Path-Connectivity of the Free Space

Abstract

This paper revisits the notion of free configuration space and reviews some of its path-connectivity related properties. Literature on motion planning reveals at least three different definitions for the free configuration space of a robot in the presence of obstacles. This paper shows that, assuming regularity of both object and obstacles, those three definitions are equivalent. We show the three definitions regularize the free space and therefore prevent the existence of “thin bits”, or low dimensional strata. The paper concludes discussing a series of properties regarding the existence and smoothability of contact-free paths between pairs of configurations.