Visibility-based Probabilistic Roadmaps

Presentation for the course : Advanced Robotics Behdad Soleimani

9 March 2009

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Outline

Overview Definitions Algorithm Analysis Experiments Pros and Cons Experimental Comparison : Narrow Passages Adaptive and Relaxed VPRM

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Overview

Basic PRM Visibility-based PRM

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Definitions

• Local Method (admissibility)

• Roadmap (adjacency)

• Visibility Domain (reachability)

• Free-space Coverage (ε-goodness)

• Visibility Roadmap (undirected set of guards and connection nodes)

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AlgorithmEssence: cover the CSfree with guards, and connect them using connection nodes

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Size of visibility roadmaps : bounded

Termination Criterion, Probabilistic Coverage

Side-effects : due to random generation

Visibility & Connectivity

Analysis

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Experiments (1)

Robot Arm (6DOF)

Local Method : Linear

Roadmap’s size : 26

CPU time : (for solving the first problem)370 sec

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Experiments (1 cont.)

Robot Arm (6DOF)

Local Method : Linear

Roadmap’s size : 26

CPU time : (for solving the first problem)370 sec

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Experiments (2)

Rolling Bridge (4DOF)

Local Method : Manhattan

Roadmap’s size : 25

CPU time : (for solving the first problem)2 sec

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Experiments (2 cont.)

Rolling Bridge (4DOF)

Local Method : Manhattan

Roadmap’s size : 25

CPU time : (for solving the first problem)2 sec

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Pros and Cons Small Size

Termination condition

Two main steps of the PRM-based algorithms : Sampling the CSfree and generating new nodes (more

expensive!) Testing and connecting the node to the existing roadmap (far

less expensive!) Visib-PRM : O(n) , Basic-PRM : O(n2) n: no. of random collision-free configurations

Two main shortcomings: “unlucky” sampling, narrow passages

Note : Visibility-based PRM is NOT a method for solving Narrow Passage Problem, although it tends to perform better in those situations than the Basic PRM.

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Experimental Comparison : Narrow Passages (1)

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Experimental Comparison : Narrow Passages (2)Workspace dimensions : 200 * 200 * 150

Width of rectangular passage : 50

Moving object : 5 blockslength 50 , cross-section 10

• Values averaged over 10 runs• Same set of configurations for both algorithm

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Adaptive & Relaxed VPRM (1)

RELAXED (x) : Relaxed Acceptance Test of VPRM

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Adaptive & Relaxed VPRM (2)

Modified Visibility-based PRM

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References T. Siméon, J.-P. Laumond., and C. Nissoux, “Visibility based

probabilistic roadmaps for motion planning.” Advanced Robotics Journal, 14(6), 2000.

J.-P. Laumond, T. Siméon , “Notes on visibility roadmaps and path planning” 4th Workshop on Algorithmic Foundations of Robotics (WAFR), Hannover, USA (2000).

T-M Bu, Z-J Li, and Z Sun, “Adaptive and Relaxed Visibility-based PRM”, In proc. of IEEE International Conference on Robotics and Biomimetics (ROBIO), pp 174-179, 2005

THANK YOU

During this presentation, approximately 500 children died… two-thirds of them were preventable.