1. Rajankumar Bhatt December 12, 2003 Slide 1 of 36 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Formation Motion Planning for Payload Transport by Modular Wheeled Mobile Manipulators Rajankumar Bhatt Advisor : Dr. Venkat Krovi Mechanical and Aerospace Engineering Department State University of New York at Buffalo.

2. Rajankumar Bhatt December 12, 2003 Slide 2 of 36 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Agenda Introduction Implementation Results Conclusion Future Work

3. Rajankumar Bhatt December 12, 2003 Slide 3 of 36 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Robot Collectives Smaller robots to perform task of single large robot –Cheaper, less powerful but better performance Issues –Control many robots –Coordinate their actions Types of Cooperation –Information based cooperation –Physical cooperation The CMU Millibots Loosely coupled Tightly coupled Introduction Implementation Results Conclusion FutureWork

4. Rajankumar Bhatt December 12, 2003 Slide 4 of 36 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Formation with Payload A Wheeled Mobile Manipulator Formation of Wheeled Mobile Manipulators Material handling Applications Cooperatively performs tasks that cannot be performed by single mobile robot Re-configurability and accommodation for disturbances Introduction Implementation Results Conclusion FutureWork Increased workspace Redundancy Transporting a Payload

5. Rajankumar Bhatt December 12, 2003 Slide 5 of 36 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo State-of-The-Art Behavior based approach Specify simple behaviors for different goals Emergent behavior by combination of multiple simple behaviors Issue is “How to decompose global behaviors into component modules? ” Advantages are decentralization, limited communication (Balch, T. and Arkin, R. C., 1998; ) Virtual Leader (Includes Leader follower/Virtual structures) Motion of followers specified with respect to that of leader Problem reduces to control of single robot Robots considered as point objects (Shahidi, R.; Shayman, M.; Krishnaprasad, P.S., 1991) Robots considered with nonholonomic constraints (Young, Beard and Kelsey, 2001) Introduction Implementation Results Conclusion FutureWork

6. Rajankumar Bhatt December 12, 2003 Slide 6 of 36 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo State-of-The-Art (Cont’d) Manipulation Behavior-based multiple robot system –(Wang, Z., Nakano, E., Matsukawa, T. and Hanada, K., 1996; Sugar and Kumar, 1999) Cooperative manipulation of object by two robots –(Abou-Samah M. and Krovi, V., 2002) Introduction Implementation Results Conclusion FutureWork Abou-Samah M. and Krovi, V., 2002

7. Rajankumar Bhatt December 12, 2003 Slide 7 of 36 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Mathematical Modeling Homogeneous Transformation Spatial Twist Body Fixed Twist Similarity Transform Introduction Implementation Results Conclusion FutureWork Inertial Frame Moving Frame Preferred representation

8. Rajankumar Bhatt December 12, 2003 Slide 8 of 36 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Mathematical Modeling (Cont’d) More about Twists Twist as linear operator Introduction Implementation Results Conclusion FutureWork Twist Vector

9. Rajankumar Bhatt December 12, 2003 Slide 9 of 36 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Mathematical Modeling (Cont’d) No side ways slip Nonholonomic Constraint can be characterized as: Does not constrain configuration Ability to control 3-dof by 2 inputs However, poses difficulty in control Complex maneuvers may be required Introduction Implementation Results Conclusion FutureWork

10. Rajankumar Bhatt December 12, 2003 Slide 10 of 36 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Mathematical Modeling (Cont’d) Body Fixed Twist based approach General Mobile Manipulator Introduction Implementation Results Conclusion FutureWork

11. Rajankumar Bhatt December 12, 2003 Slide 11 of 36 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Mathematical Modeling (Cont’d) Body Fixed Twist Simple equations in end-effector frame Invariant with respect to selection of global frame General Mobile Manipulator Modules Type I: RRR Mobile Manipulator Type II: RR Mobile Manipulator Type III: R Mobile Manipulator Introduction Implementation Results Conclusion FutureWork

12. Rajankumar Bhatt December 12, 2003 Slide 12 of 36 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo What do we want to do? Point P moving on arbitrary curve Given path and a number of mobile robots Determine optimal motion plans for each mobile robot Subject to Nonholonomic constraints Other regional constraints Using Metrics defined on Introduction Implementation Results Conclusion FutureWork

13. Rajankumar Bhatt December 12, 2003 Slide 13 of 36 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Team-Fixed Frame Without payload With payload Olfati-Saber and Murray, 2002 Any robot location can be origin Align x-axis in the direction of nearest neighbor Belta and Kumar, 2002 Origin located at center of mass Axis directed along principal inertial directions Center of mass of payload Point of reference on payload Introduction Implementation Results Conclusion FutureWork

14. Rajankumar Bhatt December 12, 2003 Slide 14 of 36 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Formation Parameterization Configuration of Frame Configuration of Entire Formation An Alternate Parameterization of Formation (Polar) Relation between Two Parameterizations Introduction Implementation Results Conclusion FutureWork Orientation of mobile robots not considered

15. Rajankumar Bhatt December 12, 2003 Slide 15 of 36 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Metrics (Objective Function) Manipulability (Jacobian) based Performance Measures Yoshikawa’s Measure of Manipulability Condition Number Isotropicity Index Energy (Riemannian metric) based Performance Measures (Zefran, 1996) family of left invariant metrics on (specialized from ) 1Klein 2Park arbitrary 3Energy Introduction Implementation Results Conclusion FutureWork

