On-Orbit Assembly of Flexible Space Structures with SWARM

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

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

3. Self-assemblingWirelessAutonomousReconfigurableModules (SWARM) Testbed • 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 docking port SPHERES satellite flexible beam element propulsion module

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

5. Incremental Test Plan

6. Test 1: Beam Control

7. SWARM as a Robot Manipulator δ3 δ2 ki δ1 mi y 0 x

8. SWARM Dynamics δ3 Beam joints modeled as torsional springs δ2 Fy δ1 y 0 x Fx “Linear in the parameters” Inertia Matrix Inertia Matrix Coriolis Matrix Coriolis Matrix Potential Terms Potential Terms

9. SWARM Dynamics δ3 Beam joints modeled as torsional springs δ2 Fy δ1 y 0 x Fx underactuated

10. Simplified Dynamic Model • Most important measurement for docking is tip deflection • Reduces complexity of dynamic model for control and estimation δf k1 y 0 x

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

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

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

15. Side View Image DSP Estimator LED(X,Y) State Estimate 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

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

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

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

19. Test 1: Beam Maneuvering Test

20. Toward Assembly: Tests 3, 4, 6

21. Typical Assembly Sequence Docking Beam Maneuvering Beam Docking

22. Typical Assembly Sequence Docking Beam Maneuvering Beam Docking

23. Typical Assembly Sequence Docking Beam Maneuvering Beam Docking

24. Typical Assembly Sequence Docking Beam Maneuvering Beam Docking

25. Test 6: Hardware Assembly Test

26. Trajectory Tracking Performance

27. Test 3: Beam Docking

28. Trajectory Tracking Performance

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 Acknowledgments: This work was performed under NASA SBIR Contract No. NNM07AA22C Self-Assembling Wireless Autonomous Reconfigurable Modules.

30. Backup Slides

31. Perpendicular Docking

32. Stability for Fully Actuated Adaptive

33. Flexible Structure Dynamics Shahravi, 2005

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

35. Dynamics Derivation Q1 m1,I1 Q2 Kinetic Energy: Q3 Potential Energy: m2,I2 m3,I3 Inertia Matrix Coriolis Matrix Potential Terms m4,I4