On soft predicates in subdivision motion planning

Cong Wang, Yi Jen Chiang, Chee Yap

Research output: Contribution to journalArticle

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<sup>2</sup>×S<sup>1</sup>. 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)
Pages (from-to)589-605
Number of pages17
JournalComputational Geometry: Theory and Applications
Volume48
Issue number8
DOIs
StatePublished - Jun 3 2015

Fingerprint

Motion Planning
Motion planning
Subdivision
Predicate
Clearance
Exact Algorithms
Path
Halting Problem
Probabilistic Algorithms
Global Search
Computational Geometry
Search Strategy
Computational geometry
Paradigm
Output
Arbitrary
Demonstrate
Acoustic waves
Experiment

Keywords

  • Exact algorithms
  • Motion planning
  • Resolution-exact algorithms
  • Soft predicates
  • Subdivision algorithms

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Computer Science Applications
  • Computational Mathematics
  • Control and Optimization
  • Geometry and Topology

Cite this

On soft predicates in subdivision motion planning. / Wang, Cong; Chiang, Yi Jen; Yap, Chee.

In: Computational Geometry: Theory and Applications, Vol. 48, No. 8, 03.06.2015, p. 589-605.

Research output: Contribution to journalArticle

Wang, Cong ; Chiang, Yi Jen ; Yap, Chee. / On soft predicates in subdivision motion planning. In: Computational Geometry: Theory and Applications. 2015 ; Vol. 48, No. 8. pp. 589-605.
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