An Approximation Algorithm for the Robot Localization Problem

Localization is a fundamental problem in robotics. The robot possesses line-of-sight sensors, a compass, and a map of its polygonal environment; it must determine its location at a minimum cost of travel distance. Localization is NP-hard [3], even to minimize within a c log n factor [15], where n is the number of polygon vertices. No approximation algorithm for the problem has been known. We give a strongly polynomial time O(log n log r)-factor approximation algorithm, where r is the number of reflex vertices. Technical features of the algorithm include a new edge-visibility based partition decomposition of the plane, and the idea of repeatedly planning travel on a “majority-rule” map, which permits a plan to be a route rather than a decision tree.