This technical note deals with the guaranteed characterization of the part of the space that has been explored by a robot. The main difficulty of the problem is to take into account the uncertainty associated with the trajectory and the fact that the dimension of the visible space at time t may be smaller than that of the workspace. An example involving an experiment made with an actual underwater robot is presented in order to illustrate the efficiency of the approach.

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Thick ellipsoids were recently introduced by the authors to represent uncertainty in state variables of dynamic systems, not only in terms of guaranteed outer bounds but also in terms of an inner enclosure that belongs to the true solution set with certainty. Because previous work has focused on the definition and computationally efficient implementation of arithmetic operations and extensions of nonlinear standard functions, where all arguments are replaced by thick ellipsoids, this paper introduces novel operators for specifically evaluating quasi-linear system models with bounded parameters as well as for the union and intersection of thick ellipsoids. These techniques are combined in such a way that a discrete-time state observer can be designed in a predictor-corrector framework. Estimation results are presented for a combined observer-based estimation of state variables as well as disturbance forces and torques in the sense of an unknown input estimator for a hovercraft.

In this paper we will apply interval methods to solve the problem of robust localization of an underwater robot. The localization problem is cast into a constraint satisfaction problem (CSP) where constraint propagation algorithms are particularly efficient. The method is designed to work in real environments with numerous outliers. Besides, we used a new approach to represent the map by a binary image. This allow us to represent even unstructured maps. We tested the algorithm on a real data set gathered by an underwater robot in a marina located in Costa Brava.