1. NUS CS5247 Using a PRM Planner to Compare Centralized and Decoupled Planning for Multi-Robot Systems By Gildardo Sánchez and Jean-Claude Latombe In Proc. IEEE Int. Conf. on Robotics and Automation 2002 Presented by Melvin Zhang

2. NUS CS52472 Overview  Motivation  Coordinating multiple robots  Centralized planning  Decoupled planning  SBL planner  Experiment setup  Results  Summary  Comments

3. NUS CS52473 Motivation  Some industrial settings (spot welding) requires 4-10 robots with 20-60 dof each  Manual programming time consuming and error prone  Multi robot planning can be classified as centralized decoupled  Decoupled approach is prevalent, as lost of completeness is assumed to be small  How valid is this statement?

4. NUS CS52474 Coordinating multiple robots (Demo)

5. NUS CS52475 Coordinating multiple robots  Assuming p robots with n dof each  Centralized planning Treat multiple robots as a single robot Plan in the composite C-space Complexity ~ e np  Decoupled planning Plan for each robot independently Coordinate them later Complexity ~ pe n

6. NUS CS52476 Centralized planning  Reduce problem to planning for single robot  Collisions between robots are self-collisions of the single composite robot  Advantages Complete, if the underlying planner is complete  Drawbacks Computationally expensive, Not applicable when global state of all robots is unknown

7. NUS CS52477 Decoupled planning  Plans path of each robot independently  Coordinate them later  Several schemes Velocity turning Robot prioritization  Advantages Faster as C-space has fewer dimensions  Drawbacks Incomplete No coordinated trajectory of paths found in first phase

8. NUS CS52478 Decoupled planning – Two schemes  Velocity tuning Separately plan a path of each robot to avoid collision with obstacles Compute the trajectory of the robots to avoid inter- robot collision  Global coordination – plan in [0,1] p  Pairwise coordination – plan in [0,1] 2  After path is fixed, dof of each robot is 1  Pairwise coordination plan s 1 and s 2 plan s 1,2 with s 3,... plan s 1,...,n-1 with s n

9. NUS CS52479 Decoupled planning – Two schemes  Robot prioritization Plan path of the first robot in its C-space Plan trajectory of i th robot assuming that robots 1,…,i-1 are moving obstacles

10. NUS CS524710 Decoupled planning - Incompleteness  Initial configurationGoal configuration  Paths generated in first phase  No coordinated solution found in second phase

11. NUS CS524711 SBL planner  Single-query Roadmap is used to answer a single planning query  Bi-directional Grow a tree of milestones from both start and end configuration  Lazy in checking collision Avoid unnecessary collision checking on edges 4-40 times faster than classical single-query bidirectional PRM planner

12. NUS CS524712 Characteristics of SBL planner  Plot of number of failure vs max milestones allowed (S)  Two thresholds S min and S max for a problem instance  If (S < S min ) planner fails consistently  If (S > S max ) planner succeeds consistently

13. NUS CS524713 Experiment setup  Planners Centralized planning (C-SBL) Decoupled planning, global coordination (DG-SBL) Decoupled planning, pairwise coordination (DP-SBL)  Three problem instances, {PI, PII, PIII}  Number of robots involved, {2, 4, 6}  Number of runs 100 for C-SBL 20 for DG-SBL and DP-SBL  For each call to the SBL planner, at most 50,000 milestones are allowed

14. NUS CS524714 Problem I

15. NUS CS524715 Problem II

16. NUS CS524716 Problem III

17. NUS CS524717 Results – C-SBL  Result for C-SBL

18. NUS CS524718 Results – Failure rate  Rate of failure increases sharply for 4 and 6 robots  Failure occurs during coordination  Successful run of decoupled planner, no of milestones smaller than 50,000 -> failure due to incompleteness of decoupled approach

19. NUS CS524719 Results – Running time  Running time for all 3 planners are comparable  Centralize planning is feasible using SBL planner

20. NUS CS524720 Summary  Decoupled planning may not find a solution when tight coordination is required Loss of completeness is significant in practice  Using SBL, planning time for decoupled and centralized planning is comparable Centralized planning is technically feasible

21. NUS CS524721 Comments  Tight coordination is specified using specific problem instances Similar to the concept of expansiveness, is it possible to develop some characterization of “tight coordination”?  Centralized and decoupled can be viewed as two extremes of coordination Can we find a continuum of planners in which the level of coordination can be parameterized? One idea is to use a hierarchy of robots

22. NUS CS524722 Thank you for listening  Questions ?

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