An Equivalence Relation for Local Path Sets

Ross Alan Knepper, Siddhartha Srinivasa, and Matthew T. Mason
The Ninth International Workshop on the Algorithmic Foundations of Robotics, December, 2010.


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Abstract
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%.

Notes
Grant ID: Tiergartenstrasse 17 69121 Heidelberg Germany
Associated Center(s) / Consortia: Center for the Foundations of Robotics
Associated Lab(s) / Group(s): Manipulation Lab
Number of pages: 16

Text Reference
Ross Alan Knepper, Siddhartha Srinivasa, and Matthew T. Mason, "An Equivalence Relation for Local Path Sets," The Ninth International Workshop on the Algorithmic Foundations of Robotics, December, 2010.

BibTeX Reference
@inproceedings{Knepper_2010_6723,
   author = "Ross Alan Knepper and Siddhartha Srinivasa and Matthew T. Mason",
   editor = "David Hsu, Volkan Isler, Jean-Claude Latombe, and Ming C. Lin",
   title = "An Equivalence Relation for Local Path Sets",
   booktitle = "The Ninth International Workshop on the Algorithmic Foundations of Robotics",
   publisher = "Springer",
   address = "Tiergartenstrasse 17 69121 Heidelberg Germany",
   month = "December",
   year = "2010",
}