Air Bearing System for Space Dynamics and Control Simulations Dr. John T. Wen, Professor, Electrical, Computer, & Systems Eng. David Carabis, Ph.D. Student, Mechanical, Aerospace, & Nuclear Eng. Rensselaer Polytechnic Institute September 24, 2017 Gravity Offload Testbeds for Space Robotic Mission Simulation Full-day Workshop at 2017 IROS 1
Overview • Develop technology and perform ground-based testing to support operations for potential satellite servicing missions. • Problem Statement: – Dual arm capture, transport and docking with vision/force feedback – Delay compensation in compliance control – Evaluation on air bearing testbed – Evaluation on space robot dynamic simulation 2
Outline • Air bearing testbed • Outer loop vision and force feedback • Delay compensation in compliance control • Dual arm tracking, grasping, transport, berthing • Grasp slip prevention control • Dynamic simulation • Future Work: – Flexible material modeling, simulation, and manipulation 3
Air Bearing Testbed • Full 3-DOF motion in reduced friction environment (4’x8’) • Self contained, with on-board 3000psi air tank (reduced to 40psi) • Three flat air bearings for max load 150lb (sled mass~25lb) • Run time ~35 min, fill time ~ 50min. 4
Industrial Robot Controller with External Commands • Inner loop: robot joint controller (high rate, high gain) • Outer loop: joint increment (med rate, long latency) • Sensor loop: force/torque, relative position (low rate, not guaranteed real-time) Outer loop f q Inner loop u = ∆ q q c e − t d s q Robot s Sensor Measurements Sensor loop 5
Sensor (Vision and Force) Outer Loop Control f q u = ∆ q x q c Contact F e − t d s Robot q Fwd Kin s Human input x des Visual SLAM Jacobian or Inv Kin Vision Based Control Force F/T Control Sensor F des 6
Control Design Issues • Force/impedance control • Effect of 3me delay • Grasp stability • Redundancy resolu.on • Singularity avoidance • Collision avoidance (self collision, environment) • Joint/load flexibility • Environmental impedance (for inser.on/docking) • Sensor loop non-real-.me • Human interface 7
Multi-Arm Grasp Load Dynamics ~ p 1 C X A T M c α c + b c = i F i x c ~ p 2 C i � I 0 ~ p c A i = ~ − ( R OC p iC ) × I p 1 ~ Contact Kinematics p 2 F i = H ⊥ T H T i F i = 0 η i i Point Contact with Friction H i = [ I, 0] Grasp Model Stable Grasp Condition: i H ⊥ T X A T M c α c + b c = η i = G η N ( G ) = { 0 } i i G = Grasp η ∈ Friction Cone Map 8 A T f s = A T f ∗ s = 0
Outer Loop Based Motion and Force Control Arm Kinematics Use V i * as virtual ~ p 1 C input for x c control x c V i = J i ˙ q i = u i ~ p 2 C Force Control Motion Control ~ p c ~ p 1 (Generalized damper) (P or PI) V ∗ i s = − K s ( f s − f ∗ s ) V ∗ c = − K p ( x c − x ∗ c ) ~ p 2 ( H T ) + AV ∗ Gf s = Gf ∗ s = 0 V ∗ i m = A i V ∗ c , c = 0 Motion/Force Control with Move-Squeeze Decomposition V ∗ i = V ∗ i m + V ∗ i s Collision avoidance: penalty function Berthing: use x c * as virtual input for berthing control 9
Delay Compensation in Force Control Jacobian Inner-Loop Pseudo-Inverse Dynamics Jacobian Time Delays Surface 10
Dual Arm Force Control with Delay Compensation Impedance Controller Smith Predictor Phase Margin x x Gain Margin D. Kruse, J.T. Wen, “Application of the Smith-Astrom Predictor to Robot Force Control,” IEEEE Conference on Automation Science and Engineering (CASE), Gothenburg, Sweden, Aug, 2015. 11
Dual Arm Load Capture (Motoman): Vision+Force • Motoman HSC + Robot Raconteur + • 2ms joint increment command MATLAB/Simulink and measurement • ALVAR-Tag Target Tracking • ~16ms delay + 1 st order filter • Consensus Grasp + Load Transport • Vision loop ~ 30Hz 12
Dual Arm Load Capture (Baxter): Vision+Force • Same controller as Motoman with re- • ~6ms joint increment command tuned gains and measurement (non-real-time) • Camera update < 2Hz (bottleneck • Baxter cameras + force measurements unclear at this point) • ROS + RR/ROS Bridge + MATLAB 13
