A Generalized A* Algorithm for Finding Globally Optimal Paths in Weighted Colored Graphs

Abstract

Both geometric and semantic information of the search space are imperative for a good plan. We encode those properties in a weighted colored graph (geometric information in terms of edge weight and semantic information in terms of edge and vertex color) and propose a generalized A^∗ to find the shortest path among the set of paths with minimal inclusion of low-ranked color edges. We prove the completeness and optimality of this Class-Ordered A^∗ (COA^∗ ) algorithm with respect to the hereto defined notion of optimality. The utility of COA^∗ is numerically validated in a ternary graph with feasible, infeasible, and unknown vertices and edges for the cases of a 2D mobile robot, a 3D robotic arm, and a 5D robotic arm with limited sensing capabilities. We compare the results of COA^∗ to that of the regular A^∗ algorithm, the latter of which finds a shortest path regardless of the semantic information, and we show that the COA^∗ dominates the A^∗ solution in terms of finding less uncertain paths.