1. Chin Pei Tang May 3, 2004 Slide 1 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Chin Pei Tang (chintang@eng.buffalo.edu) Advisor : Dr. Venkat Krovi Mechanical and Aerospace Engineering State University of New York at Buffalo Manipulability-Based Analysis of Cooperative Payload Transport by Robot Collectives

2. Chin Pei Tang May 3, 2004 Slide 2 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Agenda Motivation & Our System Literature Survey & Research Issues Kinematic Model Twist-Distribution Analysis Manipulability Cooperative Systems Conclusion & Future Work Part I Part II

3. Chin Pei Tang May 3, 2004 Slide 3 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo 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. Chin Pei Tang May 3, 2004 Slide 4 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo 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. Chin Pei Tang May 3, 2004 Slide 5 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Features Accommodate changes in the relative configuration Detect relative configuration changes Compensate for external disturbances Using the compliant linkage Using sensed articulation Using redundant actuation of the bases Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

6. Chin Pei Tang May 3, 2004 Slide 6 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo 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. Chin Pei Tang May 3, 2004 Slide 7 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo 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. Chin Pei Tang May 3, 2004 Slide 8 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo 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 MARSUniv. of Alberta CRIP NASA Cooperative Rovers Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

9. Chin Pei Tang May 3, 2004 Slide 9 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo 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. Chin Pei Tang May 3, 2004 Slide 10 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo 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. Chin Pei Tang May 3, 2004 Slide 11 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Mathematical Preliminaries Twist Matrix  Twist Vector Similarity Transformation Body-fixed Twist Homogeneous Matrix Representation Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

12. Chin Pei Tang May 3, 2004 Slide 12 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Kinematic Model Mobile Platform Reaching any point in the plane Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

13. Chin Pei Tang May 3, 2004 Slide 13 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Kinematic Model Nonholonomic Constraints Mobile Platform Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

14. Chin Pei Tang May 3, 2004 Slide 14 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Kinematic Model Nonholonomic Constraints Mobile Platform Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

15. Chin Pei Tang May 3, 2004 Slide 15 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Kinematic Model Mobile Platform Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

16. Chin Pei Tang May 3, 2004 Slide 16 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Kinematic Model Manipulator Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

17. Chin Pei Tang May 3, 2004 Slide 17 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Kinematic Model Manipulator Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

18. Chin Pei Tang May 3, 2004 Slide 18 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Kinematic Model Twist Vectors Assembled Jacobian Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

19. Chin Pei Tang May 3, 2004 Slide 19 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo 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. Chin Pei Tang May 3, 2004 Slide 20 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Twist-Distribution Analysis Partition the Jacobian Passive Distributions Active Distributions Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

21. Chin Pei Tang May 3, 2004 Slide 21 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Twist-Distribution Analysis Can any arbitrary twist be realized using only the active distribution? Feasibility check Not constructive Reciprocal Wrench Alternate constructive approach Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

22. Chin Pei Tang May 3, 2004 Slide 22 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Condition: Transform an arbitrary twist from {E k } to {M}: 0 The Motion Planning Strategy Given arbitrary twist To understand this condition better: Achieved by aligning the forward travel direction with the direction of the velocity Twist-Distribution Analysis Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

23. Chin Pei Tang May 3, 2004 Slide 23 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Manipulability Jacobian Matrix Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion Joint manipulation rates spaceTask 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

24. Chin Pei Tang May 3, 2004 Slide 24 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Manipulability – SVD Singular Value Decomposition Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

25. Chin Pei Tang May 3, 2004 Slide 25 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo RR Manipulator Example Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

26. Chin Pei Tang May 3, 2004 Slide 26 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo 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. Chin Pei Tang May 3, 2004 Slide 27 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Yoshikawa’s Measure Condition Number Isotropy Index Adopted measure Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion RR Manipulator Example

28. Chin Pei Tang May 3, 2004 Slide 28 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Manipulability (Closed-Loop) Generalized Coordinates Forward Kinematic Closed-Loop Kinematic Constraints Not easy to compute Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

29. Chin Pei Tang May 3, 2004 Slide 29 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Manipulability (Closed-Loop) Partition according to active/passive manipulation variable rates Exact ActuationRedundant Actuation Manipulability Jacobian Solved explicitly Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

30. Chin Pei Tang May 3, 2004 Slide 30 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Cooperative Model Team up End-effectors need to be re-aligned Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

31. Chin Pei Tang May 3, 2004 Slide 31 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Kinematic Model (with end-effector offset angle) Similarity Transformation Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

32. Chin Pei Tang May 3, 2004 Slide 32 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo 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. Chin Pei Tang May 3, 2004 Slide 33 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Simulation Parameters (3-RRR Nomenclature) Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

34. Chin Pei Tang May 3, 2004 Slide 34 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Case I: MB static R1 actuated Generalized Coordinates Forward Kinematics General Constraints Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

35. Chin Pei Tang May 3, 2004 Slide 35 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Case Study I-A Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

36. Chin Pei Tang May 3, 2004 Slide 36 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Case Study I-B Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

37. Chin Pei Tang May 3, 2004 Slide 37 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Case II: MB static, R2 actuated Generalized Coordinates Forward Kinematics General Constraints Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

38. Chin Pei Tang May 3, 2004 Slide 38 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Case II: MB static, R2 actuated Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

39. Chin Pei Tang May 3, 2004 Slide 39 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Case III: MB moves, R1 and R2 passive Generalized Coordinates Forward Kinematics General Constraints Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

40. Chin Pei Tang May 3, 2004 Slide 40 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Self-Motion Feasible motions of passive joints due to the actuations but not violating constraints Feasible self-motion when all the active joints locked Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion Underconstrained Dimension of self-motion manifold Lock this number of joints

41. Chin Pei Tang May 3, 2004 Slide 41 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Self-Motion Lock this number of joints 2 Cases: - Locking R1 - Locking R2 Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

42. Chin Pei Tang May 3, 2004 Slide 42 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Case IV: MB moves, R1 locked Generalized Coordinates Forward Kinematics General Constraints Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

43. Chin Pei Tang May 3, 2004 Slide 43 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Case IV: MB moves, R1 locked Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

44. Chin Pei Tang May 3, 2004 Slide 44 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Case V: MB moves, R2 locked Generalized Coordinates Forward Kinematics General Constraints Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

45. Chin Pei Tang May 3, 2004 Slide 45 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Case V: MB moves, R2 locked Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

46. Chin Pei Tang May 3, 2004 Slide 46 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Case Study – Configuration Optimization Subject to: Closed-Kinematic Loop Constraints Constrained Optimization Problem Unconstrained Optimization Problem Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

47. Chin Pei Tang May 3, 2004 Slide 47 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Configuration Optimization – Case IV Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

48. Chin Pei Tang May 3, 2004 Slide 48 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Configuration Optimization – Case V Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

49. Chin Pei Tang May 3, 2004 Slide 49 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo 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. Chin Pei Tang May 3, 2004 Slide 50 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Future Work Global Manipulability Force Manipulability Singularity Analysis Decentralized Control Redundant Actuation Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

51. Chin Pei Tang May 3, 2004 Slide 51 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Thank You! Acknowledgments: Dr. V. Krovi Dr. T. Singh Dr. J. L. Crassidis & all the audience…

52. Chin Pei Tang May 3, 2004 Slide 52 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Twist Matrix as Velocity Operator

53. Chin Pei Tang May 3, 2004 Slide 53 of 51 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Single Module Payload Transport