1. Presentation for the course : Advanced Robotics Behdad Soleimani 9 March 2009

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

3. 3 Basic PRMVisibility-based PRM

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

5. 5 Essence: cover the CS free with guards, and connect them using connection nodes

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

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

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

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

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

11.  Small Size  Termination condition  Two main steps of the PRM-based algorithms :  Sampling the CS free 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(n 2 ) n: no. of random collision-free configurations  Two main shortcomings: “unlucky” sampling, narrow passages 11 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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13. 13 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. 14 RELAXED (x) : Relaxed Acceptance Test of VPRM

15. 15 Modified Visibility-based PRM

16.  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” 4 th 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 16

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