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Invariant Manifold Approach for the Stabilization of Nonholonomic Chained Systems: Application to a Mobile Robot

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Abstract

In this paper it is shown that a class ofn-dimensional nonholonomic chained systems can bestabilized using the invariant manifold approach. First, we derive aninvariant manifold for this class of systems and we show that, once onit, all the closed-loop trajectories tend to the origin under a linearsmooth time-invariant state feedback. Thereafter, it is shown that thismanifold can be made attractive by means of a discontinuoustime-invariant state feedback. Finally, a mobile robot is taken as anexample demonstrating the effectiveness of our study.

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Authors and Affiliations

  1. Department of Electrical Engineering, Lakehead University, 955 Oliver Road, Thunder Bay, Ontario, P7B 5E1, Canada

    A. Tayebi

  2. Process Control Laboratory, ENP, Alger, Algeria

    M. Tadjine

  3. Laboratoire des Systèmes Automatiques, Université de Picardie Jules Verne, 80000, Amiens, France

    A. Rachid

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  1. A. Tayebi
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  2. M. Tadjine
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  3. A. Rachid
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Tayebi, A., Tadjine, M. & Rachid, A. Invariant Manifold Approach for the Stabilization of Nonholonomic Chained Systems: Application to a Mobile Robot. Nonlinear Dynamics 24, 167–181 (2001). https://doi.org/10.1023/A:1008318423148

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