Contact Dynamics Analysis for HTV Capturing by SSRMS

Trans. JSASS Aerospace Tech. Japan Vol. 12, No. ists29, pp. Pc_9-Pc_14, 2014 Original Paper

1) 1) 2) 3) By Akihiko HONDA , Mitsushige ODA , Hiroki NAKANISHI and Satoshi SUZUKI

1) Department of Mechanical and Aerospace Engineering, Tokyo Institute of Technology, Tokyo, Japan 2) Japan Aerospace Exploration Agency, Tsukuba, Japan 3) Advanced Engineering Services Co.,Ltd., Tsukuba, Japan (Received June 24th, 2013)

This paper discusses a contact dynamics which is happened when a massive spacecraft named H-II Transfer Vehicle (HTV) is captured by a Space Station Remote Manipulator System (SSRMS). If the point of the first contact is different from the planned one, then HTV’s motion will be completely change and may collide with ISS. Therefore, if we can predict motion of HTV depending on the telemetry data in real operation time, it will be useful to assure safety of the mission. To develop a dynamics simulator, at first, we studied telemetry data obtained in the 1st HTV (HTV-1) capture operation. Then, we developed a simple models with some parameters. In that phase, some preliminary experiment and deliberation in kinematics was conducted to model mechanical behavior and determine parameters. Then, optimization of parameters was conducted to identify some unknown parameters of contact dynamics based on telemetry data. And with following the course of optimization, we discuss key parameters which have large effect on dynamic HTV’s behavior and can be used in developing a low calculation-cost model. Finally, we apply key parameters and compare the results with an actual telemetry data of HTV-2 to verify its efficiency.

Key Words: Contact Dynamics, Numerical Analysis, Parameter Identification, HTV, SSRMS,

Nomenclature Missions like the HTV capture becomes more important : elapsed time from start a capture factor to conduct such as orbital construction, debris removal operation with snare wire and re-supply. Therefore researches are proposed their (ݐ : stiffness of snare wire solution to assure safety of these missions. M. Oda et al4

: spring constant of contact developed a new control method of space robot arm to reduce ܭ a disturbances to satellite’s attitude. And K. Senda, et al5) : stiffness of Grapple Fixture base ܭ developed an air-float test bed for flexible manipulator to : angular velocity of wire elements ܭ verify their control method on the ground. On the other hand, ௪௜௥௘ : contact force between snare wire and ߱ S. Matsunaga, et al6) proposed a new debris handling end ௖ Grapple Fixture ܨ : displacement of snare wire effector using wires. As an approach of the dynamics p : parameter set simulator, Ou Ma developed flexible SSRMS model and ݔ conducted a simulation in which SSRMS handles some payloads7). And Uyama, et al. developed a model of snare Subscripts 8) : number of iterations wire and draw a comparison with experiment .

݇ 1. Introduction ©JAXA

This paper discusses a contact dynamics which is occured when a massive spacecraft named H-II Transfer Vehicle (HTV) is captured by the Space Station Remote Manipulator System (SSRMS). HTV is an un-manned logistics supply vehicle1) whose mass is 16 metric tons and to carry logistics to the International Space Station (ISS). When SSRMS captures HTV, HTV will make rendezvous manoeuver to ISS and makes HTV’s relative velocity against ISS to be near zero.

Then, SSRMS approaches HTV and captures a grapple fixture 2) (GF) mounted on HTV. Images of both HTV and SSRMS are Fig. 1. Overview of space station supplier; HTV and Space Station shown in Fig. 1. Remote Manipulator System; SSRMS.

