Several motion planning methods using networks of ran- domly generated nodes in the free space have been shown to perform well in a number of cases, however their perfor- mance degrades when paths are required to pass through nar- row passages in the free space. In [16] we proposed MAPRM, a method of sampling the conguration space in which ran- domly generated congurations, free or not, are retracted onto the medial axis of the free space without having to rst compute the medial axis; this was shown to increase sam- pling in narrow passages. In this paper we give details of the MAPRM algorithm for the case of a free- ying rigid body moving in three dimensions, and show that the retrac- tion may be carried out without explicitly computing the C- obstacles or the medial axis. We give theoretical arguments to show that this improves sampling in narrow corridors, and present preliminary experimental results comparing the per- formance to uniform random sampling from the free space.