Directed topological complexity

Eric Goubault, Michael Farber, Aurélien Sagnier

Research output: Contribution to journalArticlepeer-review

Abstract

It has been observed that the motion planning problem of robotics reduces mathematically to the problem of finding a section of the path-space fibration, leading to the notion of topological complexity, as introduced by M. Farber. In this approach one imposes no limitations on motion of the system assuming that any continuous motion is admissible. In many applications, however, a physical apparatus may have constrained controls, leading to constraints on its potential dynamics. In the present paper we adapt the notion of topological complexity to the case of directed topological spaces, which encompass such controlled systems, and also systems which appear in concurrency theory. We study properties of this new notion and make calculations for some interesting classes of examples.

Original languageEnglish
Pages (from-to)11-27
Number of pages17
JournalJournal of Applied and Computational Topology
Volume4
Issue number1
DOIs
StatePublished - Mar 2020
Externally publishedYes

Keywords

  • Concurrent systems
  • Controlled systems
  • Directed topology
  • Homotopy theory
  • Robot motion planning
  • Topological complexity

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