### Abstract

Original language | English |
---|---|

Pages (from-to) | 4503-4512 |

Number of pages | 10 |

Journal | Proceedings of the American Mathematical Society |

Volume | 143 |

Issue number | 10 |

Early online date | 5 Jun 2015 |

DOIs | |

Publication status | Published - 2015 |

### Fingerprint

### Keywords

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

### Cite this

*Proceedings of the American Mathematical Society*,

*143*(10), 4503-4512. https://doi.org/10.1090/proc/12443

**Sequential motion planning of non-colliding particles in Euclidean spaces.** / Gonzalez, Jesus; Grant, Mark.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 143, no. 10, pp. 4503-4512. https://doi.org/10.1090/proc/12443

}

TY - JOUR

T1 - Sequential motion planning of non-colliding particles in Euclidean spaces

AU - Gonzalez, Jesus

AU - Grant, Mark

N1 - 10 pages; Final version, to appear in Proc. Amer. Math. Soc

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

KW - math.AT

KW - 55R80, 55S40 (Primary), 55M30, 68T40 (Secondary)

KW - robot motion planning

KW - higher topological complexity

KW - sectional category

KW - configuration spaces

KW - moving obstacles

U2 - 10.1090/proc/12443

DO - 10.1090/proc/12443

M3 - Article

VL - 143

SP - 4503

EP - 4512

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 10

ER -