Comparing Centralized and Decoupled Planning in Multi-Robot Systems Using a PRM Planner

1. 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 NUS CS5247

2. Overview • Motivation • Coordinating multiple robots • Centralized planning • Decoupled planning • SBL planner • Experiment setup • Results • Summary • Comments NUS CS5247

3. 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? NUS CS5247

4. Coordinating multiple robots (Demo) NUS CS5247

5. 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 ~ enp • Decoupled planning • Plan for each robot independently • Coordinate them later • Complexity ~ pen NUS CS5247

6. 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 NUS CS5247

7. 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 NUS CS5247

8. 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 s1 and s2 • plan s1,2 with s3, • ... plan s1,...,n-1 with sn NUS CS5247

9. Decoupled planning – Two schemes • Robot prioritization • Plan path of the first robot in its C-space • Plan trajectory of ith robot assuming that robots 1,…,i-1 are moving obstacles NUS CS5247

10. Decoupled planning - Incompleteness • Initial configuration Goal configuration • Paths generated in first phase • No coordinated solution found in second phase NUS CS5247

11. 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 NUS CS5247

12. Characteristics of SBL planner • Plot of number of failure vs max milestones allowed (S) • Two thresholds Smin and Smax for a problem instance • If (S < Smin) planner fails consistently • If (S > Smax) planner succeeds consistently NUS CS5247

13. 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 NUS CS5247

14. Problem I NUS CS5247

15. Problem II NUS CS5247

16. Problem III NUS CS5247

17. Results – C-SBL • Result for C-SBL NUS CS5247

18. 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 NUS CS5247

19. Results – Running time • Running time for all 3 planners are comparable • Centralize planning is feasible using SBL planner NUS CS5247

20. 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 NUS CS5247

21. 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 NUS CS5247

22. Thank you for listening • Questions ? NUS CS5247

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