Sequential motion planning of non-colliding particles in Euclidean spaces

Jesus Gonzalez, Mark Grant

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)
12 Downloads (Pure)


In terms of Rudyak's generalization of Farber's topological complexity of the path motion planning problem in robotics, we give a complete description of the topological instabilities in any sequential motion planning algorithm for a system consisting of non-colliding autonomous entities performing tasks in space whilst avoiding collisions with several moving obstacles. The Isotopy Extension Theorem from manifold topology implies, somewhat surprisingly, that the complexity of this problem coincides with the complexity of the corresponding problem in which the obstacles are stationary.
Original languageEnglish
Pages (from-to)4503-4512
Number of pages10
JournalProceedings of the American Mathematical Society
Issue number10
Early online date5 Jun 2015
Publication statusPublished - 2015

Bibliographical note

10 pages; Final version, to appear in Proc. Amer. Math. Soc


  • math.AT
  • 55R80, 55S40 (Primary), 55M30, 68T40 (Secondary)
  • robot motion planning
  • higher topological complexity
  • sectional category
  • configuration spaces
  • moving obstacles


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