This thesis deals with mobile robot localization problems, and more precisely with the interest of a set-membership approach to those problems. Nowadays most of the approaches to localize a robot are probabilistics. This document proposes alternatives based on interval analysis. First a set-membership approach dealing with the global localization problem is presented. The global localization problem aims to localize a robot without any knowledge of its initial pose (position and orientation). The presented method casts the localization problem into a constraint satisfaction problem (CSP). It allows to localize the robot by using the knowledge of the environment and LIDAR sensor measurements. This approach is validated by several experimentations and is compared to the well known Monte Carlo Localization (MCL). Then a visibility relation is studied. Two points are visible if the segment defined by those two points does not intersect any obstacle, otherwise they are non-visible. By using interval analysis, contractors associated to the visibility and non-visibility relations are presented. After a theoretical presentation of the visibility, two applications of those contractors are illustrated: the pose tracking of a team of robots using a boolean information, and a new constraint for the global localization algorithm.
