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Navigating Tight Spaces Efficiently with Probabilistic Roadmaps: The Small-Step Retraction Method

Explore research on efficient navigation through tight passages using innovative strategies and techniques in robotics planning with Probabilistic Roadmaps (PRM) by Mitul Saha and Jean-Claude Latombe. Learn about the Small-Step Retraction Method for overcoming obstacles in planning paths through narrow passages. Discover how this approach improves planning efficiency and addresses common challenges faced in complex geometric scenarios.

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Navigating Tight Spaces Efficiently with Probabilistic Roadmaps: The Small-Step Retraction Method

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  1. Finding “Narrow Passages” withProbabilistic Roadmaps: The Small-Step Retraction Method Mitul Saha and Jean-Claude Latombe Research supported by NSF, ABB and GM Artificial Intelligence Lab Stanford University

  2. Roadmap components local path milestone Probabilistic Roadmaps (PRM) goal configuration start configuration free-space c-obstacle Configuration-space components [Kavraki, Svetska, Latombe, Overmars, 1996]

  3. PRM planners solve complicated problems Complex geometries: obstacles: 43530 polygons Robot: 4053 polygons High dimensional

  4. low density of free samples high density of free samples Main Issue: “Narrow Passages” narrow passage free samples colliding local path colliding samples The efficiency of PRM planners drops dramatically in spaces with narrow passages

  5. Main Issue: “Narrow Passages” • Problems with “narrow passages” are commonly encountered

  6. ? Main Issue: “Narrow Passages” • Proposed strategies: • Filtering strategies, e.g., Gaussian sampling [Boor et al. ‘99] and bridge test [Hsu et al. ‘03]  rely heavily on rejection sampling • Retraction strategies, e.g., [Wilmart et al. ‘99][Lien et al. ‘03]  waste time moving many configurations out of collision

  7. difficult narrow passages easy narrow passages Motivating Observation planning time decreasing width of the narrow passage

  8. Small-Step Retraction Method start Fattening goal widened passage c-obstacle fattened free space free space Roadmap construction and repair (2 & 3) (1) • Slightly fatten the robot’s free space • Construct a roadmap in fattened free space • Repair the roadmap into original free space

  9. start goal c-obstacle free space Small-Step Retraction Method Roadmap construction and repair Fattening widened passage fattened free space • Free space can be “indirectly” fattened by • reducing the scale of the geometries (usually of • the robot) in the 3D workcell with respect to • their medial axis • -This can be pushed into the pre-processing • phase

  10. start goal widened passage c-obstacle fattened free space free space Small-Step Retraction Method Roadmap construction and repair Fattening start Repair during construction Pessimist Strategy Optimist Strategy Repair after construction goal fattened free space

  11. start • Optimist may fail due to • “false passages” but Pessimist • is probabilistically complete • Hence Optimist is less reliable, • but much faster due to its • lazy strategy goal widened passage c-obstacle fattened free space free space Small-Step Retraction Method Roadmap construction and repair Fattening start Repair during construction Pessimist Strategy Optimist Strategy Repair after construction goal fattened free space

  12. start goal widened passage c-obstacle fattened free space free space Small-Step Retraction Method Roadmap construction and repair Fattening start Pessimist Strategy Repair during construction Integrated planner: 1. Try Optimist for N time. 2. If Optimist fails, then run Pessimist Optimist Strategy Repair after construction goal fattened free space

  13. Fattening “preserves” topology/ connectivity of the free space Fattening “alters” the topology/ connectivity of the free space (h) A recent PRM planner Our planner Quantitative Results (c) (a) (b) Alpha 1.1 (g) Alpha 1.0 (f) (d) (e) Upto 3 orders of magnitude improvement in the planning time was observed

  14. Quantitative Results • Test environments “without” narrow passages • SSRP and SBL have similar performance (i) (j)

  15. Conclusion • SSRP is very efficient at finding narrow passages and still works well when there is none • The main drawback is that there is an additional pre-computation step

  16. Finding “Narrow Passages” withProbabilistic Roadmaps: The Small-Step Retraction Method

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