Turning a Corner with a Dubins Car

We study the problem of computing shortest collision-free Dubins paths when turning a corner. We present a sufficient condition for a closed-form solution. Specifically, consider S as the set consisting of paths of the form RSRSR, RSRSL, LSRSR and LSRSL that pass through the interior corner, where sub-paths RSR, RSL, and LSR are elementary Dubins paths composed of segments which are either straight (S) or turning left (L) or right (R). We find the closed-form optimal path around a corner when S is nonempty. Our solution can be used in an efficient path planner, for example, when navigating corridors. It can also be used as a subroutine for planners such as RRTs.