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Inevitable Collision States in Replanning with Sampling-based Algorithms Kostas Bekris Computer Science and Engineering May 7, ICRA 2010

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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

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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] Inevitable Collision States

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

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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]

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Sampling-based Replanning Things to consider in relation to safety 1The actual ICS checker 1How is it integrated with the replanning scheme? ICS checker ICS checker state ICS or not?

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1a. Conservative, Safe ICS checker 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 [Fraichard, Asama ’04]

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

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1b. Relaxing the guarantees 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” [Zucker ‘06] [Chan, Kuffner, Zucker ‘08]

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

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1. Schools of thought towards ICS 1School of Complacency – It’s not a real problem for my system 2School 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? 3Conservative School of Safety – Collision avoidance is the only guarantee we provide

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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

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2. Use of ICS-checker in Replanning Given an ICS-checker – How do you use it in order to provide safety? Replanning / Partial Motion Planning Framework Time Complete planning problem x00x00x00x00 x01x01x01x01 x02x02x02x02 x03x03x03x03 x04x04x04x04 replanning cycle 0 replanning cycle 1 replanning cycle 2 replanning cycle 3 replanning cycle 4 x05x05x05x05

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

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

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

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Example

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

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

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Safe Multi-Robot Motion Coordination B Initial state x(t N+1 ) Goal V A plan A 1 plan A 2 plan A 3 Goal V B Goal V C A C current contingency for B current contingency for C states x(t N+2 ) [Bekris, Tsianos, Kavraki ’07,’09]

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Safe Multi-Robot Motion Coordination plan A 1 plan A 2 plan A 3 Initial state x(t N+1 ) Goal V A Goal V B Goal V C A C B [Bekris, Tsianos, Kavraki ’07,’09]

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Safe Multi-Robot Motion Coordination Goal V A Goal V B Goal V C Initial state x(t N+1 ) A C B [Bekris, Tsianos, Kavraki ’07,’09]

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Safe Multi-Robot Motion Coordination Initial state x(t N+1 ) Goal V A Goal V B Goal V C A C B [Bekris, Tsianos, Kavraki ’07,’09]

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Importance of Safety Averages over 10 experiments Without our safety requirementsWith Requirements Number of Vehicles Occurrence of 1 st collision (in sec) Success Rate %100% 4210%100% %100% 1630%100% 16 Labyrinth Percentage of successful exploration experiments

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Example

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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

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

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