Smoothed analysis of probabilistic roadmaps

Authors:
Siddhartha Chaudhuri;Vladlen Koltun
Affiliations:
Computer Science Department, Stanford University, 353 Serra Mall, Stanford, CA 94305, USA;Computer Science Department, Stanford University, 353 Serra Mall, Stanford, CA 94305, USA
Venue:
Computational Geometry: Theory and Applications
Year:
2009

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Abstract

The probabilistic roadmap algorithm is a leading heuristic for robot motion planning. It is extremely efficient in practice, yet its worst case convergence time is unbounded as a function of the input's combinatorial complexity. We prove a smoothed polynomial upper bound on the number of samples required to produce an accurate probabilistic roadmap, and thus on the running time of the algorithm, in an environment of simplices. This sheds light on its widespread empirical success.