### Abstract

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 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 |

### Keywords

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

## Fingerprint Dive into the research topics of 'Sequential motion planning of non-colliding particles in Euclidean spaces'. Together they form a unique fingerprint.

## Cite this

Gonzalez, J., & Grant, M. (2015). Sequential motion planning of non-colliding particles in Euclidean spaces.

*Proceedings of the American Mathematical Society*,*143*(10), 4503-4512. https://doi.org/10.1090/proc/12443