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¯₀, and then tries to construct a one-parameter family of trajectories, whose terminal points q¯_s describe, as s varies, a path that joins q₀ to the desired terminal point q¯