Fuzzy distance functions for motion planning

The problem of planning motions offline for a robot in the presence of obstacles via an algorithm that does not proceed by a discretization of the search space involves defining good heuristics to characterize the proximal relationships between two rigid bodies and the development of algorithms for their computation. Several measures are presented, and schemes for their computation are developed. The performances of the algorithms are determined in terms of their running time. The advantage of the fuzzy model is that it lends itself easily to numerical computation involving manipulation of the coordinates of the extreme points.<>