Sequential motion planning of non-colliding particles in Euclidean spaces
Algebraic Topology
2014-01-13 v2
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.
Keywords
Cite
@article{arxiv.1309.4346,
title = {Sequential motion planning of non-colliding particles in Euclidean spaces},
author = {Jesus Gonzalez and Mark Grant},
journal= {arXiv preprint arXiv:1309.4346},
year = {2014}
}
Comments
10 pages; Final version, to appear in Proc. Amer. Math. Soc