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Probabilistic Roadmap

Probabilistic Roadmap. Hadi Moradi. Overview. What is PRM? What are previous approaches? What’s the algorithm? Examples. What is it?. A planning method which computes collision-free paths for robots of virtually any type moving among stationary obstacles. Problems before PRMs.

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Probabilistic Roadmap

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  1. Probabilistic Roadmap Hadi Moradi

  2. Overview • What is PRM? • What are previous approaches? • What’s the algorithm? • Examples

  3. What is it? • A planning method which computes collision-free paths for robots of virtually any type moving among stationary obstacles

  4. Problems before PRMs • Hard to plan for many dof robots • Computation complexity for high-dimensional configuration spaces would grow exponentially • Potential fields run into local minima • Complete, general purpose algorithms are at best exponential and have not been implemented

  5. Weaker Completeness • Complete planner  • Heuristic planner  • Probabilistic completeness:

  6. Motivation • Geometric complexity • Space dimensionality

  7. Example 360 270 180 a 90 a x 0 x 0.25 0.75 0.5 1.0 PR manipulator Cylinder

  8. Example: Random points 360 270 180 a 90 a x 0 x 0.25 0.75 0.5 1.0 PR manipulator Cylinder

  9. Random points in collision 360 270 180 a 90 a x 0 x 0.25 0.75 0.5 1.0 PR manipulator Cylinder

  10. Connecting Collision-free Random points 360 270 180 a 90 a x 0 x 0.25 0.75 0.5 1.0 PR manipulator Cylinder

  11. local path milestone mg mb Probabilistic Roadmap (PRM) free space [Kavraki, Svetska, Latombe,Overmars, 95]

  12. The Principles of PRM Planning • Checking sampled configurations and connections between samples for collision can be done efficiently. • A relatively small number of milestones and local paths are sufficient to capture the connectivity of the free space.

  13. The Learning Phase • Construct a probabilistic roadmap

  14. The Query Phase • Find a path from the start and goal configurations to two nodes of the roadmap

  15. The Query Phase • Need to find a path between an arbitrary start and goal configuration, using the roadmap constructed in the learning phase.

  16. What if we fail? • Maybe the roadmap was not adequate. • Could spend more time in the Learning Phase • Could do another Learning Phase and reuse R constructed in the first Learning Phase.

  17. Example – Results • This is a fixed-based articulated robot with 7 revolute degrees of freedom. • Each configuration is tested with a set of 30 goals with different learning times.

  18. Results With expansion Without expansion

  19. Issues • Why random sampling? • Smart sampling strategies • Final path smoothing

  20. Bad Good Issues: Connectivity

  21. Disadvantages • Spends a lot of time planning paths that will never get used • Heavily reliant on fast collision checking • An attempt to solve these is made with Lazy PRMs • Tries to minimize collision checks • Tries to reuse information gathered by queries

  22. References • Kavraki, Svestka, Latombe, Overmars, IEEE Transactions on Robotics and Automation, Vol. 12, No. 4, Aug. 1996

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