Predictive variable structure control of nonholonomic chained systems

A novel variable structure control strategy for a class of second-order nonlinear systems is presented based on the phase-plane analysis and computing prediction. In this strategy control is switched by online prediction of the trajectory behaviour of the closed-loop system; control switching does not occur continuously, so the chattering that occurs in conventional variable structure control methods can be avoided completely. It is proved that the states of the closed-loop system can be stabilized to the origin exponentially and the trajectory of the closed-loop system does not overshoot in general. As an application, the proposed predictive variable structure control strategy is used to stabilize nonholonomic systems in chained form. An example of a wheeled mobile robot is studied and associated simulation results demonstrate the effectiveness of the proposed control strategy.

[1]  Richard M. Murray,et al.  Non-holonomic control systems: from steering to stabilization with sinusoids , 1995 .

[2]  Richard M. Murray,et al.  Nonholonomic control systems: from steering to stabilization with sinusoids , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

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

[4]  Zhong-Ping Jiang,et al.  Iterative design of time-varying stabilizers for multi-input systems in chained form , 1996 .

[5]  Jong-Hwan Kim,et al.  Variable Structure Control of Nonholonomic Wheeled Mobile Robot , 1995, ICRA.

[6]  R. Murray,et al.  Exponential stabilization of driftless nonlinear control systems using homogeneous feedback , 1997, IEEE Trans. Autom. Control..

[7]  V. I. Utkin,et al.  Stabilization of non-holonomic mobile robots using Lyapunov functions for navigation and sliding mode control , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

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

[9]  Alessandro Astolfi,et al.  Stability study of a fuzzy controlled mobile robot , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[10]  R. W. Brockett,et al.  Asymptotic stability and feedback stabilization , 1982 .

[11]  Sergey V. Drakunov,et al.  Stabilization and tracking in the nonholonomic integrator via sliding modes , 1996 .

[12]  Giuseppe Oriolo,et al.  Cyclic learning control of chained-form systems with application to car-like robots , 1996 .

[13]  João Pedro Hespanha,et al.  Stabilization of nonholonomic integrators via logic-based switching , 1999, Autom..

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

[15]  A. Astolfi.  Discontinuous control of nonholonomic systems , 1996 .

[16]  Abdelhamid Tayebi,et al.  Invariant manifold approach for the stabilization of nonholonomic systems in chained form: application to a car-like mobile robot , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[17]  Alessandro Astolfi.  Discontinuous Control of the Brockett Integrator , 1998, Eur. J. Control.

[18]  Sergey V. Drakunov,et al.  Stabilization of a nonholonomic system via sliding modes , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[19]  H. Nijmeijer,et al.  Practical stabilization of nonlinear systems in chained form , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[20]  Alessandro Astolfi,et al.  Exponential stabilization of a car-like vehicle , 1995, Proceedings of 1995 IEEE International Conference on Robotics and Automation.

[21]  Sergey V. Drakunov,et al.  Tracking in nonholonomic dynamic systems via sliding modes , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[22]  Weiliang Xu,et al.  Variable structure exponential stabilization of chained systems based on the extended nonholonomic integrator , 2000 .

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

[24]  R. Murray,et al.  Exponential stabilization of driftless nonlinear control systems via time-varying, homogeneous feedback , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

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