1. SPHERES Reconfigurable Control Allocation for Autonomous Assembly Swati Mohan, David W. Miller MIT Space Systems Laboratory AIAA Guidance, Navigation, and Controls Conference 2008 08-21-2008

2. SPHERES 2 Outline Motivation Reconfigurable control overview SPHERES Overview Control allocation methods Testing Results Conclusions

3. SPHERES 3 Motivation: Autonomous Assembly On-orbit assembly is an enabling technology Challenges: Sequencing, Accurate Sensors & Actuators, etc Current methods high in risk, cost, and time –Human EVAs, Tele-operated robotic arms –Limited to Low Earth Orbit Desire to fully automate assembly process using robotics Additional Challenges for Autonomous Robotic On-Orbit Assembly: –Design challenges Autonomy Autonomous Control and Reconfiguration –Systems challenges No unified design principles or guidelines Requirements may vary drastically with application International Space Station Space Solar Power Station Space Telescope (ex. JWST) Address reconfigurable control system design for autonomous robotic on-orbit assembly.

4. SPHERES 4 Motivation: Control Allocation Suppose we want to … assemble N segments from an initial to final configuration, using a propellant tug with docking capability Issue: How to maintain performance at each docking/undocking to complete assembly, in spite of large mass and stiffness property variations? Initial ConfigFinal ConfigAssembler Tug OnlyTug + SegTug + Seg + BaseTug Only, BaseTug + Seg, BaseTug Only, Base Assembly Sequence Configuration: static configuration for a given time period, (eg. Tug Only, Tug + Segment) Transition: change from one configuration to another (eg. Docking: Tug  Tug + Segment) Single Control System  Tug Need to design control system to handle all configurations Want to maintain performance (ie stability, efficiency, accuracy) and versatility (ex. minimal hardcoded transitions and properties)

5. SPHERES 5 Reconfigurable control Reconfigurable control – on-line model calculation: –Identify a vector of properties p upon which the model depends –Develop the analytic expressions to calculate the model (N) based on the vector p –At each transition, update the vector p –At each update of the vector p, re-calculate the model N based on the analytic expressions –Use the model N to calculate the control input (u) Goal: Implement and Demonstrate on hardware Currently implemented p

6. SPHERES 6 SPHERES Overview + Z - Y - X Ultrasonic Receivers CO 2 Tank Adjustable Regulator Pressure Gauge Thruster Satellite body axes Diameter 0.22 m Dry Mass 3.5 kg Wet Mass 4.3 kg Thrust (single thruster) 0.11 N CO 2 Capacity 170g Control Panel Lexan Shell

7. SPHERES 7 Control Allocation Methods Assumptions of SPHERES baseline control allocation algorithm –Symmetric thruster placement –Center of mass fixed in center of thruster envelope –Fixed thruster configuration Intermediate reconfigurable control allocation algorithms –Mixer A: Reconfigurable to thruster configuration Assumes symmetric thrusters Application – Docking to an active payload –Mixer B: Reconfigurable to center of mass location Assumes fixed thruster configuration Application – Docking to a passive payload Mixer C: Reconfigurable to thruster configuration AND center of mass location –Generalized mixer –Removes all assumptions of baseline SPHERES control allocation algorithm

8. SPHERES 8 Mixer C Implementation Control Vector (Hardcoded) Mixing Matrix Calculate thruster forces & durations Thruster on / off times Original Reconfigurable InputsOutputs Thruster Config (r gc, F) Calc location of thruster (r cm ) from r gc and CM Calculate thruster forces & durations Thruster on / off times Torque = r cm x F Mapping Matrix Invert to get full Mixing Matrix Control Vector Control Allocation Algorithm on SPHERES

9. SPHERES 9 Testing Objectives: –Stability: actuation of control input stabilizes the system –Accuracy: can achieve ± 2cm position control required for docking –Fuel Performance: fuel usage is improved by updating the model Four test configurations –C1: SPHERE only –C2: SPHERE + Battery Proof Mass –C3: SPHERE + SPHERE Proof Mass –C4: 2 SPHERE attached (joint firing) Test Cases –Attitude Control only –Position and Attitude Control

