A heuristic approach to finding diverse short paths

We present an algorithm that seeks to find a set of diverse, short paths through a roadmap graph. The usefulness of a such a set is illustrated in robotic motion planning and routing applications wherein a precomputed roadmap of the environment is partially invalidated by some change, for example, relocation of obstacles or reconfiguration of the robot. Our algorithm employs the heuristic that nearby configurations are likely to be invalidated by the same change. To find diverse short paths, the algorithm finds the shortest detour avoiding a collection of balls imposed on the graph as simulated obstacles. Different collections yield different short paths. Paths may then be checked for validity as a cheap alternative to checking or reconstructing the entire roadmap. We describe a formal definition of path set diversity and several measures on which to evaluate our algorithm. We compare the speed and quality of our heuristic algorithm's results against an exact algorithm that computes the optimally shortest set of paths on the roadmap having a minimum diversity. We show that, with tolerable loss in shortness, we produce equally diverse path sets orders of magnitude more quickly.