1. On-Orbit Assembly of Flexible Space Structures with SWARM Jacob Katz, Swati Mohan, and David W. Miler MIT Space Systems Laboratory AIAA Infotech@Aerospace 2010 April 22, 2010 1

2. Autonomous On-Orbit Assembly Enabling technology for  Large telescopes  Orbiting solar arrays  Interplanetary spacecraft Challenges –Flexible structures (solar panels, lightweight materials) –Multiple payloads with uncertain parameters 2

3. S elf-assembling W ireless A utonomous R econfigurable M odules (SWARM) Testbed docking port 2007-2009 (Phase II) SBIR sponsored by MSFC 2D flat floor demonstration Goals: maneuvering and docking with flexibility Hardware:  SPHERES on propulsion module  Flexible segmented beam  Docking ports propulsion module flexible beam element SPHERES satellite 3

4. Key Challenges Requirements for assembly  Follow trajectories for positioning and docking  Minimize vibrational disturbances Desired  Handle parameter uncertainty for unknown payloads Fewer actuators than degrees of freedom: underactuated control This talk:  Ideas for adaptive control  Initial hardware testing 4

5. Incremental Test Plan 5

6. Test 1: Beam Control 6

7. SWARM as a Robot Manipulator 7 mimi δ1δ1 δ2δ2 δ3δ3 00 y kiki x

8. SWARM Dynamics Beam joints modeled as torsional springs δ1δ1 δ2δ2 δ3δ3 00 y FyFy FxFx x 8 Inertia MatrixCoriolis MatrixPotential TermsInertia MatrixCoriolis MatrixPotential Terms “Linear in the parameters”

9. SWARM Dynamics 9 Beam joints modeled as torsional springs δ1δ1 δ2δ2 δ3δ3 00 y FyFy FxFx x underactuated

10. Simplified Dynamic Model Most important measurement for docking is tip deflection Reduces complexity of dynamic model for control and estimation 10 δfδf 00 y x k1k1

11. Nonlinear Adaptive Control for Robot Manipulators 11 weighted tracking error tracking time constant kinematic regressor parameter vector control vector state vector PD gains adaptation gains adaptive feed-forward PD term Tracking Error Control Law Adaptation Law dim(τ) = dim(q), how do we apply this to underactuated control?

12. Underactuated Adaptive Control 12 Main idea: perform tracking in a lower dimensional task space y subject to For example: weighted combination of beam deflection and base rotation

13. Underactuated Adaptive Control 13 Main idea: perform tracking in a lower dimensional task space y

14. Underactuated Adaptive Control 14 Important to note inherent sacrifice in underactuated control  Lose guarantee of tracking convergence for arbitrary state trajectories  Best we can do is achieve tracking in the output space  Need to show zero output error implies convergence of internal states Main idea: perform tracking in a lower dimensional task space y

15. Beam State Estimation Overview Requirement Provide an estimate of beam state variables Design Camera mounted to SPHERES body frame Observe infrared LED on beam end Calculate beam deflection using LED position State estimate relative to SPHERES body frame DSP Image Estimator LED (X,Y) State Estimate Side View

16. Image Processing Demonstration Threshold Centroid X Y pixels Time (s) Estimator DSP 16

17. Beam Estimator f u Z ≈ Beam Len X Image Plane IR LED Schematic View Perspective Projection Measure beam angle directly using perspective projection Differentiate δ f using LQE DSP Estimator 17

18. Beam Simulation Full nonlinear model built in Simulink/SimMechanics Simulation of SWARM thrusters, camera, and control/estimation system Autocoding capability for rapid deployment and testing 18

19. Test 1: Beam Maneuvering Test 19

20. Toward Assembly: Tests 3, 4, 6 20

21. Typical Assembly Sequence 1.Docking 2.Beam Maneuvering 3.Beam Docking 21

22. Typical Assembly Sequence 1.Docking 2.Beam Maneuvering 3.Beam Docking 22

23. Typical Assembly Sequence 1.Docking 2.Beam Maneuvering 3.Beam Docking 23

24. Typical Assembly Sequence 1.Docking 2.Beam Maneuvering 3.Beam Docking 24

25. Test 6: Hardware Assembly Test 25

26. Trajectory Tracking Performance 26

27. Test 3: Beam Docking 27

28. Trajectory Tracking Performance 28

29. Conclusions and Future Work Conclusions Robot manipulator analogy is a useful tool for analyzing flexible assembly problem Adaptive control with a simple dynamic model looks promising but further testing will be required to compare it to other methods Future Work Adaptive control in hardware testing Look into better trajectories for beam vibration control 6DOF extensions and on-orbit assembly testing with SPHERES 29 Acknowledgments: This work was performed under NASA SBIR Contract No. NNM07AA22C Self-Assembling Wireless Autonomous Reconfigurable Modules.

30. Backup Slides 30

31. Perpendicular Docking 31

32. Stability for Fully Actuated Adaptive 32

33. Flexible Structure Dynamics 33 Shahravi, 2005

34. Docking Drives Control Approach 1. Move 2. Damp 3. Dock (+) Trajectory specified for satellite end (collocated) (-) Requires accurate pointing and low vibration (+) Relative metrology to guide beam end into docking port (-) Trajectory specified for docking end (non-collocated) 34 Start simple: collocated trajectory with beam damping

35. Dynamics Derivation Kinetic Energy: Potential Energy: m 1, I 1 m 2,I 2 m 3,I 3 m 4,I 4 Q1Q1 Q2Q2 Q3Q3 Inertia MatrixCoriolis MatrixPotential Terms 35