Using polygon distances for localization

We consider the localization problem for a robot, which has only a range sensor and a polygonal map of its environment. An idealized version of this problem, where the robot additionally has a compass, was solved by Guibas, Motwani, and Raghavan. Unfortunately, their method is restricted to scenarios where all the sensors and the map are exact, that is, without any noise. Our approach for adapting their scheme to realistic scenarios is to use polygon distances for modeling the similarity between a range scan and the preprocessed visibility information. Suitable distances for this approach should have certain properties, for example, they should be stable under the presence of noise and they should be fast to compute. We introduce a polygon distance, the so-called polar coordinate metric for star-shaped polygons, which satisfies most of these requirements. We show how this metric can be computed efficiently and how it is used within our approach. Furthermore, we present some useful extensions of our approach, which can easily be added using the properties of the polar coordinate metric and of the localization algorithms.