2003
DOI: 10.1007/s00454-002-0760-9
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Topological Complexity of Motion Planning

Abstract: 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 study the topo… Show more

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Cited by 346 publications
(594 citation statements)
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“…Thus, by Theorem 3.1, together with the computations of complexity for T and T 2 (see [7,Theorem 12]) we have…”
Section: Examples and Computationsmentioning
confidence: 99%
See 4 more Smart Citations
“…Thus, by Theorem 3.1, together with the computations of complexity for T and T 2 (see [7,Theorem 12]) we have…”
Section: Examples and Computationsmentioning
confidence: 99%
“…A more geometrical measure for the complexity of motion planning was introduced by M. Farber [7] who observed that algorithmic solutions normally yield robust mapping plans. He then defined the concept of the topological complexity of motion planning in the working space of a mechanical device as the minimal number of continuous partial solutions to the motion planning problem.…”
Section: Prior Workmentioning
confidence: 99%
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