Bounds on the Travel Cost of a Mars Rover Prototype Search Heuristic
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 $\Omega(n\log n/\log\log n)$ 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 log2 n) upper bound.