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Abstract. D * is a greedy heuristic planning method that is widely used in robotics, including several Nomad class robots and the Mars rover prototype, to reach a destination in unknown terrain. We obtain nearly sharp lower and upper bounds of Ω(n log n/ log log n) and O(n log n), respectively, on the worst-case total distance traveled by the robot, for the grid graphs on n vertices typically used in robotics applications. For arbitrary graphs we prove an O(n log 2 n) upper bound.

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No abstract