A major problem in mobile robot navigation using a map is that an accurate map needs a lot of building cost. A framework of navigation using a roughly measured map would be a solution of this problem. The paper proposes a Topological-Geometrical map, or TG map for short, which permits inaccurate description, and a method of mobile robot localization on a TG map. A TG map is built by defining the relative poses between geometrical entities in the environment. The models of the geometrical entities are supposed to be predefined, and the relative poses between them can be as inaccurate as those measured by eye. These features allow the map-building cost to be small. The robot pose is represented in a local frame attached on each entity since the robot pose based on a global reference frame might be inconsistent because of the inaccuracy of the map. Errors in relative poses between entities are represented by probability density functions, and the robot pose is estimated using a variant of Markov localization which is augmented so as to incorporate map errors into data fusion process. Simulation and experiments show that the robot pose is estimated correctly on a TG map by the proposed method.
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