On soft predicates in subdivision motion planning

Cong Wang, Yi Jen Chiang, Chee Yap

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We propose to design new algorithms for motion planning problems using the well-known Domain Subdivision paradigm, coupled with "soft" predicates. Unlike the traditional exact predicates in computational geometry, our primitives are only exact in the limit. We introduce the notion of resolution-exact algorithms in motion planning: such an algorithm has an "accuracy" constant K > 1, and takes an arbitrary input "resolution" parameter ε > 0 such that: if there is a path with clearance Kε, it will output a path with clearance ε/K; if there are no paths with clearance ε/K, it reports "no path". Besides the focus on soft predicates, our framework also admits a variety of global search strategies including forms of the A* search and probabilistic search. Our algorithms are theoretically sound, practical, easy to implement, without implementation gaps, and have adaptive complexity. Our deterministic and probabilistic strategies avoid the Halting Problem of current probabilistically complete algorithms. We develop the first provably resolution-exact algorithms for motion-planning problems in SE(2) = R 2 × S1. To validate this approach, we implement our algorithms and the experiments demonstrate the efficiency of our approach, even compared to probabilistic algorithms.

Original languageEnglish (US)
Title of host publicationProceedings of the 29th Annual Symposium on Computational Geometry, SoCG 2013
Pages349-358
Number of pages10
StatePublished - Jul 8 2013
Event29th Annual Symposium on Computational Geometry, SoCG 2013 - Rio de Janeiro, Brazil
Duration: Jun 17 2013Jun 20 2013

Publication series

NameProceedings of the Annual Symposium on Computational Geometry

Other

Other29th Annual Symposium on Computational Geometry, SoCG 2013
CountryBrazil
CityRio de Janeiro
Period6/17/136/20/13

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Keywords

  • Computational geometry
  • Exact algorithms
  • Motion planning
  • Resolution-exact algorithms
  • Robotics
  • Soft predicates
  • Subdivision algorithms

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Computational Mathematics

Cite this

Wang, C., Chiang, Y. J., & Yap, C. (2013). On soft predicates in subdivision motion planning. In Proceedings of the 29th Annual Symposium on Computational Geometry, SoCG 2013 (pp. 349-358). (Proceedings of the Annual Symposium on Computational Geometry).