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

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.