Robust stabilization of flat and chained systems

A design method for robust stabilization of at systems , feedback equivalent to chained ones, is proposed. The method is based on iterations of well chosen open-loop steering controls. Robustness is characterized by exponential convergence to the equilibrium for any driftless systems close to the original one. The case of chained systems of dimension 4 is treated in details. Simulation of a car-like robot are given.

[1]  Claude Samson,et al.  Time-varying Feedback Stabilization of Car-like Wheeled Mobile Robots , 1993, Int. J. Robotics Res..

[2]  S. Sastry,et al.  Nonholonomic motion planning: steering using sinusoids , 1993, IEEE Trans. Autom. Control..

[3]  Philippe Martin,et al.  Flatness and motion planning : the car with n trailers. , 1992 .

[4]  Jean-Baptiste Pomet.  Explicit design of time-varying stabilizing control laws for a class of controllable systems without drift , 1992 .

[5]  M. Fliess,et al.  Flatness, motion planning and trailer systems , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[6]  S. Shankar Sastry,et al.  Stabilization of trajectories for systems with nonholonomic constraints , 1992, Proceedings 1992 IEEE International Conference on Robotics and Automation.

[7]  C. Samson.  Control of chained systems application to path following and time-varying point-stabilization of mobile robots , 1995, IEEE Trans. Autom. Control..

[8]  A. Bloch,et al.  Control and stabilization of nonholonomic dynamic systems , 1992 .

[9]  J. Coron.  Linearized Control Systems and Applications to Smooth Stabilization , 1994 .

[10]  O. J. Sordalen,et al.  Exponential stabilization of mobile robots with nonholonomic constraints , 1992 .

[11]  O. J. Sørdalen,et al.  Exponential stabilization of nonholonomic chained systems , 1995, IEEE Trans. Autom. Control..

[12]  M. Fliess,et al.  Flatness and defect of non-linear systems: introductory theory and examples , 1995 .