Pc_9 Trans. JSASS Aerospace Tech. Japan Vol. 12, No. ists29 (2014)

If we can predict a motion of HTV depending on the 2.2. Latching end effector and grapple fixture telemetry data from HTV and SSRMS in real operation time, To grasp with LEE, there are a GFs (Grapple©JAXA©JAXA Fixture) on it will be useful to assure safety of the mission. And, HTV. Fig.2 shows shapes of LEE and GF, and Fig.3 shows developing a real-time dynamics simulator has advantages in the capture sequence using these mechanisms. At a tip of the easily changing mechanical and environmental conditions and LEE, there are three metal, movable wires to fix the shaft part diversion to other missions. Therefore, we have been focusing of GF. The wires snare the shaft with closing and guide a and researching on dynamics simulator / teleoperation system position of the GF to center of LEE. After tighten up the shaft, for the contact operation. Current problems for the real-time the wires start pulling up the shaft and fix an attitude of GF dynamics simulator are existence of some unknown with adjusting a LEE to guide parts of the GF. Therefore, it is parameters in a contact dynamics and high calculation cost of important to analyze a contact wires and the shaft to simulate models. an initial contact phenomenon of capture operation. In this paper, we develop a dynamics simulator based on a one developed by Nakanishi9), et al and identify the some unknown parameters of contact dynamics with telemetry data. In developing the models, some preliminary experiment and deliberation in kinematics were conducted. And then, optimization of parameters was conducted to identify some unknown parameters of contact dynamics. For the purpose, we developed an optimization routine using the Nelder-Mead Simplex Method. And with following the course of optimization, we discuss key parameters which have large effect on dynamic behavior of HTV and can be used in Fig. 2. Overview of LEE and GF. developing a low calculation-cost dynamics model. Finally, we apply key parameters to our dynamics simulator with initial condition of HTV-2 and compare results with an actual telemetry data to verify its efficiency

2. HTV Capture with SSRMS

2.1. HTV and SSRMS HTV is an unmanned spacecraft which transport supplies to ISS. HTV was developed by JAXA to contribute ISS project after a retirement of a Space Shuttle. Major parameters of Fig. 3. Capture sequence using GF and LEE. HTV are indicated in Table 1. 3. Model Configuration Table 1. Major Parameters of HTV. Total Weight 16 [t] The models were developed with general-purpose multi Total Length 9.8 [m] body dynamics simulation software called ADAMS/View. Diameter 4.4 [m] And transient mechanical analysis was conducted by ADAMS/Solver. In this section, modeling capture The primary feature of HTV is that it docks to CBM mechanisms and preliminary experiment to determine models (Common Berthing Mechanism) of ISS. This feature provides are explained. an advantages to transportation because aperture size of CBM 3.1. Dynamics model of HTV and SSRMS is larger than other docking mechanisms. However, CBM HTV was modeled based on geometrical data provided by does not allow to dock directly unlike other mechanisms. JAXA. To adjust a dynamical behavior, a bushing element Therefore HTV is captured by a SSRMS10,11) (Space Station connects a GF parts and HTV main body. And mass and Remote Manipulator) once after rendezvous and attached to rotary inertia properties were also assigned based on provided CBM2). data. At the first place in simulation, the HTV is set to The SSRMS is a large, lightweight robotic arm used in provided initial velocity and then shifts to free draft condition. construction and transport operation on ISS. Table 2 are major SSRMS was also modeled base on geometrical data. parameters of SSRMS. The SSRMS has 7 degrees of freedom SSRMS has some number of operation modes and be assumed and 3 degrees of freedoms are allocated in both side of tip and to change modes in HTV capture operation. Therefore, 1 degree of freedom is in center. As end effector, SSRMS has time-variable force element which simulates a joint stiffness LEE12) (Latching End Effector) on both sides. torque and back drive torque is assign to each joint. The joint stiffness torque is applied on both in a manual operation mode Table 2. Major Parameters of SSRMS. and limp mode. On the other hand, the back drive torque is Max Length 17.6 [m] applied only in the limp mode. Total Weight 1.8 [t] Weight capacity 116 [t]