Desired Squeeze Force Scheduling Fast motion away from contact Gentle contact first and then Slow approach near contact ramp up force (to avoid bouncing) 0 -40 -100 -60 -200 fd (N) fd (N) -300 -80 -400 -100 -500 -600 -120 0 0.1 0.2 0.3 -100 -50 0 d (m) Measured Force (N) 14
Consensus Dual Arm Grasping i = − K i ( x i − x ∗ i ) − K ij (( x i − x ∗ i ) − ( x j − x ∗ j )) V ∗ (+ integral terms) 5 5 0 0 -5 -5 Force (N) Force (N) -10 -10 Left Arm Left Arm -15 -15 Right Arm Right Arm -20 -20 -25 -25 24.5 25 25.5 26 24.5 25 25.5 26 Time (s) Time (s) (a) Centered, vision consensus. (b) Off-centered, vision consensus. 5 5 0 0 -5 Force (N) -5 Force (N) -10 -10 -15 Left Arm Left Arm -15 Right Arm Right Arm -20 -20 -25 -25 24.5 25 25.5 26 24.5 25 25.5 26 Time (s) Time (s) (d) Off-centered, no vision consen- (c) Centered, no vision consensus. sus. 15
Load Transport Oscillatory load Contact pad vibration Left Arm 0 motion at 1 Right Arm Fd rad/sec Force (N) -50 -100 -150 Motion-induced 0 20 40 contact force Time (s) - How to choose squeeze force setpoint f s * in the presence of motion? - How to suppress vibration due to structural flexibility 16
Slip Prevention Control Objective: Maintain stable grasp during motion � � � f ∗ min such that � s i f ∗ si f ∗ s i � f ∗ θ s inom � s i + f m i − e T � n i ( f ∗ s i + f m i ) e n i � f ∗ � ≤ µ d e T n i ( f ∗ s i + f m i ) • Explicit solution in planar two point contacts • Prediction of f m : approximate with projected measured force • Limiting case: f s à ∞ , µ d limited by grasp location 17
Slip Prevention Control If no feasible solution: � � s i + f m i − e T n i ( f ∗ s i + f m i ) e n i � f ∗ � ≤ µ d e T n i ( f ∗ s i + f m i ) • Transport: Slow down object θ motion • Berthing: Reduce berthing contact force 18
7 7 7 7 Slip Prevention Control Experiments TABLE I: Comparison of friction threshold violation. No Compensation ( % ) | µ | > µ d | µ | > 2 µ d | µ | > 3 µ d Threshold Case 1, Mean 42.7 16.6 12.2 Case 1, StdDev 2.2 0.5 2.5 Case 2, Mean 43.6 17.1 6.8 Case 2, StdDev 0.6 1.0 0.6 Compensation ( % ) Threshold | µ | > µ d | µ | > 2 µ d | µ | > 3 µ d Case 1, Mean 18.7 2.2 0.4 Case 1, StdDev 1.2 0.6 0.3 Case 2, Mean 26.4 5.5 1.3 Case 2, StdDev 1.2 0.4 0.2 Left Right 19
Slip Prevention Control Experiments: Berthing Left Right 20
Slip Prevention Control Experiments: Video 21
Space Robot Arm Simulation M ( q )¨ q + C ( q, ˙ q ) ˙ q + F ( ˙ q ) + G ( q ) • Based on current data = τ − J T ( q ) f • Both Newton-Euler and Lagrange-Euler in MATLAB • Joint Friction (linear region to avoid discontinuity) • Joint Level Control (based on existing controller design) • Contact Dynamics (simple switching of dynamics) • Gearing/joint flexibility effect to be added 22
Future Work • Flexible Dynamics Suppression (Input Shaping) • Docking and grasping with Marman bands • Space arm simulation (joint flexibility, grasp stability, docking) • Multiple flying robot grasping / transport/docking • Flexible material modeling and handling 23
Soft Material Simulation Bullet ◦ Posi.on-based dynamics ◦ Approxima.on of physical interac.ons ◦ Fast computa.on ◦ Solu.on for link distance aNer external forces applied (pulling, gravity, etc.) Simula.on parameters: minimize distance from measured point cloud ◦ Known grasp loca.ons ◦ Blue : measured point cloud ◦ Green : cloth es.ma.on Loose fit Too tight fit Best fit 24
Other Issues Effect of non-real-time implementation for sensor feedback loop Beyond bimanual manipulation: 25
Acknowledgment Thanks to NASA Goddard for supporting this research and Brian Roberts, Craig Carignan, and Billy Gallagher for guidance and support. Thanks to Center for Automation Technologies and Systems (CATS) at RPI (supported by New York State Office of Science, Technology and Innovation, NYSTAR), and staff and students (Glenn Saunders, Ken Myers, Dan Kruse) for equipment, facilities and technical support. 26
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