1. Workspace Analysis in Multirobot Manipulation International Symposium on Robotics Stockholm, Sweden. Oct 7-11, 2002 Workspace Analysis in Multirobot Manipulation Ramon Costa-Castelló, Luis Basañez

2. Workspace Analysis in Multirobot Manipulation International Symposium on Robotics Stockholm, Sweden. Oct 7-11, 2002 CONTENTS Introduction Basic Definitions Multirobot System Analysis Dexterous Workspace Reachable Workspace Application to RX-90 robot Dexterous Figure Construction Reachable Figure Construction Two RX-90 cell Conclusions

3. Workspace Analysis in Multirobot Manipulation International Symposium on Robotics Stockholm, Sweden. Oct 7-11, 2002 INTRODUCTION Multirobot Cell

4. Workspace Analysis in Multirobot Manipulation International Symposium on Robotics Stockholm, Sweden. Oct 7-11, 2002 INTRODUCTION Multirobot Manipulation Advantages Load Capacity Increase Dexterity Improvement Flexible Objects Multirobot Manipulation Drawbacks Coordination Needed Workspace Reduction

5. Workspace Analysis in Multirobot Manipulation International Symposium on Robotics Stockholm, Sweden. Oct 7-11, 2002 INTRODUCTION Workspace Approaches Analytical Methods Singularity Analysis Exact approach Volumetric Methods Workspace discretization Approximation Obstacles Intersection Approach Intersection of several geometric figures Quicker approach Work cell Design capabilities

6. Workspace Analysis in Multirobot Manipulation International Symposium on Robotics Stockholm, Sweden. Oct 7-11, 2002 CONTENTS Introduction  Basic Definitions Multirobot System Analysis Dexterous Workspace Reachable Workspace Application to RX-90 robot Dexterous Figure Construction Reachable Figure Construction Two RX-90 cell Conclusions

7. Workspace Analysis in Multirobot Manipulation International Symposium on Robotics Stockholm, Sweden. Oct 7-11, 2002 The kinematics f of a mechanism is the relation between the configuration space C and the operational space O Workspace: elements of O in which the robot end-effector can be placed in Reachable Workspace: set of positions reachable by the robot end-effector in at least one orientation Dexterous workspace: set of positions reachable by the robot in all orientations BASIC DEFINITIONS

8. Workspace Analysis in Multirobot Manipulation International Symposium on Robotics Stockholm, Sweden. Oct 7-11, 2002 CONTENTS Introduction Basic Definitions  Multirobot System Analysis Dexterous Workspace Reachable Workspace Application to RX-90 robot Dexterous Figure Construction Reachable Figure Construction Two RX-90 cell Conclusions

9. Workspace Analysis in Multirobot Manipulation International Symposium on Robotics Stockholm, Sweden. Oct 7-11, 2002 MULTIROBOT SYSTEMS ANALYSIS Individual kinematics Multirobot System Configuration Space

10. Workspace Analysis in Multirobot Manipulation International Symposium on Robotics Stockholm, Sweden. Oct 7-11, 2002 MULTIROBOT SYSTEMS ANALYSIS Position and Orientation Constraining Equations

11. Workspace Analysis in Multirobot Manipulation International Symposium on Robotics Stockholm, Sweden. Oct 7-11, 2002 MULTIROBOT SYSTEMS ANALYSIS Dexterous Workspace

12. Workspace Analysis in Multirobot Manipulation International Symposium on Robotics Stockholm, Sweden. Oct 7-11, 2002 MULTIROBOT SYSTEMS ANALYSIS Dexterous Workspace

13. Workspace Analysis in Multirobot Manipulation International Symposium on Robotics Stockholm, Sweden. Oct 7-11, 2002 MULTIROBOT SYSTEMS ANALYSIS Dexterous Workspace

14. Workspace Analysis in Multirobot Manipulation International Symposium on Robotics Stockholm, Sweden. Oct 7-11, 2002 MULTIROBOT SYSTEMS ANALYSIS Dexterous Workspace

15. Workspace Analysis in Multirobot Manipulation International Symposium on Robotics Stockholm, Sweden. Oct 7-11, 2002 MULTIROBOT SYSTEMS ANALYSIS Dexterous Workspace

16. Workspace Analysis in Multirobot Manipulation International Symposium on Robotics Stockholm, Sweden. Oct 7-11, 2002 MULTIROBOT SYSTEMS ANALYSIS Dexterous Workspace

17. Workspace Analysis in Multirobot Manipulation International Symposium on Robotics Stockholm, Sweden. Oct 7-11, 2002 MULTIROBOT SYSTEMS ANALYSIS Dexterous Workspace

18. Workspace Analysis in Multirobot Manipulation International Symposium on Robotics Stockholm, Sweden. Oct 7-11, 2002 Dexterous Workspace Definition Expression Manipulation MULTIROBOT SYSTEMS ANALYSIS

19. Workspace Analysis in Multirobot Manipulation International Symposium on Robotics Stockholm, Sweden. Oct 7-11, 2002 Workspace Dexterous Figure Dexterous Figure definition Dexterous Workspace from Dexterous Figure MULTIROBOT SYSTEMS ANALYSIS

20. Workspace Analysis in Multirobot Manipulation International Symposium on Robotics Stockholm, Sweden. Oct 7-11, 2002 MULTIROBOT SYSTEMS ANALYSIS Reachable Workspace

21. Workspace Analysis in Multirobot Manipulation International Symposium on Robotics Stockholm, Sweden. Oct 7-11, 2002 MULTIROBOT SYSTEMS ANALYSIS Reachable Workspace

22. Workspace Analysis in Multirobot Manipulation International Symposium on Robotics Stockholm, Sweden. Oct 7-11, 2002 MULTIROBOT SYSTEMS ANALYSIS Reachable Workspace

