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

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  • Jaulin, L.
  • Walter, E.
  • Lévêque, O.
  • Meizel, D.

Abstract

Characterizing the set of all parameter vectors such that their image by a vector belongs to a given set is a set-inversion problem. The algorithm set inversion via interval analysis (SIVIA) 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.

Suggested Citation

  • Jaulin, L. & Walter, E. & Lévêque, O. & Meizel, D., 2000. "Set inversion for χ-algorithms, with application to guaranteed robot localization," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 52(3), pages 197-210.
    • Handle: RePEc:eee:matcom:v:52:y:2000:i:3:p:197-210
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    References listed on IDEAS

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    1. Jaulin, Luc & Walter, Eric, 1993. "Guaranteed nonlinear parameter estimation from bounded-error data via interval analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 35(2), pages 123-137.
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    Cited by:

    1. Tikhomirov, Boris I. (Тихомиров, Борис) & Frenkel, Alexander A. (Френкель, Александр), 2017. "On Unified Socio-Economic Policy and Strategic Planning [О Единой Социально-Экономической Политике И Стратегическом Планировании]," Ekonomicheskaya Politika / Economic Policy, Russian Presidential Academy of National Economy and Public Administration, vol. 4, pages 82-117, August.

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