This thesis studies the simultaneous localization and mapping problem for submarine robots, and its resolution methods using interval analysis. The principle of SLAM (Simultaneous Localization And Mapping) is the following: a submarine robot usually knows its initial position (when it is at the surface thanks to a GPS), its moving model (approximately) and has sensors enabling it to estimate its position (pressure sensor to get its depth, DVL to get its speed and measure its distance to the sea floor, inertial navigation system to get its orientation) and see its surrounding environment (sonar). However, in spite of all these sensors, the more it moves, the more its position estimation errors increase: the robot is lost. By going next to the same objects (or any distinguishable mark in its environment) several times, it should be able to evaluate their position (with a given accuracy) the first time from its own position (cartography from localization), then compute and correct its trajectory evaluation by taking them as mark next time when it is lost (localization from cartography). Because measurements from sensors or variables used to describe the behaviour of robots are often erroneous, they can be represented using different ways: probabilistic distributions, particles, continuous sets... Sensors or actuators manufacturers usually provide bounds (related to precision, accuracy...). Therefore, we can represent these values as intervals. Set-membership methods such as interval analysis enable to obtain results from equations involving intervals. The main advantage of these methods is that it is sure that no solution is lost (taking into account the assumptions made), contrary to probabilistic approaches, where the most probable solutions are obtained. In this thesis, the use of intervals computations for the SLAM of underwater robots and a comparison between several existing methods are studied. Additionally, a new method to handle better the problem of fleeting data (data that are only significant during short and unknown time intervals), often met with data from sonars, will be proposed. Applications of this work are for example in the development of autonomous submarine robots (often called AUVs for Autonomous Underwater Vehicles or UUVs for Unmanned Underwater Vehicles). Indeed, contrary to teleoperated robots, they must be able to localize themselves in their environment to do their work. These robots can do several missions: hydrographic data collection, shipwrecks or objects (sea mines...) localization, surveillance (pollution detection, pipelines surveys...)... Nowadays, those tasks are mostly done by humans, directly with divers or indirectly using teleoperated submarines when the conditions are dangerous or difficult.
