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Models and motion planning

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Algorithm Theory — SWAT'98 (SWAT 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1432))

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Abstract

We study the consequences of two of the realistic input models proposed in the literature, namely unclutteredness and small simple-cover 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(n f/2) in the plane, and O(n 2f/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.

This research was partially supported by the Netherlands' Organization for Scientific Research (NWO).

Supported by the Israel Science Foundation founded by the Israel Academy of Sciences and Humanities.

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Authors and Affiliations

  1. Department of Computer Science, Utrecht University, P.O.Box 80.089, 3508, TB Utrecht, The Netherlands

    Mark de Berg, Mark Overmars, A. Frank van der Stappen & Jules Vleugels

  2. Department of Mathematics and Computer Science, Ben-Gurion University of the Negev, 84105, Beer-Sheva, Israel

    Matthew J. Katz

Authors
  1. Mark de Berg
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  2. Matthew J. Katz
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  3. Mark Overmars
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  4. A. Frank van der Stappen
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  5. Jules Vleugels
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Editor information

Stefan Arnborg Lars Ivansson

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© 1998 Springer-Verlag Berlin Heidelberg

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de Berg, M., Katz, M.J., Overmars, M., Frank van der Stappen, A., Vleugels, J. (1998). Models and motion planning. In: Arnborg, S., Ivansson, L. (eds) Algorithm Theory — SWAT'98. SWAT 1998. Lecture Notes in Computer Science, vol 1432. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0054357

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  • DOI: https://doi.org/10.1007/BFb0054357

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  • Print ISBN: 978-3-540-64682-2

  • Online ISBN: 978-3-540-69106-8

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