Pc_10 A. HONDA et al.: Contact Dynamics Analysis for HTV Capturing by SSRMS

3.2. Mechanical model of latching end effecter 3.2.2. Moving speed The snare wires are modeled with rotational rod elements as Preliminary experiment was conducted to determine a change shown in Fig.4. Contact force functions are applied on of moving speed of wire using a mock-up of LEE and imaging between grapple shaft and rod elements and that reaction force sensor. From a result of the experiment, we conclude a moving is calculated based on differences between angular rotation speed of wire is nearly-constant if a mechanism is drove at command value and simulated operation-result value. Details constant rate. Fig. 6 shows result of the preliminary experiment. are mentioned in next part. From this result, the rod elements were modeled rotating at steady rate . Information about a real operating time was not provided fully, the rotate rate is a variable changed with ߱௪௜௥௘ operating time which the snare wire is moving to tighten up the shaft of GF.

Fig. 4. Behavior of snare wire modeled with a rotation of rod elements.

3.2.1. Reaction force Fig. 6. Moving speed of snare wires. To modeling a vertical reaction force of snare wire, a simple model of the stretched wire which is fixed at both side is introduced into our model (Fig.5). In this model, the wire is 3.3. Dynamics model of grapple fixture deformed by force . The condition of and no slack To simulate a contact force in aparallel direction to a contact plane, a friction parameter was assigned between GF in wire is set to initial condition. In this time, relationship between and displacementܨ x is representedܨ ൌͲ as Eq. (1). and snare wire of LEE. Using a coulomb friction force function of ADAMS/View, the friction phenomenon between

ܨ a shaft of GF and snare wire was modeled as indicated in Table 3.And for the calculation stability, the small mass and inertia is assigned to GF.

Fc Table 3. Friction parameters between GF and Snare wire. Static coefficient of friction 0.3 [-] Dynamic coefficient of friction 0.1 [-] Sticition transition velocity 1.010-2 [m/sec] Friction transition velocity 1.0 [m/sec]

Stiffness of wire : Kwire 4. Parameter Identification Fig. 5. Modeling for contact force occurred between snare wires and shaft of GF. 4.1. Simulation conditions Some parameters of contact dynamics we needed are not cleared because of measurement difficulty. For example, the contact force is needed to simulate the contact dynamics, (1) however is unclear. Similarly, Stiffness of GF base ௖ ݈ ௖ ܨ ൌ ʹܭ ቆͳെ ଶ ଶ ଶ ଶቇ ܨ , Angular velocity of wire elements and ܭ ݔ൅ݔ ܮඥ݈ ൅ʹξ݈ െ ଶ ଶ production errors are also not cleared. To identify௪௜௥௘ the conditions of simulation is set as below.߱ Initial ܭ,൅ݔቁ parameters ܮൈ ቀඥ݈ െ If the displacement is sufficiently-smaller than , position, velocity and attitude of HTV and ISS are set based Eq. (1) can be written as ଶ ଶ on telemetry data of HTV1 capture operation conducted at ܮݔ ξ݈ െ (2) ଶ ଶ July, 2009. Angles of SSRMS’s joints is adjusted to fit a result ݈ െܮ of image analysis. In the image analysis, the camera image of a contact௖ݔ dynamics. Based ܭconstantଶ inݔൌ ܭʹ as௖ ؆springܨ is defined ݈ grapple target and target mounted on GF was used to calculate on௖ the capture procedure and its mechanisms, the l, L and ܭ can be assumed as much larger than x. Therefore we a relative displacements and orientations. Through SSRMS adoptedଶ ଶ linear function as in our simulator. has 7 degrees of freedom, the shoulder roll axis positioned on ξ݈ െܮ base of SSRMS is fixed in solving an inverse kinematics. ܨ௖

Pc_11 Trans. JSASS Aerospace Tech. Japan Vol. 12, No. ists29 (2014)

From the dynamic behavior indicated in telemetry data, simulator for simplification. simulation time step is set to 0.05[sec]. SSRMS is assumed set to the manual mode in the tighten-up phase and transit to limp mode. Therefore, until 29.5[sec] in which the grapple fixture assumed as fixed with snare wire, SSRMS set to manual mode and then transit to limp mode. 4.2. Parameter optimization To identify parameters, we defined a non-liner optimization problem as below.

