inevitable collision states in replanning with sampling-based algorithms
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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 - PowerPoint PPT PresentationTRANSCRIPT
Inevitable Collision States inReplanning with Sampling-based Algorithms
Kostas BekrisComputer 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– exploration– planning in dynamic environments– multi-agent challenges: pursuit-evasion problems or
coordination problems
• 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
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]
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]
Sampling-based Replanning
• Things to consider in relation to safety1 The actual ICS checker
2 How is it integrated with the replanning scheme?
ICScheckerstate ICS or not?
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]
1a. Conservative, Safe ICS checker
• Dealing with infeasibility - conservative approx.:– If a state is safe for a subset of plans, then truly not ICS
ICScheckerstate 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]
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]
1b. Relaxing the guarantees
• Or use learning:
• Use Support Vector Machines to learn a classifier
[Kalisiak, van de Panne ‘07]
1. Schools of thought towards ICS
1 School of Complacency– It’s not a real problem for my system
2 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?
3 Conservative School of Safety– Collision avoidance is the only guarantee we provide
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
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
x00 x0
1 x02 x0
3 x04
replanningcycle 0
replanningcycle 1
replanningcycle 2
replanningcycle 3
replanningcycle 4
x05
• 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]
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]
2. Minimalistic Approach – Retain Tree
• Retain valid part of tree:• The retained tree must be checked for safety
currentlyexecuted
pathexecution
horizon
Checksafety
[Bekris, Kavraki ’07]
Example
Example
Example
Example
Comparison in Computational Cost
DDSceneMeandros
CarSceneMeandros
DDSceneLabyrinth
CarSceneLabyrinth
Straightforward approach
Minimalistic approach
Alternative Trajectoriesproduced in 1 sec
100
10
Multi-Agent Problems
Trajectory computed from“perfect prediction”or communication
A
B
C
D
A
B
C
D
A
B
D
C
Safe Multi-Robot Motion Coordination
B
Initial statex(tN+1)
Goal VA
plan A1
plan A2
plan A3
Goal VB
Goal VC
A
C
current contingency for B
current contingency for C
statesx(tN+2)
[Bekris, Tsianos, Kavraki ’07,’09]
Safe Multi-Robot Motion Coordination
plan A1
plan A2
plan A3
Initial statex(tN+1)
Goal VA
Goal VB
Goal VC
A
C
B
[Bekris, Tsianos, Kavraki ’07,’09]
Safe Multi-Robot Motion Coordination
Goal VA
Goal VB
Goal VC
Initial statex(tN+1)
A
C
B
[Bekris, Tsianos, Kavraki ’07,’09]
Safe Multi-Robot Motion Coordination
Initial statex(tN+1)
Goal VA
Goal VB
Goal VC
A
C
B
[Bekris, Tsianos, Kavraki ’07,’09]
Importance of Safety
Averages over 10 experiments
Without our safety requirements With Requirements
Number of Vehicles
Occurrence of 1st collision (in sec)
Success Rate Success Rate
2 287.10 10% 100%4 21 0% 100%8 3.67 0% 100%16 3 0% 100%
16 vehicles @ Labyrinth
Percentage of successful exploration experiments
Example
Example
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
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