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Both geometric and semantic information of the search space is imperative fora good plan. We encode those properties in a weighted colored graph (geometricinformation in terms of edge weight and semantic information in terms of edgeand vertex color), and propose a generalized A* to find the shortest path amongthe set of paths with minimal inclusion of low-ranked color edges. We prove thecompleteness and optimality of this Class-Ordered A* (COA*) algorithm withrespect to the hereto defined notion of optimality. The utility of COA* isnumerically validated in a ternary graph with feasible, infeasible, and unknownvertices and edges for the cases of a 2D mobile robot, a 3D robotic arm, and a5D robotic arm with limited sensing capabilities. We compare the results ofCOA* to that of the regular A* algorithm, the latter of which finds theshortest path regardless of uncertainty, and we show that the COA* dominatesthe A* solution in terms of finding less uncertain paths.

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