Analysis of Greedy Robot-Navigation Methods

Robots often have to navigate robustly despite incomplete information about the terrain or their location in the terrain. In this case, they often use greedy methods to make planning tractable. In this paper, we analyze two such robot-navigation methods. The first method is Greedy Localization, which determines the location of a robot in known terrain by always moving it to the closest location from which it will make an observation that reduces the number of its possible locations, until it has reduced that number as much as possible. We reduce the upper bound on the number of movements of Greedy Localization from O(n 3 2 ) to O(n log n) on grid graphs and thus close to the known lower bound of Ω(n log n/ log log n), where n is the number of (unblocked) vertices of the graph that discretizes the terrain. The second method is Dynamic A* (D*), which is used on several prototypes of both urban reconnaissance and planetary robots. It moves a robot in initially unknown terrain from given start coordinates to given goal coordinates by always moving the robot on a shortest presumed unblocked path from its current coordinates to the goal coordinates, pretending that unknown terrain is unblocked, until it has reached the goal coordinates or there are no more presumed unblocked paths. We reduce the upper bound on the number of movements of D* from O(n 3 2 ) to O(n log n) on arbitrary graphs and O(n log n) on planar graphs (including grid graphs) and thus close to the known lower bound of Ω(n log n/ log log n), where n is the number of (blocked and unblocked) vertices of the graph that discretizes the terrain.