Near-quadratic bounds for the motion planning problem for a polygon in a polygonal environment

Dan Halperin*, Micha Sharir

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We consider the problem of planning the motion of an arbitrary k-sided polygonal robot B, free to translate and rotate in a polygonal environment V bounded by n edges. We show that the combinatorial complexity of a single connected component of the free configuration space of B is k3n22O(log(2/3) n). This is a significant improvement of the naive bound O((kn)3); when k is constant, which is often the case in practice, this yields a near-quadratic bound on the complexity of such a component, which almost settles (in this special case) a long-standing conjecture regarding the complexity of a single cell in a three-dimensional arrangement of surfaces. We also present an algorithm that constructs a single component of the free configuration space of B in time O(n2+ε), for any ε>0, assuming B has a constant number of sides. This algorithm, combined with some standard techniques in motion planning, yields a solution to the underlying motion planning problem, within the same asymptotic running time.

Original languageEnglish
Title of host publicationAnnual Symposium on Foundatons of Computer Science (Proceedings)
Editors Anon
PublisherPubl by IEEE
Pages382-391
Number of pages10
ISBN (Print)0818643706
StatePublished - 1993
Externally publishedYes
EventProceedings of the 34th Annual Symposium on Foundations of Computer Science - Palo Alto, CA, USA
Duration: 3 Nov 19935 Nov 1993

Publication series

NameAnnual Symposium on Foundatons of Computer Science (Proceedings)
ISSN (Print)0272-5428

Conference

ConferenceProceedings of the 34th Annual Symposium on Foundations of Computer Science
CityPalo Alto, CA, USA
Period3/11/935/11/93

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