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Inevitable Collision States in Replanning with Sampling-based Algorithms

This paper addresses the challenges of using sampling-based algorithms for motion planning in dynamic environments, focusing on Inevitable Collision States (ICS). These represent configurations where collisions are unavoidable due to dynamics or obstacles. The study explores various algorithms for path replanning amid uncertainties, discussing the intersection of safety and computational efficiency. It highlights the need for effective ICS checkers and proposes a framework for reintegration into replanning cycles, emphasizing the relevance of avoiding collisions through strategic decision-making in robotic systems.

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Inevitable Collision States in Replanning with Sampling-based Algorithms

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  1. Inevitable Collision States inReplanning with Sampling-based Algorithms Kostas Bekris Computer Science and Engineering May 7, ICRA 2010

  2. Inevitable Collision States • Introduced due to dynamics in problems that require recomputation of a path • planning among unknown static obstacles • exploration • planning in dynamic environments • multi-agent challenges: pursuit-evasion problems or coordination problems

  3. Inevitable Collision States • In dynamics environments • motion constraints are not necessary to get ICS • Different names in the literature: • Obstacle Shadows [Reif, Sharir ’85] • Regions of Inevitable Collisions [LaValle, Kuffner ’01] • Inevitable Collision States [Fraichard ’04]

  4. Reactive Collision Avoidance Dynamic Window [Fox et al. ‘97] Nearness Diagram Navigation [Minguez, Montano ‘04] Velocity Obstacles [Fiorini, Shiller ‘98] Vector Field Histogram [Borenstein, Korem ‘91]

  5. Replanning with a Global Algorithm • For problems where the state-space can be effectively discretized • D* family of algorithms [Stenz ‘95] [Koenig, Likhachev ’02] • Otherwise: • Replanning with sampling-based algorithms • Techniques that do not reason about safety [Leven, Hutchinson ‘02] [Bruce, Veloso ‘02] [Kallman, Mataric ’02] [van den Berg, Ferguson, Kuffner ‘06] [ Ferguson, Kalra, Stentz ‘06] [Gayle, Klinger, Xavier ‘07] [Zucker, Kuffner, Branicky ‘07] • Techniques that reason about safety or deal with dynamics [Hsu, Kindel, Latombe, Rock ‘02] [Frazzoli, Dahleh, Feron ‘02] [Bruce, Veloso ‘03] [Fraichard, Asama ’04 ] [Petti, Friachard ‘05] [Zucker ‘06] [Kalisiak, van den Panne ‘07] [Bekris, Kavraki ‘07] [Tsianos, Kavraki ‘08] [Chan, Kuffner, Zucker ‘08] [Vatcha, Xiao ‘08]

  6. Sampling-based Replanning ICS checker state ICS or not? • Things to consider in relation to safety • The actual ICS checker • How is it integrated with the replanning scheme?

  7. 1a. Conservative, Safe ICS checker • [Fraichard, Asama ’04] • Computing whether a state is truly ICS or not: • Requires reasoning over an infinite horizon • Necessary to guarantee safety • Requires the union of all ICS states for each obstacle • Necessary to guarantee safety • Requires reasoning over all feasible plans of the robot

  8. 1a. Conservative, Safe ICS checker model of the environment’s evolution ICS checker proven safe or not proven safe? state [Fraichard, Asama ‘04] [Petti, Fraichard ‘05] [Parthasarathi, Fraichard ’05][Fraichard ‘07] [Martinez-Gomez, Fraichard ’08,’09] evasive maneuvers • Dealing with infeasibility - conservative approx.: • If a state is safe for a subset of plans, then truly not ICS

  9. 1b. Relaxing the guarantees [Zucker ‘06] [Chan, Kuffner, Zucker ‘08] • Reduce guarantees and focus on efficiency • Alternative motivation: • prune states during single-shot planning • One way to approximate: • Finite horizon • Consider the ICS of individual obstacles separately • Precomputations and other approximations for polygonal environments • Define regions of • “potential collision” and • “near-collision”

  10. 1b. Relaxing the guarantees [Kalisiak, van de Panne ‘07] • Or use learning: • Use Support Vector Machines to learn a classifier

  11. 1. Schools of thought towards ICS • School of Complacency • It’s not a real problem for my system • School of Computational Efficiency • Many advantages of being computationally efficient • You can search more during the same amount of time • In real systems, you have uncertainty • Why care about guarantees, when no real guarantees can be provided? • Conservative School of Safety • Collision avoidance is the only guarantee we provide

  12. 1. Challenges for the future • It is upon the people who believe that safety is critical to prove that ICS is indeed a major issue • Benchmark problems on real systems are needed • How often being complacent about ICS leads to collisions? • How conservative and slow are the solutions that provide safety? Do practically provide safety? • Are fast, relaxed approximations sufficient? • What about hybrid schemes? • First quickly prune states with a classifier and among the safe ones apply conservative schemes

  13. 2. Use of ICS-checker in Replanning Complete planning problem replanning cycle 0 replanning cycle 1 replanning cycle 2 replanning cycle 3 replanning cycle 4 Time x00 x01 x02 x03 x04 x05 • Given an ICS-checker • How do you use it in order to provide safety? • Replanning / Partial Motion Planning Framework

  14. 2. Straightforward integration [Frazzoli, Dahleh, Feron ‘02] [Petti, Fraichard ’05] G Time No need to know the duration of the planning cycle Whenever a problem arises, follow the evasive maneuver

  15. 2. Minimalistic approach [Bekris, Kavraki ’07] G Time • For given or controlled duration of planning cycle • Check only states which are candidates to be initial states

  16. 2. Minimalistic Approach – Retain Tree • Retain valid part of tree: • The retained tree must be checked for safety [Bekris, Kavraki ’07] Check safety currently executed path execution horizon

  17. Example

  18. Example

  19. Example

  20. Example

  21. Comparison in Computational Cost Alternative Trajectories produced in 1 sec 100 Straightforward approach Minimalistic approach 10 DD Scene Meandros Car Scene Meandros DD Scene Labyrinth Car Scene Labyrinth

  22. Trajectory computed from “perfect prediction” or communication A C D B Multi-Agent Problems A A C C D D B B

  23. states x(tN+2) Safe Multi-Robot Motion Coordination Goal VB [Bekris, Tsianos, Kavraki ’07,’09] C current contingency for C plan A1 Goal VA Initial state x(tN+1) A plan A2 plan A3 current contingency for B Goal VC B

  24. Goal VB C Goal VA Initial state x(tN+1) A Goal VC B Safe Multi-Robot Motion Coordination [Bekris, Tsianos, Kavraki ’07,’09] plan A1 plan A3 plan A2

  25. C Initial state x(tN+1) A B Safe Multi-Robot Motion Coordination Goal VB [Bekris, Tsianos, Kavraki ’07,’09] Goal VA Goal VC

  26. Goal VB C Goal VA Initial state x(tN+1) A Goal VC B Safe Multi-Robot Motion Coordination [Bekris, Tsianos, Kavraki ’07,’09]

  27. Importance of Safety 16 vehicles @ Labyrinth Percentage of successful exploration experiments

  28. Example

  29. Example

  30. Some extensions Safe multi-robot motion coordination on real systems Asynchronous coordination Evaluation of the best way to integrate ICS-checker with replanning framework Safe reciprocal motion coordination

  31. Thank you for your attention! Kostas Bekris’ research is supported by: • the National Science Foundation (CNS 0932423), • the Office of Naval Research, • the Nevada NASA Space Grant Consortium and • internal funds by the University of Nevada, Reno

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