“Visibility-based Probabilistic Roadmaps for Motion Planning”

Siméon, Laumond, Nissoux

Presentation by: Mathieu BredifCS326A: 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:

qVisibility =

Local planer =

Dynamic CollisionChecking on:-Straight lines

-Manhattan paths-Non-holonomic

…

Ensuring Coverage

• Free Space Coverage with Guard nodes

SharedVisibility

Guard

Ensuring Coverage

• Free Space Coverage with Guard nodes

SharedVisibility

Guard

Creating Connections

• Completing roadmap with Connection nodes

Connection

SharedVisibility

Guard

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.