2D dubins path in environments with obstacle

Abstract

We recapitulate the achievement about the Dubins path as well as some precise proofs which are important but omitted by Dubins. Then we prove that the shortest path (R -geodesic) in environments with an obstacle consists of no more than five segments, each of which is either an arc or a straight line. To obtain such R -geodesic, an effective algorithm is presented followed by a numerical simulation as verification. © 2013 Dongxiao Yang et al.