Robot Localization Using Polygon Distances

We present an approach to the localization problem, for which polygon distances play an important role. In our setting of this problem the robot is only equipped with a map of its environment, a range sensor, and possibly a compass. To solve this problem, we first study an idealized version of it, where all data is exact and where the robot has a compass. This leads to the pure geometrical problem of fitting a visibility polygon into the map. This problem was solved very efficiently by Guibas, Motwani, and Raghavan. Unfortunately, their method is not applicable for realistic cases, where all the data is noisy. To overcome the problems we introduce a distance function, the polar coordinate metric, that models the resemblance between a range scan and the structures of the original method. We show some important properties of the polar coordinate metric and how we can compute it efficiently. Finally, we show how this metric is used in our approach and in our experimental Robot Localization Program RoLoPro.