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Paper WeB07.6

McCarthy, Zoe (University of Illinois at Urbana-Champaign), Bretl, Timothy (University of Illinois at Urbana-Champaign), Hutchinson, Seth (University of Illinois)

Proving Path Non-Existence Using Sampling and Alpha Shapes

Scheduled for presentation during the Regular Session "Sampling-Based Motion Planning" (WeB07), Wednesday, May 16, 2012, 11:45−12:00, Meeting Room 7 (Remnicha)

2012 IEEE International Conference on Robotics and Automation, May 14-18, 2012, RiverCentre, Saint Paul, Minnesota, USA

This information is tentative and subject to change. Compiled on October 24, 2017

Keywords Motion and Path Planning, Collision Avoidance

Abstract

In this paper, we address the problem determining the connectivity of a robot's free configuration space. Our method iteratively builds a constructive proof that two configurations lie in disjoint components of the free configuration space. Our algorithm first generates samples that correspond to configurations for which the robot is in collision with an obstacle. These samples are then weighted by their generalized penetration distance, and used to construct alpha shapes. The alpha shape defines a collection of simplices that are fully contained within the configuration space obstacle region. These simplices can be used to quickly solve connectivity queries, which in turn can be used to define termination conditions for sampling-based planners. Such planners, while typically either resolution complete or probabilistically complete, are not able to determine when a path does not exist, and therefore would otherwise rely on heuristics to determine when the search for a free path should be abandoned. An implementation of the algorithm is provided for the case of a 3D Euclidean configuration space, and a proof of correctness is provided.

 

 

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