Juan Luis Cano and Mariano Sanchez for the opportunity of an internship at Deimos and to the colleagues that really made my stay in Madrid great, especially Luca, Massimo and Annalisa. Thanks to the Astronet-II students across Europe for their fellowship and for sharing countless adventures, in particular to Alex who, being in Milan, vii made me feel within the network also when I was visiting home. Huge thanks go to Karen Collar for her amazing work of coordination and support to all students, researchers and academics of the SSC, solving so many problems and making every endeavour possible. At Surrey I made good friends that made daily life great and research struggles bearable. Special thanks go to Eli my fellow Astronet researcher at the SSC and great friend, we supported each other throughout this PhD years and shared awesome adventures in trips to conferences around the world! Thanks to Mamatha, Alessandro, Chiara, Marcello, JT, Gabi, Paco, Daniele, Jason, Alex, Craig and to all the students at the SSC sharing the pursuit of space science. In particular I want to thank the fellow members of the Astro- dynamics Group: Bet, Chris, Claudio, Andrew, Eli, Brian, Luke, Jim, Theo, Oier and Evridiki. Thanks to Pasquale and Federica, to the friends of many sailing adventures Claudio, Alex, Matt, James, and Curro and to the Surrey climbers Martin, Ibad, Giulia and Iwona. Thanks to my friends back in Italy and around the world which have always been present and lightened up my visits back home: Andrea and Monica, Marianna and Thom, Elena, Irene, Matteo, and Emanuele. Thanks to my family, to my parents Mariagrazia and Giampaolo and to my brother Luca and his wife Gloria: I am always grateful for your constant support and encouragement. Finally, there are no words able to express my gratitude to Anna who mar- ried me before this work was even finished. Thank you for your understanding, for being a wonderful wife and best friend, and for your strength in enduring the struggles of distance while letting me follow my dreams. viii All that is gold does not glitter, Not all those who wander are lost; The old that is strong does not wither, Deep roots are not reached by the frost. – J.R.R. Tolkien To Anna and to my family ix x Table of Contents List of Figures xxii List of Tables xxiv List of Acronyms and Abbreviations xxv List of Symbols xxvii 1 Introduction1 1.1 Asteroids: The Next Destination................2 1.2 Motivation.............................4 1.3 Problem Overview........................5 1.3.1 Missions to asteroids: the current approach.......5 1.3.2 Spacecraft autonomy...................7 1.3.3 Autonomous GNC at asteroids: the proposed approach8 1.4 Aim and Objectives........................8 1.5 Research Novelties........................9 1.6 Publications............................ 10 1.7 Training Schools......................... 11 1.8 Thesis Outline........................... 11 1.9 Acknowledgement......................... 12 2 Background 13 2.1 Asteroids characteristics..................... 13 2.1.1 Asteroid Orbits...................... 14 2.1.2 Masses, Shapes and Densities.............. 16 2.1.3 Asteroid Rotation Rates................. 18 2.2 Ground observations....................... 19 2.2.1 Lightcurve Analysis.................... 19 xi 2.2.2 RADAR Imaging..................... 21 2.2.3 Radio science at asteroids................ 21 2.3 On-board measurements..................... 22 2.3.1 Optical Navigation.................... 22 2.3.2 LIDAR measurements.................. 23 2.4 Modelling the gravitational potential.............. 23 2.4.1 Spherical Harmonics and developments......... 23 2.4.2 MacCullagh’s Formula.................. 24 2.4.3 Triaxial Ellipsoids..................... 25 2.4.4 Polyhedral models.................... 26 2.4.5 Mascon models...................... 27 2.5 Spacecraft Limitations...................... 29 2.6 Review of asteroid exploration.................. 31 2.6.1 Galileo (NASA/ESA)................... 31 2.6.2 Deep Space 1 (NASA).................. 31 2.6.3 NEAR-Shoemaker (NASA)................ 32 2.6.4 Stardust (NASA)..................... 33 2.6.5 Hayabusa (JAXA).................... 33 2.6.6 Dawn (NASA)...................... 35 2.6.7 Rosetta (ESA)...................... 35 2.6.8 Hayabusa2 (JAXA).................... 37 2.6.9 OSIRIS-REx (NASA)................... 38 2.7 Summary............................. 39 3 Orbital Dynamics Around Asteroids in Uniform Rotation 41 3.1 Asteroid Rotation and
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