Topological complexity of collision free motion planning algorithms in the presence of multiple moving obstacles

Michael Farber, Mark Grant, Sergey Yuzvinsky

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We study motion planning algorithms for collision free control of multiple objects in the presence of moving obstacles. We compute the topological complexity of algorithms solving this problem. We apply topological tools and use information about cohomology algebras of configuration spaces. The results of the paper may potentially be used in systems of automatic traffic control.

Original languageEnglish
Title of host publicationTopology and Robotics
EditorsM Farber, R Ghrist, M Burger, D Koditschek
Place of PublicationProvidence
PublisherAmerican Mathematical Society
Pages75-83
Number of pages9
ISBN (Print)978-0-8218-4246-1
Publication statusPublished - 2007
EventWorkshop on Topology and Robotics - Zurich, Switzerland
Duration: 10 Jul 200614 Jul 2006

Publication series

NameContemporary Mathematics
PublisherAmerican Mathematical Society
Volume438
ISSN (Print)0271-4132

Conference

ConferenceWorkshop on Topology and Robotics
CountrySwitzerland
Period10/07/0614/07/06

Keywords

  • robot motion planning
  • avoiding obstacles
  • moving obstacles
  • Schwarz genus
  • topological complexity
  • configuration spaces

Cite this

Farber, M., Grant, M., & Yuzvinsky, S. (2007). Topological complexity of collision free motion planning algorithms in the presence of multiple moving obstacles. In M. Farber, R. Ghrist, M. Burger, & D. Koditschek (Eds.), Topology and Robotics (pp. 75-83). (Contemporary Mathematics; Vol. 438). Providence: American Mathematical Society.

Topological complexity of collision free motion planning algorithms in the presence of multiple moving obstacles. / Farber, Michael; Grant, Mark; Yuzvinsky, Sergey.

Topology and Robotics. ed. / M Farber; R Ghrist; M Burger; D Koditschek. Providence : American Mathematical Society, 2007. p. 75-83 (Contemporary Mathematics; Vol. 438).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Farber, M, Grant, M & Yuzvinsky, S 2007, Topological complexity of collision free motion planning algorithms in the presence of multiple moving obstacles. in M Farber, R Ghrist, M Burger & D Koditschek (eds), Topology and Robotics. Contemporary Mathematics, vol. 438, American Mathematical Society, Providence, pp. 75-83, Workshop on Topology and Robotics, Switzerland, 10/07/06.
Farber M, Grant M, Yuzvinsky S. Topological complexity of collision free motion planning algorithms in the presence of multiple moving obstacles. In Farber M, Ghrist R, Burger M, Koditschek D, editors, Topology and Robotics. Providence: American Mathematical Society. 2007. p. 75-83. (Contemporary Mathematics).
Farber, Michael ; Grant, Mark ; Yuzvinsky, Sergey. / Topological complexity of collision free motion planning algorithms in the presence of multiple moving obstacles. Topology and Robotics. editor / M Farber ; R Ghrist ; M Burger ; D Koditschek. Providence : American Mathematical Society, 2007. pp. 75-83 (Contemporary Mathematics).
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