Invariant manifold approach for the stabilization of nonholonomic systems in chained form: application to a car-like mobile robot

It is shown that the class of n-dimensional nonholonomic chained systems can be exponentially stabilized using the invariant manifold techniques. To this end, an invariant manifold, on which all the closed-loop trajectories tend to the origin, is derived for this class of systems under a linear smoo...

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Bibliographic Details
Published inProceedings of the 36th IEEE Conference on Decision and Control Vol. 4; pp. 4038 - 4043 vol.4
Main Authors Tayebi, A., Tadjine, M., Rachid, A.
Format Conference Proceeding
LanguageEnglish
Published IEEE 1997
Subjects
Control systems
Mechanical systems
Mobile robots
Null value
Sliding mode control
Stability
State feedback
Sufficient conditions
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ISBN0780341872
9780780341876
ISSN0191-2216
DOI10.1109/CDC.1997.652498

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Summary:It is shown that the class of n-dimensional nonholonomic chained systems can be exponentially stabilized using the invariant manifold techniques. To this end, an invariant manifold, on which all the closed-loop trajectories tend to the origin, is derived for this class of systems under a linear smooth time-invariant state feedback. Thereafter, this manifold is made attractive by means of a discontinuous, time-invariant, state feedback. The proposed control scheme ensures exponential stability of the closed-loop system in a large domain excluding, at the initial time, the null value of the first state variable. Finally, our controller is applied for the stabilization of a car-like mobile robot and simulation results are given to highlight its effectiveness.
ISBN:0780341872
9780780341876
ISSN:0191-2216
DOI:10.1109/CDC.1997.652498