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Visibility-based Probabilistic Roadmaps

Visibility-based Probabilistic Roadmaps. Presentation for the course : Advanced Robotics . Behdad Soleimani. 9 March 2009. Outline. Overview Definitions Algorithm Analysis Experiments Pros and Cons Experimental Comparison : Narrow Passages Adaptive and Relaxed VPRM.

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Visibility-based Probabilistic Roadmaps

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  1. Visibility-based Probabilistic Roadmaps Presentation for the course : Advanced Robotics Behdad Soleimani 9 March 2009

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

  3. Overview Basic PRM Visibility-based PRM

  4. Definitions • Local Method (admissibility) • Roadmap (adjacency) • Visibility Domain (reachability) • Free-space Coverage (ε-goodness) • Visibility Roadmap (undirected set of guards and connection nodes)

  5. Algorithm Essence: cover the CSfree with guards, and connect them using connection nodes

  6. Analysis • Size of visibility roadmaps : bounded • Termination Criterion, Probabilistic Coverage • Side-effects : due to random generation • Visibility & Connectivity

  7. Experiments (1) Robot Arm (6DOF) Local Method : Linear Roadmap’s size : 26 CPU time : (for solving the first problem) 370 sec

  8. Experiments (1 cont.) Robot Arm (6DOF) Local Method : Linear Roadmap’s size : 26 CPU time : (for solving the first problem) 370 sec

  9. Experiments (2) Rolling Bridge (4DOF) Local Method : Manhattan Roadmap’s size : 25 CPU time : (for solving the first problem) 2 sec

  10. Experiments (2 cont.) Rolling Bridge (4DOF) Local Method : Manhattan Roadmap’s size : 25 CPU time : (for solving the first problem) 2 sec

  11. 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.

  12. Experimental Comparison : Narrow Passages (1)

  13. Experimental Comparison : Narrow Passages (2) • Workspace dimensions : • 200 * 200 * 150 • Width of rectangular passage : • 50 • Moving object : • 5 blocks • length 50 , cross-section 10 • Values averaged over 10 runs • Same set of configurations for both algorithm

  14. Adaptive & Relaxed VPRM (1) RELAXED (x) : Relaxed Acceptance Test of VPRM

  15. Adaptive & Relaxed VPRM (2) Modified Visibility-based PRM

  16. 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

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

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