Chin Pei Tang (chintang@eng.buffalo) Advisor : Dr. Venkat Krovi

1. Manipulability-Based Analysis of Cooperative Payload Transport by Robot Collectives Chin Pei Tang (chintang@eng.buffalo.edu) Advisor : Dr. Venkat Krovi Mechanical and Aerospace Engineering State University of New York at Buffalo

2. Part I Part II Agenda • Motivation & Our System • Literature Survey & Research Issues • Kinematic Model • Twist-Distribution Analysis • Manipulability • Cooperative Systems • Conclusion & Future Work

3. Motivation • Why Cooperation? • Tasks are too complex • Distinct benefits – “Two hands are better than one” • Instead of building a single all-powerful system, build multiple simpler systems • Motivated by the biological communities Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

4. Our System • Flexible, scalable and modular framework for cooperative payload transport • Autonomous wheeled mobile manipulator • Differentially-driven wheeled mobile robots (DD-WMR) • Multi-link manipulator mounted on the top Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

5. Features Accommodate changes in the relative configuration Using the compliant linkage Detect relative configuration changes Using sensed articulation Compensate for external disturbances Using redundant actuation of the bases Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

6. Research Issues • Challenges • Nonholonomic (wheel) / holonomic (closed-loop) constraints • Mobility / workspace increased (but also increases redundancy) • Mixture of active/passive components Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

7. Literature Survey • Applications of Robot Collectives • Collective foraging, map-building and reconnaissance • Coordination & Control • Formation Paradigm • Leader-follower [Desai et. al., 2001] • Virtual structures [Lewis and Tan, 1997] • Mixture of approaches [Leonard and Fiorelli, 2001], [Lawton, Beard and Young, 2003] No physical interaction Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

8. Literature Survey • Physical Interaction • Teams of simple robots • box pushing [Stilwell and Bay, 1993], [Donald et. al., 1997] • caging [Pereira et. al., 2002], [Wang & Kumar, 2002] • Teams of mobile manipulators [Khatib et. al., 1996] • Design modifications [Kosuge et. al., 1998], [Humberstone & Smith, 2000] Upenn MARS Univ. of Alberta CRIP NASA Cooperative Rovers Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

9. Literature Survey • Performance Measures • Single agent • Service angle [Vinogradov et. al, 1971], conditioning [Yang and Lai, 1985], manipulability [Yoshikawa, 1985], singularity [Gosselin and Angeles, 1990], dexterity [Kumar and Waldron, 1981], etc. • Multiple agents (Robot teams) • Social entropy – Measuring diversity of robots in a team (Information-theoretic) [Balch, 2000] • Kinetic energy – Left-invariant Riemannian metrics [Bhatt et. al., 2004] • Manipulability • Serial chain – Yoshikawa’s measure [Yoshikawa, 1985], condition number [Craig and Salisbury, 1982], isotropy index [Zanganeh and Angeles, 1997] • Closed chain [Bicchi and Prattichizza, 2000], [Wen and Wilfinger, 1999] Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

10. Research Issues • Part I – Physical Cooperation • System level constraints • Motion planning strategy • Part II – Performance Evaluation & Optimization • Performance measures • Formulation that takes holonomic/nonholonomic constraints and active/passive joints into account • Different actuation schemes • Optimal configuration Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

11. Mathematical Preliminaries Homogeneous Matrix Representation Body-fixed Twist Similarity Transformation Twist Matrix  TwistVector Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

12. Mobile Platform Kinematic Model Reaching any point in the plane Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

13. Nonholonomic Constraints Kinematic Model Mobile Platform Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

14. Nonholonomic Constraints Kinematic Model Mobile Platform Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

15. Kinematic Model Mobile Platform Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

16. Kinematic Model Manipulator Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

17. Kinematic Model Manipulator Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

18. Assembled Jacobian Kinematic Model Twist Vectors Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

19. Mobility Verification • Verify that arbitrary end-effector motion is feasible. • Partitioning of feasible motion distribution: • Actively-realizable (using wheeled bases) • Passively-accommodating (using articulations) • Configuration dependent partitioning • Steer the actively-realizable vector-fields Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

