Transcript “Visibility-based Probabilistic Roadmaps for Motion Planning” Siméon, Laumond, Nissoux Presentation by: Mathieu Bredif CS326A: Paper Review Winter 2004

“Visibility-based Probabilistic Roadmaps for
Motion Planning”
Siméon, Laumond, Nissoux
Presentation by: Mathieu Bredif
CS326A: Paper Review
Winter 2004
Motivation
• Save computation time without sacrificing coverage and
connectivity.
• Visibility PRM is an optimized variation of basic PRM
Ensuring Coverage
• Visibility Domain of configuration q:
q
Visibility =
Local planer =
Dynamic Collision
Checking on:
-Straight lines
-Manhattan paths
-Non-holonomic
…
Ensuring Coverage
• Free Space Coverage with Guard nodes
Shared
Visibility
Guard
Ensuring Coverage
• Free Space Coverage with Guard nodes
Shared
Visibility
Guard
Creating Connections
• Completing roadmap with Connection nodes
Shared
Visibility
Guard
Connection
Implementation Strategy
Implementation Strategy
Implementation Strategy
Implementation Strategy
Implementation Strategy
Implementation Strategy
Implementation Strategy
Implementation Strategy
Termination criterion
• Meanwhile: 1/ntry = estimation of the volume of
the subset of the free space not yet covered by
visibility domains.
• M is max number of failures before the insertion
of a new guard node.
• (1-1/M) = estimation of the coverage.
Pathological Case
• Probability of connection between guard nodes
depend on where they are (randomly) placed.
Possible Improvements
• It might be nice to have movable guards to
prevent pathological case.
• Use sampling techniques to find narrow passages
(First Paper).
Visibility PRM – Basic PRM comparison
• Heavier Node “filtering” process BUT reduction
in calls to the local method, from O(n2) to O(n).
• Remaining problems of randomly chosen
configuration points (inherent to PRM).
Conclusions
• Roadmap size is reduced.
– Faster Queries
– Few potential routes to choose from (good or bad?)
• Control of the coverage by (1-1/M)
• Computation Costs seem to be lower than with
Basic-PRM.