Carnegie Mellon University
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An Equivalence Relation for Local Path Sets

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journal contribution
posted on 2010-12-01, 00:00 authored by Ross A Knepper, Siddhartha SrinivasaSiddhartha Srinivasa, Matthew T. Mason

We propose a novel enhancement to the task of collision-testing a set of local paths. Our approach circumvents expensive collision-tests, yet it declares a continuum of paths collision-free by exploiting both the structure of paths and the outcome of previous tests. We define a homotopy-like equivalence relation among local paths and provide algorithms to (1) classify paths based on equivalence, and (2) implicitly collision-test up to 90% of them. We then prove both correctness and completeness of these algorithms before providing experimental results showing a performance increase up to 300%.




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