Models and motion planning

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

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


We study the complexity of the motion planning problem for a bounded-reach robot in the situation where the n obstacles in its workspace satisfy two of the realistic models proposed in the literature, namely unclutteredness and small simple-cover complexity. We show that the maximum complexity of the free space of a robot with f degrees of freedom in the plane is Θ(n f/2 + n) for uncluttered environments as well as environments with small simple-cover complexity. The maximum complexity of the free space of a robot moving in a threedimensional uncluttered environment is Θ(n2f/3 + n). All these bounds fit nicely between the Θ(n) bound for the maximum free-space complexity for low-density environments and the Θ(nf) bound for unrestricted environments. Surprisingly-because contrary to the situation in the plane-the maximum free-space complexity is Θ(nf) for a three-dimensional environment with small simple-cover complexity.

Original languageEnglish
Pages (from-to)53-68
Number of pages16
JournalComputational Geometry: Theory and Applications
Issue number1
StatePublished - 1 Jan 2002


  • Free space complexity
  • Input models
  • Motion planning


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