Proximal Motion Planning Algorithms

TL;DR

This paper explores the concept of topological complexity in proximity spaces, introducing new proximal TC measures and illustrating their application with examples involving robot vacuum cleaners.

Contribution

It introduces proximal and descriptive proximal topological complexity measures and analyzes their properties and applications in robotic navigation scenarios.

Findings

Proximal TC numbers have fundamental properties similar to classical TC.

Examples on robot vacuum cleaners demonstrate the applicability of proximal TC.

Proximal homotopic distances relate to navigational complexity.

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.