Proximal Motion Planning Algorithms
Algebraic Topology
2023-05-24 v1
Abstract
In this paper, we transfer the problem of measuring navigational complexity in topological spaces to the nearness theory. We investigate the most important component of this problem, the topological complexity number (denoted by TC), with its different versions including relative and higher TC, on the proximal Schwarz genus as well as the proximal (higher) homotopic distance. We outline the fundamental properties of some concepts related to the proximal (or descriptive proximal) TC numbers. In addition, we provide some instances of (descriptive) proximity spaces, specifically on basic robot vacuum cleaners, to illustrate the results given on proximal and descriptive proximal TC.
Cite
@article{arxiv.2305.13726,
title = {Proximal Motion Planning Algorithms},
author = {Melih İs and İsmet Karaca},
journal= {arXiv preprint arXiv:2305.13726},
year = {2023}
}
Comments
27 pages, 4 figures