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

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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

NUS CS5247


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 demo

Coordinating multiple robots (Demo)

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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 schemes1

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 configurationGoal 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

Blank slide

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Blank slide

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