Simultaneous Localization and Mapping in Unstructured Environments

This thesis deals with the simultaneous localization and mapping (SLAM) problem in unstructured environments, \textit{i.e.} which cannot be described by geometrical features. This type of environment frequently occurs in an underwater context. Unlike classical approaches, the environment is not described by a collection of punctual features or landmarks, but directly by sets. These sets, called shapes, are associated with physical features such as the relief, some textures or, in a more symbolic way, the space free of obstacles that can be sensed around a robot. In a theoretical point of view, the SLAM problem is formalized as an hybrid constraint network where the variables are vectors and subsets of $\mathbb{R}^{n}$. Whereas an uncertain real number is enclosed in an interval, an uncertain shape is enclosed in an interval of sets. The main contribution of this thesis is the introduction of a new formalism, based on interval analysis, able to deal with these domains. As an application, we illustrate our method on a SLAM problem based on bathymetric data acquired by an autonomous underwater vehicle (AUV).