Nonholonomic path planning optimization for Dubins´ vehicles

In this paper we deal with the problem of path length optimization for nonholonomic robots modeled as Dubins´ vehicles. We present an improved solution that computes paths through two-dimensional waypoints, that are shorter than those produced by one of the most used techniques in the literature. We initially present an optimization cost function that proves to be better suited for the nonholonomic constraints of the vehicles that are the focus of this work. We also propose an improvement for the Alternating Algorithm, used to determinate the orientation angles on the calculation of the Dubins´ Path through the waypoints. Finally, we use a recently developed optimization meta-heuristic, called Continuous-GRASP (C-GRASP), to generate a path that is shorter than paths obtained with classical techniques. Our results show significant improvements on the search for optimal paths for the case of nonholonomic vehicles. Our methodology was thoroughly evaluated and validated in simulation, and the results have shown a decrease on path´s length of 28% on average, compared with the classic technique found in literature. In some cases a reduction of approximately 50% was obtained.