Autonomous robots, motion algorithms and topology

Abstract

In this survey article we show that the task of programming a robot to move autonomously can be assisted by using methods and concepts of algebraic topology. We start by explaining the main motivations and basic results and then progress to cover certain most recent developments. In particular, we discuss the rationality conjecture involving the infinite sequence of topological complexities and the theory of sequential parametrised motion planning algorithms. We analyse the problem of controlling multiple robots in the presence of many obstacles in the Euclidean space, and in the final section of the paper we present an explicit motion algorithm (inspired by topological ideas) for controlling swarms of robots avoiding collisions with multiple obstacles.