On the generation of nearly optimal, planar paths of bounded curvature and bounded curvature gradient

We present a numerically efficient scheme to generate a family of path primitives that can be used to construct paths that take into consideration point-wise constraints on both the curvature and its derivative. The statement of the problem is a generalization of the Dubins problem to account for more realistic vehicle dynamics. The problem is solved by appropriate concatenations of line segments, circular arcs and pieces of clothoids, which are the path primitives in our scheme. Our analysis reveals that the use of clothoid segments, in addition to line segments and circular arcs, for path generation introduces significant changes on issues such as path admissibility and length minimality, when compared with the standard Dubins problem.