TOPOLOGY OF ROBOT MOTION PLANNING
Michael Färber · Kluwer Academic Publishers eBooks · 2005
Abstract In this paper we discuss topological problems inspired by robotics. We study in detail the robot motion planning problem. With any path-connected topological space X we associate a numerical invariant TC(X) measuring the “complexity of the problem of navigation in X.„We examine how the number TC(X) determines the structure of motion planning algorithms, both deterministic and random.