Set inversion for χ-algorithms with application to guaranteed robot localization

Luc Jaulin (1, 2, 3) , Eric Walter (4) , Olivier Leveque (3) , Dominique Meizel (3)

1 STIC - Département STIC [Brest]
2 Lab-STICC - Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance
3 LISA - Laboratoire d'Ingéniérie des Systèmes Automatisés
4 L2S - Laboratoire des signaux et systèmes

Characterizing the set of all parameter vectors such that their image by a vector function belongs to a given set is a set-inversion problem. The algorithm SIVIA (Set Inversion Via Interval Analysis) makes it possible to perform this task in an approximate but guaranteed way. In the examples treated so far, the function to be inverted was given either explicitly or by a sequential algorithm. In this paper, this approach is extended to the case of branching algorithms involving if statements. As an illustration, the static localization of a robot from bounded-error range measurements is considered. The notion of remoteness, introduced for an archetypal but realistic sonar model, allows this problem to be cast into the set-inversion framework.

Mots clés: Bounded-error; interval analysis; Nonlinear estimation; Robot localization; Set-inversion

Domaines: Sciences de l'ingénieur [physics]

Luc Jaulin, Eric Walter, Olivier Leveque, Dominique Meizel. Set inversion for χ-algorithms with application to guaranteed robot localization. Mathematics and Computers in Simulation, 2000, 52, pp.197-210. ⟨hal-00844879⟩