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arXiv · 2009.06023

Topology of parametrised motion planning algorithms

Daniel C. Cohen·Michael Farber·Shmuel Weinberger
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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.

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BibTeXRIS

Daniel C. Cohen, Michael Farber, Shmuel Weinberger. 2020-09-13. Topology of parametrised motion planning algorithms. https://doi.org/10.1137/20m1358505

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