Models and motion planning

Mark De Berg, Matthew J. Katz, Mark Overmars, A. Frank Van Der Stappen, Jules Vleugels

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

5 Scopus citations


We study the consequences of two of the realistic input models proposed in the literature, namely unclutteredness and small simplecover complexity, for the motion planning problem. We show that the complexity of the free space of a bounded-reach robot with f degrees of freedom is O(nf/2) in the plane, and O(n2f/3) in three dimensions, for both uncluttered environments and environments of small simple-cover complexity. We also give an example showing that these bounds are tight in the worst case. Our bounds fit nicely between the θ(nf) bound for the maximum free-space complexity in the general case, and the θ(n) bound for low-density environments.

Original languageEnglish
Title of host publicationAlgorithm Theory — SWAT 1998 - 6th Scandinavian Workshop on Algorithm Theory, Proceedings
EditorsStefan Arnborg, Lars Ivansson
PublisherSpringer Verlag
Number of pages12
ISBN (Print)3540646825, 9783540646822
StatePublished - 1 Jan 1998
Event6th Scandinavian Workshop on Algorithm Theory, SWAT 1998 - Stockholm, Sweden
Duration: 8 Jul 199810 Jul 1998

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference6th Scandinavian Workshop on Algorithm Theory, SWAT 1998

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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