C-obstacle Query Computation for Motion Planning
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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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What is the problem?
Collision detection: do they intersect?
Continuous Collisiondetection,
do they intersect?
Can it escape ?
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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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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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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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Focus: C-obstacle Cell Query
A(qa)
B
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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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PD computation
• Translational PD only works for robots with translational DOFs
B
ARobot
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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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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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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?