Interval analysis for guaranteed and robust non-linear estimation in robotics

One of the challenges of interval analysis is to explore and bridge the gap between trivial illustrative examples for which it is not really needed an d actual complicated applications for which it is still powerless. Two exam ples of applications pertaining to this gap are presented in this paper. Th e first one corresponds to the forward kinematic problem for a Stewart-Goug h platform, a benchmark for numerical and symbolical computations. All real solutions are isolated in a guaranteed manner. The second example is relat ive to the localization and tracking of a vehicle in a partially known envi ronment from distance measurements provided by sonars. The unavoidable pres ence of outliers is taken into account, which makes the method actually app licable. None of these problems can be solved satisfactorily by the usual l ocal numerical methods based on iterative refinements, and the advantages p rovided by an approach based on interval analysis are evidenced.