### 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 language | English |
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Title of host publication | Topology and Robotics |

Editors | M Farber, R Ghrist, M Burger, D Koditschek |

Place of Publication | Providence |

Publisher | American Mathematical Society |

Pages | 75-83 |

Number of pages | 9 |

ISBN (Print) | 978-0-8218-4246-1 |

Publication status | Published - 2007 |

Event | Workshop on Topology and Robotics - Zurich, Switzerland Duration: 10 Jul 2006 → 14 Jul 2006 |

### Publication series

Name | Contemporary Mathematics |
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Publisher | American Mathematical Society |

Volume | 438 |

ISSN (Print) | 0271-4132 |

### Conference

Conference | Workshop on Topology and Robotics |
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Country | Switzerland |

Period | 10/07/06 → 14/07/06 |

### Keywords

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

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Topology and Robotics.*Contemporary Mathematics, vol. 438, American Mathematical Society, Providence, pp. 75-83, Workshop on Topology and Robotics, Switzerland, 10/07/06.

}

TY - GEN

T1 - Topological complexity of collision free motion planning algorithms in the presence of multiple moving obstacles

AU - Farber, Michael

AU - Grant, Mark

AU - Yuzvinsky, Sergey

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

KW - robot motion planning

KW - avoiding obstacles

KW - moving obstacles

KW - Schwarz genus

KW - topological complexity

KW - configuration spaces

M3 - Conference contribution

SN - 978-0-8218-4246-1

T3 - Contemporary Mathematics

SP - 75

EP - 83

BT - Topology and Robotics

A2 - Farber, M

A2 - Ghrist, R

A2 - Burger, M

A2 - Koditschek, D

PB - American Mathematical Society

CY - Providence

ER -