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Canonical representation of a nonstationary path following problem

  • Robotics
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Journal of Computer and Systems Sciences International Aims and scope

Abstract

The path following problem for kinematic models of wheeled robots governed by nonlinear nonstationary affine systems with scalar control is considered. The concept of a canonical representation for this problem is introduced. The path following problem in a canonical form is stated as that of stabilizing zero solution with respect to a part of the variables and is easily solved by applying the feedback linearization technique. The original problem is shown to reduce to a canonical form by applying a time-scale transformation and converting the intermediate affine system obtained to a normal form. It is noted that such a representation is not unique and depends on the choice of the time-scale transformation applied. The advantages and disadvantages of the three canonical representations obtained by means of three different, previously applied time-scale transformations are discussed. An example of the path following problem described by an affine system with a nonstationary drift field is presented.

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Authors and Affiliations

  1. Institute of Control Sciences, Russian Academy of Sciences, ul. Profsoyuznaya 65, Moscow, 117997, Russia

    A. V. Pesterev & L. B. Rapoport

  2. Javad GNSS, LLC, The Triumph Palace, Moscow, 125057, Russia

    A. V. Pesterev

  3. Bauman Moscow State Technical University, Vtoraya Baumanskaya ul. 5, Moscow, 105005, Russia

    S. B. Tkachev

  4. Institute of System Analysis, Russian Academy of Sciences, ul. 60-letiya Oktyabrya 9, Moscow, 117312, Russia

    S. B. Tkachev

Authors
  1. A. V. Pesterev
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  2. L. B. Rapoport
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  3. S. B. Tkachev
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Correspondence to A. V. Pesterev.

Additional information

Original Russian Text © A.V. Pesterev, L.B. Rapoport, S.B. Tkachev, 2015, published in Izvestiya Akademii Nauk. Teoriya i Sistemy Upravleniya, 2015, No. 4, pp. 160–176.

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Pesterev, A.V., Rapoport, L.B. & Tkachev, S.B. Canonical representation of a nonstationary path following problem. J. Comput. Syst. Sci. Int. 54, 656–670 (2015). https://doi.org/10.1134/S1064230715040115

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  • DOI: https://doi.org/10.1134/S1064230715040115

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