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

• Published in: Proceedings 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
• Language: English
• Published: IEEE 1997
• Subjects: Control systems; Mechanical systems; Mobile robots; Null value; Sliding mode control; Stability; State feedback; Sufficient conditions
• ISBN: 0780341872; 9780780341876
• ISSN: 0191-2216
• DOI: 10.1109/CDC.1997.652498

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.