1. Analysis of a Deorbiting Maneuver of a large Target Satellite using a Chaser Satellite with a Robot Arm Philipp Gahbler 1, R. Lampariello 1 and J. Sommer 2 1 DLR Institute for Robotics and Mechatronics, Germany 2 ASTRIUM Space Transportation GmbH, Bremen, Germany ASTRA 2013

2. Motivation The purpose of this work is to show that a Chaser satellite equipped with a relatively weak robot arm is capable of deorbiting a large Target satellite. The dynamics of the coupled system, consisting of the Chaser resting onto the Target during the deorbiting, must be examined to ensure that the deorbiting maneuver can be performed safely. Key questions: Is there risk of separation during deorbiting? Do we need a clamp or does the robot have to exert high forces to avoid separation?

3. Contents Description of the system consisting of Chaser and Target Identification of the critical dynamics One-dimensional analysis of the surface contact dynamics Three-dimensional analysis of the deorbiting dynamics and the robot internal forces Validation with numerical simulations Conclusions

4. Target Very large object (e.g. 8 t) Target needs to be deorbited The satellite Envisat was used as an example Envisat

5. Chaser Satellite with a mass of roughly 1 t 7 DoF robot arm for grasping Chaser grasps the Target with robot arm and rests onto it with six contact points, arranged at a radius of 0.8 m Model of a Chaser

6. System Chaser positioned relative to Target near the center of mass (CoM) of the Target Contact through a number of surface contact points as well as robot arm Surface contacts only exert force during compression Robot arm provides torques and lateral forces Combined System of Target and Chaser

7. Propulsion Chaser accelerates system with four orbit-control-thrusters (OCT) Overall thrust typically 1500 N Model of the Chaser

8. Critical Dynamics System responds to changes in thrust profile Relative distance of surface contact must be negative to prevent bumping of masses External torque occurs when thrust vector doesn’t point through the system CoM The resulting angular acceleration causes complex internal forces One-dimensional dynamics of a mass-spring-damper system caused by surface contact Three-dimensional dynamics resulting from a misalignment of the two bodies

9. One-Dimensional Dynamics Symbolic graphic of a representative system Graphic of the real system

10. One-Dimensional System Response to Rectangle Input Input function (green) and qualitative system response (blue) of representative system (low stiffness) Rectangle profile  x / A Time [sec]

11. Stored Potential Energy Input function (green) and system response (blue) of representative system Due to structural elasticity, potential energy is stored in the structure, which is released at the end of the thrust profile The stored potential energy is given by the thrust force, F thrust, and the structural stiffness, c: Therefore high stiffness is desired, to minimize the stored potential energy Using the assumed values, the potential energy is only 11.25 mJ, which the robot can easily handle Release of potential energy  x / A Time [sec]

12. Stepwise Reduction of Thrust When thrust is reduced by a fraction of the total, the system oscillates about the new steady state by the difference of the two states If the reduction is by less than half of the previous value, ∆x will always be negative System response to a stepwise reduction of the input by one half  x / A Time [sec]

13. Three-Dimensional Dynamics: Disturbance Torque External torques occur when the deorbiting thruster force doesn’t point through the CoM of the system Deviation occurs when the Chaser and the Target aren’t properly aligned, especially when the precise location of the Target CoM isn’t known The attitude control system cannot compensate for such high torques, therefore off-modulation of OCT needed While a maximum deviation of 5 cm is realistic, a deviation of 50 cm was assumed for this analysis Position of System CoM and thrust force in a system with deviation

14. Modulated Thrust Profile - Off Modulation Attitude controller will selectively turn off one or several of the four thrusters to create torque, to account for misalignments Step width and sequence can be adjusted in controller software However, individual steps should only change by one thrust level (e.g. 4 to 3 or 2 to 1) to avoid separation Simulation of modulated thrust profile for the four thrusters (ASTRIUM) Condition on off-modulation to avoid separation

15. Three Dimensional Dynamics: Lateral Forces Relation between different coordinate frames

16. Equations for the Balance of Forces on the Target

17. Effect of Friction in the Surface Contact Frictionless Case If friction is assumed to be zero, the robot can be used to compensate lateral forces

18. System Stability Direction of inertial force in relation to external torque

19. Numerical validation in SIMPACK SIMPACK is a multi-body-simulation software that allows the user to create a model and integrate it numerically Simpack program window

20. Assumed Grasping Point Combined System of Target and Chaser

21. Simulation Results of Case with Friction and no Off-modulation Lateral forces follow the curves of the angular acceleration, as expected Lateral forces well in the range of what friction can handle Plot of the six contact forces (top) and the lateral forces and torque about x-axis (bottom)

22. Simulation Results of Frictionless Case and no Off-modulation Bodies oscillate relative to each other in the y- and z-direction Different damping coefficients (provided by robot) in y- and z- direction to achieve similar convergence time Relative position (top) and velocity (bottom) of the two bodies in y- and z-direction

23. Simulation Results of Frictionless Case and no Off-modulation Lateral forces well in the range of what robot can handle Six contact forces (top), forces and torques provided by robot (bottom)

24. Conclusions The deorbiting of a heavy Target satellite is possible using a Chaser equipped with only a robot arm The system is threatened by separation when the thrust is reduced. If it is reduced by less than half of its current value, the system stays in contact At the end of a thrust profile potential energy is released, which however is low and the resulting motion can be compensated by the robot A misalignment of the thrust force causes rotational accelerations which result in internal forces between the two bodies, but these can either be compensated by friction or by the robot Additionally, the system is stable, such that the misalignment will tend to decrease It is planned to perform such a deorbiting maneuver within the DEOS project

25. Thank you!

26. Relative Motion Resulting from Excessive Reduction of Thrust Relative distance (blue) and relative acceleration (green) of an oscillation with separation

27. Simulation Results of Case with Friction and no Off-modulation Constant angular acceleration due to external torque from deviation of CoM Torque is directed in y- and z-direction, as expected, which causes the initial angular acceleration about angles beta and gamma Over time the inertia tensor causes rotation also about x-axis (alpha) Of notice is the angular acceleration profile, which determines the lateral forces Plot of angles Alpha (x), Beta (y) and Gamma (z) (top), their velocities (middle) and accelerations (bottom)