1. Inevitable Collision States in Replanning 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. 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

4. 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]

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 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?

7. 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]

8. 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]

9. 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]

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

11. 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

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 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

14. 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]

15. 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]

16. 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]

17. Example

21. 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 100 10

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

23. 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]

24. 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]

25. 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]

26. 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]

27. Importance of Safety Averages over 10 experiments Without our safety requirementsWith Requirements Number of Vehicles Occurrence of 1 st collision (in sec) Success Rate 2287.1010%100% 4210%100% 83.670%100% 1630%100% 16 vehicles @ Labyrinth Percentage of successful exploration experiments

28. 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