The complexity of the free space for a robot moving amidst fat obstacles

A. Frank van der Stappen, Dan Halperin, Mark H. Overmars

Research output: Contribution to journalArticlepeer-review

Abstract

We propose a new definition of fatness of geometric objects and compare it with alternative definitions. We show that, under some realistic assumptions, the complexity of the free space for a robot, with any fixed number of degrees of freedom moving in a d-dimensional Euclidean workspace with fat obstacles, is linear in the number of obstacles. The complexity of motion planning algorithms depends on the complexity of the robot's free space, and theoretically, the complexity of the free space can be very high. Thus, our result opens the way to devising provable efficient motion planning algorithms in certain realistic settings.

Original languageEnglish
Pages (from-to)353-373
Number of pages21
JournalComputational Geometry: Theory and Applications
Volume3
Issue number6
DOIs
StatePublished - Dec 1993

Keywords

  • Motion planning
  • combinatorial complexity
  • fatness
  • free space
  • multiple contacts

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