A set theoretic approach to the simultaneous localization and map building problem

Self localization of mobile robots is one of the most important problems in long range autonomous navigation. When moving in an unknown environment, the navigator must exploit measurements from exteroceptive sensors to build a map, identify landmarks and, at the same time, localize itself with respect to them. This problem is known as simultaneous localization and mapping (SLAM). In the paper a set theoretic approach to the SLAM problem is presented. Estimates of the position of the robot and the selected landmarks are derived in terms of uncertainty regions, under the hypothesis that the errors affecting all sensor measurements are unknown but bounded. Set approximation techniques are adopted in order to provide efficient recursive algorithms, suitable for online implementation.