(3) ଶ ǡǥሻሽ ܭǡܭ ሺݐǡ ሺݐሻ െ ൌ ෍ ෍ ሼ ǡ ǡ ௧ୀ଴ିହ In Eq. (3), function G is angular velocity around roll, pitch and yaw axis obtained from telemetry data. Function H is an angular velocity calculated by simulator. To calculate evaluate function, a squared errors are calculated between telemetry data and simulated data, and then these values are summed for analysis time and all axis. On each analysis, the evaluation function is calculated then optimized design value is worked Fig. 7. Flowchart of an optimization for parameter identification. out. The Nelder-Mead simplex method13,14) is used to update the parameters because the optimization problem was assumed to have a large nonlinear character and it is difficult to calculate a gradient of the function. In this optimization, the reflection parameter is 1[-], expansion parameter is 2[-], contraction parameter 0.5[-] and shrink parameter is 0.5[-]. The initial value of each parameter is set to values shown in Table 4. These value were quasi-optimal value calculated by hand with conventional simulation.

Table 4. Initial design value in optimization. Stiffness of wire 5.55105 [N/m] Stiffness of GF base 1.00108 [N/rad] ܭ Angular rate of snareீி wire model 29 [deg/sec] ܭ Fig. 8. Angular velocity around the roll axis of HTV.

In this calculation, as stopping criteria, the error criteria was adopted as shown in Eq.(4).

ሺ௞ሻ ሺ௞ିଵሻ (4) ฮ݌ െ݌ ฮ ሺ௞ିଵሻ ൏ ͲǤͲͳ ԡ ԡ p is a design parameter݌ set in each iteration. The flowchart of optimization is shown in Fig. 7. 4.3. Analysis result and discussion of key parameters From the optimization, design parameters for contact dynamics were calculated. Fig. 8-10 are an angular velocity which is simulated using those parameters. Fig. 8 shows the newest parameters simulate the behavior of rotation of roll Fig. 9. Angular velocity around the pitch axis of HTV. better than conventional parameters. However the simulation result also indicates much smaller value in amplitude of vibration. The reason of errors are assumed to be due to lack of flexibility in the current dynamics simulator. For instance, the SSRMS is connected to ISS with GF and it can have some amount of flexibility and cause non-linear behavior. However it is omitted and modeled as completely fixed in the current

Pc_12 A. HONDA et al.: Contact Dynamics Analysis for HTV Capturing by SSRMS

Fig. 10. Angular velocity around the yaw axis of HTV. Fig. 13. Angular velocity around the roll axis of HTV2 based on key parameters. The contact forces loaded on snare wires are shown in Fig. 12. From the figure, it is assumed that a wire 1 collides to the shaft of GF first. Then a wire 2 collides with the shaft next and the shaft is tightened up at 29.2[sec].

Fig. 14. Angular velocity around the pitch axis of HTV2 based on key parameters.

Fig. 11. Contact force loaded on the snare wires.

Besides, history of updating parameters indicates the parameter of stiffness of GF has much larger effect on the early phase of capture. It effects especially on a frequency of roll vibration. Therefore, the parameter can be determined as key parameter of HTV’s behavior. Fig. 12 shows the roll rotation rates with various value of snare wire’s stiffness. From the figure, we can see an effect to the frequency of vibration. While on the other hand, Stiffness of snare wires have a little effect on the behavior of HTV especially in early phase of contact.

Fig. 15. Angular velocity around the yaw axis of HTV2 based on key parameters.

