Interval analysis for guaranteed and robust nonlinear estimation in robotics

Eric Walter (1) , Luc Jaulin (2, 3, 4) , Michel Kieffer (1, 5, 6)

1 L2S - Laboratoire des signaux et systèmes
2 STIC - Département STIC [Brest]
3 Lab-STICC - Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance
4 LISA - Laboratoire d'Ingéniérie des Systèmes Automatisés
5 LTCI - Laboratoire Traitement et Communication de l'Information
6 IUF - Institut universitaire de France

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 and actual complicated applications for which it is still powerless. Two examples of applications pertaining to this gap are presented in this paper. The first one corresponds to the forward kinematic problem for a Stewart-Gough patform, a benchmark for numerical and symbolical computations. All real solutions are isolated in a guaranteed manner. The second example is relative to the localization and tracking of a vehicle in a unavoidable presence of outliers is taken into account, which makes the method acyually applicable. None of these problems can be solved satisfactorily by the usual local numerical methods based on iterative refinements, and the advantages provided by an approach based on interval analysis are evidenced.

Mots clés: Stewart-Gough platform; Interval analysis; outliers; robotics; robust estimation; state estimation; Stewart-Gough platform.

Domaines: Sciences de l'ingénieur [physics]

Eric Walter, Luc Jaulin, Michel Kieffer. Interval analysis for guaranteed and robust nonlinear estimation in robotics. Nonlinear Analysis: Theory, Methods and Applications, 2001, 47, pp.191-202. ⟨hal-00845193⟩