23. Workspace Analysis in Multirobot Manipulation International Symposium on Robotics Stockholm, Sweden. Oct 7-11, 2002 MULTIROBOT SYSTEMS ANALYSIS Reachable Workspace

24. Workspace Analysis in Multirobot Manipulation International Symposium on Robotics Stockholm, Sweden. Oct 7-11, 2002 MULTIROBOT SYSTEMS ANALYSIS Reachable Workspace

25. Workspace Analysis in Multirobot Manipulation International Symposium on Robotics Stockholm, Sweden. Oct 7-11, 2002 MULTIROBOT SYSTEMS ANALYSIS Reachable Workspace

26. Workspace Analysis in Multirobot Manipulation International Symposium on Robotics Stockholm, Sweden. Oct 7-11, 2002 MULTIROBOT SYSTEMS ANALYSIS Reachable Workspace

27. Workspace Analysis in Multirobot Manipulation International Symposium on Robotics Stockholm, Sweden. Oct 7-11, 2002 MULTIROBOT SYSTEMS ANALYSIS Reachable Workspace

28. Workspace Analysis in Multirobot Manipulation International Symposium on Robotics Stockholm, Sweden. Oct 7-11, 2002 MULTIROBOT SYSTEMS ANALYSIS Reachable Workspace

29. Workspace Analysis in Multirobot Manipulation International Symposium on Robotics Stockholm, Sweden. Oct 7-11, 2002 Reachable Space Approximation Reachable Figure Definition Reachable Workspace from Reachable Figure Reachable Figure Workspace MULTIROBOT SYSTEMS ANALYSIS Reachable Figure

30. Workspace Analysis in Multirobot Manipulation International Symposium on Robotics Stockholm, Sweden. Oct 7-11, 2002 CONTENTS Introduction Basic Definitions Multirobot System Analysis Dexterous Workspace Reachable Workspace  Application to RX-90 robot Dexterous Figure Construction Reachable Figure Construction Two RX-90 cell Conclusions

31. Workspace Analysis in Multirobot Manipulation International Symposium on Robotics Stockholm, Sweden. Oct 7-11, 2002 RX-90 robot APPLICATION TO RX-90 ROBOT

32. Workspace Analysis in Multirobot Manipulation International Symposium on Robotics Stockholm, Sweden. Oct 7-11, 2002 RX-90 Configuration Space section RX-90 Work Space section APPLICATION TO RX-90 ROBOT

33. Workspace Analysis in Multirobot Manipulation International Symposium on Robotics Stockholm, Sweden. Oct 7-11, 2002 RX-90 3D Workspace RX-90 selected sections APPLICATION TO RX-90 ROBOT

34. Workspace Analysis in Multirobot Manipulation International Symposium on Robotics Stockholm, Sweden. Oct 7-11, 2002 RX-90 Dexterous Figure Construction Scheme APPLICATION TO RX-90 ROBOT Dexterous Workspace

35. Workspace Analysis in Multirobot Manipulation International Symposium on Robotics Stockholm, Sweden. Oct 7-11, 2002 Reachable figure for APPLICATION TO RX-90 ROBOT Reachable Figure

36. Workspace Analysis in Multirobot Manipulation International Symposium on Robotics Stockholm, Sweden. Oct 7-11, 2002 APPLICATION TO RX-90 ROBOT Reachable Figure Reachable figure for

37. Workspace Analysis in Multirobot Manipulation International Symposium on Robotics Stockholm, Sweden. Oct 7-11, 2002 CONTENTS Introduction Basic Definitions Multirobot System Analysis Dexterous Workspace Reachable Workspace Application to RX-90 robot Dexterous Figure Construction Reachable Figure Construction  Two RX-90 cell Conclusions

38. Workspace Analysis in Multirobot Manipulation International Symposium on Robotics Stockholm, Sweden. Oct 7-11, 2002 Cell Picture TWO RX-90 CELL

39. Workspace Analysis in Multirobot Manipulation International Symposium on Robotics Stockholm, Sweden. Oct 7-11, 2002 Reference Robot Workspace and Reachable Figure TWO RX-90 CELL

40. Workspace Analysis in Multirobot Manipulation International Symposium on Robotics Stockholm, Sweden. Oct 7-11, 2002 TWO RX-90 CELL Reachable Workspace

41. Workspace Analysis in Multirobot Manipulation International Symposium on Robotics Stockholm, Sweden. Oct 7-11, 2002 CONTENTS Introduction Basic Definitions Multirobot System Analysis Dexterous Workspace Reachable Workspace Application to RX-90 robot Dexterous Figure Construction Reachable Figure Construction Two RX-90 cell  Conclusions

42. Workspace Analysis in Multirobot Manipulation International Symposium on Robotics Stockholm, Sweden. Oct 7-11, 2002 A new method to analyze multirobot workspace has been presented. The method is based in computing the intersection of the reference manipulator workspace and the reachable/dexterous figure of the other robots. The method has been applied to PUMA like manipulators. Further work : Introduction of orientation kinematics. CONCLUSIONS

43. Workspace Analysis in Multirobot Manipulation International Symposium on Robotics Stockholm, Sweden. Oct 7-11, 2002 Robots in the same Position and different Orientation

44. Workspace Analysis in Multirobot Manipulation International Symposium on Robotics Stockholm, Sweden. Oct 7-11, 2002 Orientation Range Analysis

45. Workspace Analysis in Multirobot Manipulation International Symposium on Robotics Stockholm, Sweden. Oct 7-11, 2002 Further Works Orientation Range Analysis through Analytic Methods Automatic Work Cell Design (Position and Orientation)