10. SPHERES 10 Results: Attitude Control C4

11. SPHERES 11 Results: Attitude Control C4 Two SPHERES attached by Velcro. Both can fire thrusters. Two 90˚ Z axis rotations –1 st rotation  OLD gains, T s = 40s, O=30˚ –2 nd rotation  NEW gains, T s = 20s, O=20˚ Two SPHERES attached by Velcro. Only one can fire thrusters. Two 90˚ Z axis rotations –1 st rotation  OLD gains, O=47˚ –2 nd rotation  NEW gains, O=41˚ Fuel usage given in percent usage of tank (170g CO 2 in one tank) 1.77%2.77%1.22%1.18%

12. SPHERES 12 Results: Position & Attitude Control C4: 2 SPHERES attached, joint thruster firing Targets: [0.4, 0, 0], [0.4, 0.4, 0], [-0.4, -0.4, -0.4],

13. SPHERES 13 Results: Position & Attitude Control C4: Two Satellite Joint FiringC1: Satellite Only

14. SPHERES 14 Results: Position & Attitude Control C3: SPHERES plus SPHERE Proof Mass Targets: [0.4, 0, 0], [-0.4, -0.4, -0.4], [0.4, 0.4, 0]

15. SPHERES 15 Results: Position & Attitude Control C3: Satellite with Sat Proof MassC1: Satellite Only

16. SPHERES 16 Conclusions / Future Work Motivation: –Update model on-line during a test to account for configuration changes –Want to maintain control performance in terms of stability, efficiency, and accuracy Conclusions –Demonstrated reconfiguration for attitude and position –In process of increasing accuracy in 2 SPHERE case to be sufficient for docking and assembly Future Work –Demonstrate reconfiguration in full assembly test –Introduce flexible dynamics –Augment to include sensor reconfiguration

17. SPHERES 17 Questions?

18. SPHERES 18 Back-up

19. SPHERES 19 Control Reconfiguration Methods A-Priori Information Complete No Information Method of Model DeterminationSegment Properties Operational States Transitions Gain Scheduling (Parlos & Sunkel)Known Multiple Model (Maybeck & Stevens)Known Unknown On-line Model CalculationKnownUnknown System Identification (Wilson et al)Unknown Multiple model reconfiguration (Maybeck and Stevens) –Multiple Kalman filters for each operational states –Transition between models is seamless, based on analysis of measurement residuals On-line model calculation –Takes in a properties vector (eg. p = [Mass, Inertia, Center of Mass, …] ) –Generates the model from the list of properties –Uses the model to generate the appropriate control input ISS Attitude Gain Scheduling (Parlos & Sunkel) –Implemented for docking, series of equilibrium states –Assumes look-up table for mass properties at each equilibrium state System Identification (Wilson et al) –Maneuvers to determine model (mass and inertia) using recursive least squares –Assumes thruster maneuvers

20. SPHERES 20 Approach Center of Mass (CM), Thruster locations w.r.t CM Thruster Number & Directions Thrusters available Mass, Inertia, State Space Model General Controller Gains Sensor locations w.r.t CM Sensors available Estimation statistics

21. SPHERES 21 On-line Model Calculation (2/3) Example of analytic expressions (similar for position gains) Assumes small cross products for inertias Attitude Gains: K = f(p) PD control PID control

22. SPHERES 22 On-line Model Calculation (3/3) Analytic expressions for thruster configuration update Mixing matrix (M): 6 (forces and torques) by num thrusters –Inverse of Mixing matrix converts control vector to thruster forces Control vector input Inverse of Mixing Matrix Thruster forces

23. SPHERES 23 Results: Position & Attitude (1) C1: Satellite Only C2: Satellite Plus Batt Proof Mass