Control of chained systems application to path following and time-varying point-stabilization of mobile robots

Chain form systems have recently been introduced to model the kinematics of a class of nonholonomic mechanical systems. The first part of the study is centered on control design and analysis for nonlinear systems which can be converted to the chain form. Solutions to various control problems (open-loop steering, partial or complete state feedback stabilization) are either recalled, generalized, or developed. In particular, globally stabilizing time-varying feedbacks are derived, and a discussion of their convergence properties is provided. Application to the control of nonholonomic wheeled mobile robots is described in the second part of the study by considering the case of a car pulling trailers. >

[1]  La Taille,et al.  Courbes et surfaces , 1959 .

[2]  J. Carr.  Applications of Centre Manifold Theory , 1981 .

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

[4]  E D Dickmanns,et al.  AUTONOMOUS HIGH SPEED ROAD VEHICLE GUIDANCE BY COMPUTER VISION , 1987 .

[5]  Anthony M. Bloch,et al.  Control of mechanical systems with classical nonholonomic constraints , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[6]  Claude Samson,et al.  Feedback control of a nonholonomic wheeled cart in Cartesian space , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[7]  C. Canudas de Wit,et al.  Exponential stabilization of mobile robots with nonholonomic constraints , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[8]  Mitsuji Sampei,et al.  Path tracking control of trailer-like mobile robot , 1991, Proceedings IROS '91:IEEE/RSJ International Workshop on Intelligent Robots and Systems '91.

[9]  Claude Samson,et al.  Velocity and torque feedback control of a nonholonomic cart , 1991 .

[10]  Karim Ait-Abderrahim,et al.  Feedback stabilization of a nonholonomic wheeled mobile robot , 1991, Proceedings IROS '91:IEEE/RSJ International Workshop on Intelligent Robots and Systems '91.

[11]  Georges Bastin,et al.  Modelling and control of non-holonomic wheeled mobile robots , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[12]  J. Laumond.  Controllability of a multibody mobile robot , 1991 .

[13]  Jean-Michel Coron,et al.  Global asymptotic stabilization for controllable systems without drift , 1992, Math. Control. Signals Syst..

[14]  S. Shankar Sastry,et al.  Steering car-like systems with trailers using sinusoids , 1992, Proceedings 1992 IEEE International Conference on Robotics and Automation.

[15]  J. Coron.  LINKS BETWEEN LOCAL CONTROLLABILITY AND LOCAL CONTINUOUS STABILIZATION , 1992 .

[16]  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.

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

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

[19]  D. Normand-Cyrot,et al.  An introduction to motion planning under multirate digital control , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[20]  Ole Jakob Sørdalen,et al.  Conversion of the kinematics of a car with n trailers into a chained form , 1993, [1993] Proceedings IEEE International Conference on Robotics and Automation.

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

[22]  R. Murray,et al.  Convergence Rates for Nonholonomic Systems in Power Form , 1993, 1993 American Control Conference.

[23]  Zexiang Li,et al.  Smooth Time-Periodic Feedback Solutions for Nonholonomic Motion Planning , 1993 .

[24]  R. Murray,et al.  Applications and extensions of Goursat normal form to control of nonlinear systems , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[25]  Jean-Baptiste Pomet,et al.  Time-varying exponential stabilization of nonholonomic systems in power form , 1994 .

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

[27]  Alain Micaelli,et al.  Trajectory tracking for two-steering-wheels mobile robots , 1994 .