Topological Complexity of Motion Planning

  title={Topological Complexity of Motion Planning},
  author={Michael Farber},
  journal={Discrete & Computational Geometry},
In this paper we study a notion of topological complexity TC(X) for the motion planning problem. TC(X) is a number which measures discontinuity of the process of motion planning in the configuration space X. More precisely, TC(X) is the minimal number k such that there are k different “motion planning rules”, each defined on an open subset of X×X, so that each rule is continuous in the source and target configurations. We use methods of algebraic topology (the Lusternik Schnirelman theory) to… CONTINUE READING
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Publications referenced by this paper.
Showing 1-8 of 8 references

Topology of complements to discriminants

  • V. A. Vassiliev
  • Moscow,
  • 1997
1 Excerpt

Cohomology of braid groups and complexity of algorithms, Functional Analysis and its Appl., 22(1988)

  • V. A. Vassiliev
  • 1988
1 Excerpt

On the piano movers’ problem: II. General techniques for computing topological properties of real algebraic manifolds

  • J. T. Schwartz, M. Sharir
  • Adv. Appl. Math., 4(1983),
  • 1983
1 Excerpt

On category, in the sense of Lusternik - Schnirelman

  • I. M. James
  • Topology, 17(1978),
  • 1978
1 Excerpt

The genus of a fiber

  • A. S. Schwarz
  • space, Amer. Math. Sci. Transl. 55(1966),
  • 1966
2 Excerpts

The genus of a fiber space

  • A. V.
  • Amer . Math . Sci . Transl .

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