16. Rajankumar Bhatt December 12, 2003 Slide 16 of 36 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Motion Parameterization Path Parameterization Motion Parameterization Time Parameterization for Introduction Implementation Results Conclusion FutureWork

17. Rajankumar Bhatt December 12, 2003 Slide 17 of 36 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Implementation Introduction Implementation Results Conclusion FutureWork

18. Rajankumar Bhatt December 12, 2003 Slide 18 of 36 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Adaptive Arc-length Parameterization Introduction Implementation Results Conclusion FutureWork

19. Rajankumar Bhatt December 12, 2003 Slide 19 of 36 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Geometric Motion Planning Strategy Curvature Rate of change of tangential angle Radius of Curvature Geometric Motion Planning Strategy (GMPS) requires Team-fixed frame be aligned to Serret-Frenet frame all times Introduction Implementation Results Conclusion FutureWork

20. Rajankumar Bhatt December 12, 2003 Slide 20 of 36 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo In this thesis, we consider. Geometric Motion Planning Strategy (Cont’d) Velocity of Team-fixed Frame Referenced to Team-fixed frame Velocity of Individual Modules Introduction Implementation Results Conclusion FutureWork

21. Rajankumar Bhatt December 12, 2003 Slide 21 of 36 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Geometric Motion Planning Strategy (Cont’d) Klein Metric Energy Metric Formation of Mobile Robots For Screw Motion Klein Metric = constant Introduction Implementation Results Conclusion FutureWork

22. Rajankumar Bhatt December 12, 2003 Slide 22 of 36 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Geometric Motion Planning Strategy (Cont’d) Determination of orientation of Individual modules is secondary stage Orientation and Location are decoupled Select orientation to be aligned with the velocity field Visually: –Direction of nonholonomic constraint = Direction of line joining Origin of frame of individual modules and ICR. Introduction Implementation Results Conclusion FutureWork

23. Rajankumar Bhatt December 12, 2003 Slide 23 of 36 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Results and Validation GMPS applied to formation of three mobile robots –Screw motion –Non-screw (Sinusoidal) motion Objective function –Klein Form –Energy Form Validation using analytical results Introduction Implementation Results Conclusion FutureWork

24. Rajankumar Bhatt December 12, 2003 Slide 24 of 36 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Formation Motion Planning (Cont’d) Energy Metric (Analytical) – Screw Motion Optimal Values (Analytical) Introduction Implementation Results Conclusion FutureWork

25. Rajankumar Bhatt December 12, 2003 Slide 25 of 36 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Formation Motion Planning (Cont’d) Kinetic Energy Metric (Analytical) – Screw Motion For Screw Motion Introduction Implementation Results Conclusion FutureWork

26. Rajankumar Bhatt December 12, 2003 Slide 26 of 36 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Formation Motion Planning (Cont’d) Energy Metric (Numerical) – Screw Motion Regional Constraints Optimal Solution Introduction Implementation Results Conclusion FutureWork

27. Rajankumar Bhatt December 12, 2003 Slide 27 of 36 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Formation Motion Planning (Cont’d) Energy Metric (Analytical) – Sinusoidal Motion Introduction Implementation Results Conclusion FutureWork

28. Rajankumar Bhatt December 12, 2003 Slide 28 of 36 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Formation Motion Planning (Cont’d) Energy Metric (Numerical) – Sinusoidal Motion Introduction Implementation Results Conclusion FutureWork

29. Rajankumar Bhatt December 12, 2003 Slide 29 of 36 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Formation Payload Transport Type III: R Mobile Manipulator Forms a Rigid Virtual Structure Relative locations cannot be changed Screw Motion –Initial Optimal Placement is adequate Non-Screw Motion –No Optimal configuration possible Introduction Implementation Results Conclusion FutureWork

30. Rajankumar Bhatt December 12, 2003 Slide 30 of 36 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Formation Payload Transport (Cont’d) Type II: RR Mobile Manipulator Allows some flexibility in locating with respect to Still restrictive constrained to lie in a circle centered around

31. Rajankumar Bhatt December 12, 2003 Slide 31 of 36 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Formation Payload Transport (Cont’d) Type I: RRR Mobile Manipulator Task frame based parameterization RPR Linkage

32. Rajankumar Bhatt December 12, 2003 Slide 32 of 36 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Formation Payload Transport (Cont’d) Type I: RRR Mobile Manipulator Module frame based parameterization RRR Linkage Introduction Implementation Results Conclusion FutureWork

33. Rajankumar Bhatt December 12, 2003 Slide 33 of 36 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Formation Payload Transport (Cont’d) Equivalence of Parameterization Below 3 equations can be solved for 3 unknowns Results of the unconstrained formation planning can be directly applied Introduction Implementation Results Conclusion FutureWork

34. Rajankumar Bhatt December 12, 2003 Slide 34 of 36 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Conclusion Modular, reconfigurable system Nonholonomic constraints in motion planning Optimal motion plans for formation of mobile robots Validation of numerically obtained results with analytical results Equivalence between the unconstrained case and constrained (payload transport) case. Introduction Implementation Results Conclusion FutureWork

35. Rajankumar Bhatt December 12, 2003 Slide 35 of 36 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Future Work Jacobian based Objective Function Higher order curves rather than Cubic Splines Velocity of Serret-Frenet frame being any constant or even more general case of being variable. Introduction Implementation Results Conclusion FutureWork

36. Rajankumar Bhatt December 12, 2003 Slide 36 of 36 Automation, Robotics and Mechatronics Lab, SUNY at Buffalo Thank You