Topology of parametrised motion planning algorithms
Algebraic Topology
2021-09-10 v2
Abstract
In this paper we introduce and study a new concept of parametrised topological complexity, a topological invariant motivated by the motion planning problem of robotics. In the parametrised setting, a motion planning algorithm has high degree of universality and flexibility, it can function under a variety of external conditions (such as positions of the obstacles etc). We explicitly compute the parameterised topological complexity of obstacle-avoiding collision-free motion of many particles (robots) in 3-dimensional space. Our results show that the parameterised topological complexity can be significantly higher than the standard (nonparametrised) invariant.
Cite
@article{arxiv.2009.06023,
title = {Topology of parametrised motion planning algorithms},
author = {Daniel C. Cohen and Michael Farber and Shmuel Weinberger},
journal= {arXiv preprint arXiv:2009.06023},
year = {2021}
}
Comments
To appear in SIAM Journal of Applied Algebra and Geometry