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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 Overview Motivation Coordinating multiple robots Centralized planning

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using a prm planner to compare centralized and decoupled planning for multi robot systems

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

overview
Overview
  • Motivation
  • Coordinating multiple robots
  • Centralized planning
  • Decoupled planning
  • SBL planner
  • Experiment setup
  • Results
  • Summary
  • Comments

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motivation
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?

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coordinating multiple robots
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

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centralized planning
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

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decoupled planning
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

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decoupled planning two schemes
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

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decoupled planning two schemes9
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

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decoupled planning incompleteness
Decoupled planning - Incompleteness
  • Initial configuration Goal configuration
  • Paths generated in first phase
  • No coordinated solution found in second phase

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sbl planner
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

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characteristics of sbl planner
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

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experiment setup
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

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problem i
Problem I

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problem ii
Problem II

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problem iii
Problem III

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results c sbl
Results – C-SBL
  • Result for C-SBL

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results failure rate
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

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results running time
Results – Running time
  • Running time for all 3 planners are comparable
  • Centralize planning is feasible using SBL planner

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summary
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

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comments
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

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thank you for listening
Thank you for listening
  • Questions ?

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Blank slide

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