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Inevitable Collision States in Replanning with Sampling-based Algorithms

Inevitable Collision States in Replanning with Sampling-based Algorithms. Kostas Bekris Computer Science and Engineering May 7, ICRA 2010. Inevitable Collision States. Introduced due to dynamics in problems that require recomputation of a path planning among unknown static obstacles

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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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