Discontinuous backstepping for stabilization of nonholonomic mobile robots

Presents a method of performing integrator backstepping in systems that are discontinuous, either due to their inherent structure or because of the applied control input. The proposed technique is applied to the stabilization problem of the dynamic system of a nonholonomic mobile robot. Simulation studies indicate that the methodology can also help alleviate the problem of chattering that is commonly associated with discontinuous nonholonomic controllers.

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

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

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

[4]  Eduardo Sontag,et al.  Remarks on control Lyapunov functions for discontinuous stabilizing feedback , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[5]  George J. Pappas,et al.  Modeling and feedback control of nonholonomic mobile vehicles , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[6]  Miroslav Krstic,et al.  Nonlinear and adaptive control de-sign , 1995 .

[7]  R. Brockett Control Theory and Singular Riemannian Geometry , 1982 .

[8]  Frank L. Lewis,et al.  Control of a nonholonomic mobile robot: backstepping kinematics into dynamics , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

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

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

[11]  J B Pomet,et al.  EXPLICIT DESIGN OF TIME-VARYING CONTROL LAWS FOR A CLASS OF CONTROLLABLE SYSTEMS WITHOUT DRIFT , 1992 .

[12]  G. Campion,et al.  Modelling and state feedback control of nonholonomic mechanical systems , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[13]  D. Mayne Nonlinear and Adaptive Control Design [Book Review] , 1996, IEEE Transactions on Automatic Control.

[14]  Henk Nijmeijer,et al.  Tracking Control of Mobile Robots: A Case Study in Backstepping , 1997, Autom..

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

[16]  J. Canny,et al.  Nonholonomic Motion Planning , 1992 .

[17]  L. Dai,et al.  Non-holonomic Kinematics and the Role of Elliptic Functions in Constructive Controllability , 1993 .

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

[19]  F. Clarke Optimization And Nonsmooth Analysis , 1983 .

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

[21]  B. Paden,et al.  Lyapunov stability theory of nonsmooth systems , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[22]  Gerardo Lafferriere,et al.  A Differential Geometric Approach to Motion Planning , 1993 .