20. Passive Distributions Active Distributions Twist-Distribution Analysis Partition the Jacobian Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

21. Feasibility check Alternate constructive approach Reciprocal Wrench Twist-Distribution Analysis Can any arbitrary twist be realized using only the active distribution? Not constructive Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

22. 0 Twist-Distribution Analysis Given arbitrary twist Condition: To understand this condition better: Transform an arbitrary twist from {Ek} to {M}: Achieved by aligning the forward travel direction with the direction of the velocity The Motion Planning Strategy Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

23. Manipulability • Jacobian Matrix Joint manipulation rates space Task velocity space Manipulability is defined as the measure of the flexibility of the manipulator to transmit the end-effector motion in response to a unit norm motion of the rates of the active joints in the system Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

24. Manipulability – SVD • Singular Value Decomposition Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

25. RR Manipulator Example Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

26. Manipulability Indices • Yoshikawa’s Measure (Volume of Ellipsoid) • Condition Number • Isotropy Index Not able to distinguish the ratio of major/minor axes of ellipsoid Value goes out of bound at singular position Better numerical behavior Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

27. RR Manipulator Example Yoshikawa’s Measure Condition Number Adopted measure Isotropy Index Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

28. Manipulability (Closed-Loop) Generalized Coordinates Forward Kinematic Closed-Loop Kinematic Constraints Not easy to compute Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

29. Manipulability (Closed-Loop) Partition according to active/passive manipulation variable rates Exact Actuation Redundant Actuation Manipulability Jacobian Solved explicitly Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

30. Cooperative Model Team up End-effectors need to be re-aligned Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

31. Kinematic Model (with end-effector offset angle) Similarity Transformation Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

32. Simulation • Step 1: Identify • Step 2: Construct manipulability Jacobian • Step 3: Compute isotropy index • Case I – MB static, R1 actuated • Case II – MB static, R2 actuated • Case III – MB moves, R1 & R2 passive • Case IV – MB moves, R1 locked • Case V – MB moves, R2 locked Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

33. Simulation Parameters (3-RRR Nomenclature) Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

34. Case I: MB static R1 actuated Generalized Coordinates Forward Kinematics General Constraints Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

35. Case Study I-A Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

36. Case Study I-B Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

37. Case II: MB static, R2 actuated Generalized Coordinates Forward Kinematics General Constraints Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

38. Case II: MB static, R2 actuated Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

39. Case III: MB moves, R1 and R2 passive Generalized Coordinates Forward Kinematics General Constraints Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

40. Self-Motion Feasible motions of passive joints due to the actuations but not violating constraints Feasible self-motion when all the active joints locked Underconstrained Lock this number of joints Dimension of self-motion manifold Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

41. Self-Motion Lock this number of joints • 2 Cases: • Locking R1 • Locking R2 Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

42. Case IV: MB moves, R1 locked Generalized Coordinates Forward Kinematics General Constraints Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

43. Case IV: MB moves, R1 locked Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

44. Case V: MB moves, R2 locked Generalized Coordinates Forward Kinematics General Constraints Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

45. Case V: MB moves, R2 locked Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

46. Subject to: Closed-Kinematic Loop Constraints Case Study – Configuration Optimization Constrained Optimization Problem Unconstrained Optimization Problem Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

47. Configuration Optimization – Case IV Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

48. Configuration Optimization – Case V Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

49. Conclusion • Modular Formulation • Motion-Distribution Analysis • Evaluation of Performance Measures • Manipulability Jacobian Matrix Formulation • Effect of Different Actuation Schemes • Optimal Configuration Determination Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

50. Future Work • Global Manipulability • Force Manipulability • Singularity Analysis • Decentralized Control • Redundant Actuation Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion