“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 Connection Shared Visibility Guard

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(n 2 ) 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.