Motion planning in the presence of obstacles is an important problem in robotics with numerous applications in other areas. While complete motion planning algorithms do exist, they are rarely used in practice since they are computationally infeasible in all but the simplest cases. For this reason, many recent e orts have focused on probabilistic methods, which sacrifice completeness in favor of computational feasibility and applicability. In particular, several algorithms, known as probabilistic roadmap planners, have been shown to perform well in a number of practical situations; how- ever, their performance degrades when paths are required to pass through narrow passages in the free space. In this dissertation we present a method of sampling the configuration space of a rigid body moving in three dimensions in which randomly generated configurations are retracted onto the medial axis of the free space. We develop some theory of the medial axis on the configuration space SE(3) and present algorithms that perform the retraction while avoiding explicit computation of the medial axis. Finally, we give some preliminary experimental results demonstrating the performance of the algorithm.