An efficient algorithm to find a shortest path for a car-like robot

We study the problem of finding a shortest path for a car-like mobile robot with a minimal turning radius constraint. This vehicle can move either forward or backward in an unconstrained environment. By applying necessary conditions on the segment lengths of shortest paths, we partition the configuration space into elements such that a single path type is associated with 150 elements and two path types are associated with the other 11 elements. A shortest path from a fixed initial configuration to any final configuration in an element can always be found among the paths of types associated with that element. We then present an algorithm based on this partition and we give results showing that our algorithm is 15 times faster on average than the Reeds-Shepp algorithm (1990).