Feedback linearization and stabilization of second-order non-holonomic chained systems

This paper presents a theoretical framework for non-regular feedback linearization and stabilization of second-order non-holonomic chained systems. By giving a new criterion for the problem of non-smooth non-regular feedback linearization, it is proved that second-order chained systems are non-regular static state feedback linearizable. A discontinuous control law is obtained based on linear system theory and the inversion technique. The design mechanism is generalized to higher-order non-holonomic chained systems. Simulation studies are carried out to show the effectiveness of the approach.

[1]  Mark W. Spong,et al.  Robot dynamics and control , 1989 .

[2]  Mark W. Spong,et al.  The swing up control problem for the Acrobot , 1995 .

[3]  J. Baillieul,et al.  Control problems in super-articulated mechanical systems , 1994, IEEE Trans. Autom. Control..

[4]  S. Bhat,et al.  Continuous finite-time stabilization of the translational and rotational double integrators , 1998, IEEE Trans. Autom. Control..

[5]  Einar Berglund,et al.  Control of an underwater vehicle with nonholonomic acceleration constraints , 1994 .

[6]  John Chiasson,et al.  A new approach to dynamic feedback linearization control of an induction motor , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[7]  Carlos Canudas de Wit,et al.  Theory of Robot Control , 1996 .

[8]  Giuseppe Oriolo,et al.  Steering a class of redundant mechanisms through end-effector generalized forces , 1998, IEEE Trans. Robotics Autom..

[9]  Alessandro Astolfi,et al.  Discontinuous control of high-order generalized chained systems , 1999 .

[10]  Arjan van der Schaft,et al.  Dynamics and control of a class of underactuated mechanical systems , 1999, IEEE Trans. Autom. Control..

[11]  K. Y. Wichlund,et al.  Control of Vehicles with Second-Order , 1995 .

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

[13]  R. M’Closkey,et al.  Time-varying homogeneous feedback: Design tools for the exponential stabilization of systems with drift , 1998 .

[14]  Giuseppe Oriolo,et al.  Dynamic mobility of redundant robots using end-effector commands , 1996, Proceedings of IEEE International Conference on Robotics and Automation.

[15]  Richard M. Murray,et al.  A Mathematical Introduction to Robotic Manipulation , 1994 .

[16]  P. Tsiotras,et al.  Control design for chained-form systems with bounded inputs , 2000 .

[17]  J. Lévine,et al.  On dynamic feedback linearization , 1989 .

[18]  Ilya Kolmanovsky,et al.  Developments in nonholonomic control problems , 1995 .

[19]  Xiaohua Xia,et al.  On Nonregular Feedback Linearization , 1997, Autom..

[20]  Shuzhi Sam Ge,et al.  Adaptive Neural Network Control of Robotic Manipulators , 1999, World Scientific Series in Robotics and Intelligent Systems.

[21]  D.G. Taylor,et al.  Nonlinear control of electric machines: an overview , 1994, IEEE Control Systems.

[22]  Giuseppe Oriolo,et al.  Control of mechanical systems with second-order nonholonomic constraints: underactuated manipulators , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[23]  Naoji Shiroma,et al.  Feedback control of a 3-DOF planar underactuated manipulator , 1997, Proceedings of International Conference on Robotics and Automation.

[24]  Chun-Yi Su,et al.  Adaptive variable structure set-point control of underactuated robots , 1999, IEEE Trans. Autom. Control..