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The problem that a robot navigates autonomously through its environment, builds its own map and localizes itself in the map (known a the SLAM problem), is still an open problem. Most of the approaches to solve the SLAM problem divide the space into regions and compute the probability that the robot is in each region. We propose in this paper a different solution based on the use of a reasoning process to build the map, which will provide the following advantages: (1) we will store in the map hybrid (qualitative + quantitative) information from landmarks. Qualitative representation will allow us the management of the uncertainty information provided by the robot sensors; and (2) we will store in the map relative information of the landmarks which appear in the environment, therefore the map will be independent of the point of view of the robot. Moreover, we are going to use a reasoning process which will allow us to solve three very important problems in robotics: (a) where the robot is; (b) which is the orientation of the map where the robot is; and (c) towards where the robot should go according to the map to follow a plan.
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