5. Parameter Verification

Parameter verification was conducted with new HTV2 telemetry data. In this verification, initial condition of HTV2 and identified key parameters are used as input data. It is important that simulation parameters except key parameters aren’t optimized in this analysis. We can optimize all simulation parameters to fit to each case or operation using Fig. 12. Change of roll angular velocity with stiffness between GF base above parameter identification procedure. However that and HTV main body. procedure is difficult to use in real-time simulation because of ܭ

Pc_13 Trans. JSASS Aerospace Tech. Japan Vol. 12, No. ists29 (2014) a calculation cost. In contrast, operators will be able to obtain i-SAIRAS 2001. real time dynamics prediction with sufficient accuracy with a 12) B. Walker and R. Vandersluis : Designing, Testing and Evaluation of Latching End E ector, In NASA. Lyndon B. pre or real-time identified few key parameters. Johnson The results are indicated in Fig. 13-15. Because an Space Center, The 29th Aerospaceơ Mechanisms Symposium, 1995 important event time and the amplitudes are match at order, pp.1-16. 13) J., A., Nelder, R., Mead, : A Simplex Method for Function the results suggest that we can simulate sufficiently accurate Minimization, The Computer Journal, 1965, pp.308-313 contact operation without whole parameter identification even 14) Amaya, K. : An Introduction to Optimization Method for if the condition will be changed. It is also suggests Engineers, Suuri Kougaku sha, 2008. low-calculation cost dynamics model will be able to develop using the key parameter with our procedure.

6. Conclusions

In this paper, the dynamics of HTV capture with SSRMS is simulated and the parameters of contact are optimized based on a telemetry data obtained by HTV1. The multi-body simulator and optimization software which uses a Nelder-Mead Simplex method were developed for the object. With parameter identified in optimization, the angular velocities of HTV become more accurate than simulation with past parameters. And the key parameters which have large effect on a behavior of HTV are determined by a history of parameter updating in optimization. Finally, we apply key parameters to our dynamics simulator and obtain sufficiently accurate results without optimization to all parameters. As future work, it is necessary to determine a key parameters which simulate much accurately in the amplitude of angular velocity around the roll axis.

References

1) Shibata, K. ; Safety Design of H-II Transfer Vehicle (HTV), Technical review of Mitsubishi Heavy Industries, 48 No.4, (2011) 2) Japan Aerospace Exploration Agency: ISS supplier “Kounotori”2(HTV2) mission press kit, http://iss.jaxa.jp/htv/mission/htv-2/library/presskit/ , 2011. 3) European Space Agency : ATV: Servicing the International Space Station, An ESA Communication Production, 2010. 4) Oda, M. : Dynamics and Control of a Robot Satellite, Journal of the Robotics Society of Japan, 17 (1999) No. 8 pp.1067-1071 5) Senda, K. : Control Experiments of Flexible Manipulator Mounted on a Free-Flying Space Robot, Journal of the Robotics Society of Japan, 12 (1994) No. 6 pp.899-904 6) Matsunaga, S. : A tether based method for capturing in-orbit objects, IEICE technical report SANE, Space , Aeronautical and Navigational Electronics,96(326), pp.51-56, (1996) 7) Ou Ma : Contact Dynamics Modelling for the Simulation of the Space Station Manipulators Handling Payloads, Proc. of the 1995 IEEE Int. Conf. on Robotics and Auto, 1995, pp.1252-1258 8) Uyama, N. : Contact Dynamics Modeling for Snare Wire Type of End Effector in Capture Operation, Proc. of the 11th International Symposium on Artificial Intelligence, Robotics and Automation in Space, 2012 9) Nakanishi, H., Oda, M., Suzuki, S. : The Motion Analysis of the HTV Capture with the Space Station Remote Manipulator System (SSRMS), The Robotics and Mechatronics Conference, 2012 10) Stieber, M. E., Trudel, C. P., Hunter, D. G.: ROBOTIC SYSTEMS FOR THE INTERNATIONAL SPACE STATION, Proc. of IEEE ICRA 1997, pp.3068-3073. 11) McGregor, R. and Oshinowo, L : Flight 6A: Deployment and Checkout of the Space Station Remote Manipulator Sys- tem (SSRMS), Proc of the 6th International Symposium on Artiﬁcial Intelligence and Robotics & Automation in Space,

Pc_14