A continuation method for nonholonomic path-finding problems

We study the mathematical theory of an algorithm for nonholonomic point-to-point path finding, based on a "continuation" or "deformation" method, in which one starts with an admissible trajectory that goes from the desired initial point p~ to some point q~/sub 0/, and then tries to construct a one-parameter family of trajectories, whose terminal points q~/sub s/ describe, as s varies, a path that joins q/sub 0/ to the desired terminal point q~.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>