Learned Critical Probabilistic Roadmaps for Robotic Motion ...
Visibility-based Probabilistic Roadmaps
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Transcript of Visibility-based Probabilistic Roadmaps
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.