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