The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL

C-obstacle Query Computation for Motion Planning

COMP290-58 Project Presentation

Liang-Jun Zhang12/13/2005

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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL

What is the problem?

Collision detection: do they intersect?

Continuous Collisiondetection,

do they intersect?

Can it escape ?

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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL

Query in Configuration

Configuration Space

C-Obstacle

Free space

c

p Is p in Free-space or C-obstacle?

Is l fully in Free-space?

l

Is c fully in C-obstacle space?

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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL

Why need C-obstacle query• Cell Decomposition based method• Star-shaped roadmap approach

♦ Efficiently cull them

• It is a fundamental query for Motion Planning

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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL

What is the difficulty?

1. A continuous problem2. `C-obstacle ’ query is more

expensive than `Free-space’ query

A

B

A

B

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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL

Focus: C-obstacle Cell Query

A(qa)

B

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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL

The intuition of solution

• PD: How much of the robot A penetrate into the obstacle B?

• Motion: How much can the robot A move?

• Culling Criteria

If PD > Motion it is in C-obstacle.

A(qa)

B

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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL

PD computation

• Translational PD only works for robots with translational DOFs

B

ARobot

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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL

Generalized PD

• Both translation and rotation are considered

• Defined on traveling distance when the object moves

• Convex A, B: PDG(A,B)=PDT(A,B)

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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL

Algorithm-Lower bound on PDG

1. Convex covering2. PDT over each pair3. LB(PDG) = Max over all PDTs

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Query Criteria

If PD > Motion It is in C-obstacle.

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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL

Query Criteria

If PD > Motion It is in C-obstacle.

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Upper bound of Motion

• A line segement

• a cell

qa qb

x

y

r rbraybyaxbxa qqRqqqqUB ,,,,,,

A(qa)

B

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Applied for 2D planar robot

Video

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Performance

• Culling Ratio= Culled Cells / All queried cells

• Timing 0.04ms to 0.12 ms for 2D

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Speedup For Star-shaped method

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Future work

• Method for C-obstacle space Query

• Non-path existence♦ together with star-shaped test♦ To enhance the PRM

• Difficulty♦ Conservative test♦ 6-DOF

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• Questions?