Using polygon distances for localization

The authors 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. The authors' 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. They introduce a polygon distance, the so-called polar coordinate metric for star-shaped polygons, which satisfies most of these requirements. They show how this metric can be computed efficiently and how it is used within their approach. Furthermore, they present some useful extensions of their approach, which can easily be added using the properties of the polar coordinate metric and of the localization algorithms.