Global exponential tracking control of a mobile robot system via a PE condition

This paper presents the design of a differentiable, kinematic control law that achieves global asymptotic tracking. In addition, we also illustrate how the proposed kinematic controller provides global exponential tracking provided the reference trajectory satisfies a mild persistency of excitation (PE) condition. We also illustrate how the proposed kinematic controller can be slightly modified to provide for global asymptotic regulation of both the position and orientation of the mobile robot. Finally, we embed the differentiable kinematic controller inside of an adaptive controller that fosters global asymptotic tracking despite parametric uncertainty associated with the dynamic model. Experimental results are also provided to illustrate the performance of the proposed adaptive tracking controller.

[1]  Jean-Michel Coron,et al.  A Remark on the Design of Time-Varying Stabilizing Feedback Laws for Controllable Systems without Drift , 1992 .

[2]  B. Anderson.  Exponential stability of linear equations arising in adaptive identification , 1977 .

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

[4]  Romeo Ortega,et al.  Regulation and tracking of the nonholonomic double integrator: A field-oriented control approach , 1998, Autom..

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

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

[7]  Darren M. Dawson,et al.  QMotor 2.0-a real-time PC based control environment , 1999 .

[8]  Philippe Souères,et al.  Robust path-following control with exponential stability for mobile robots , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

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

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

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

[12]  Frank L. Lewis,et al.  Control of Robot Manipulators , 1993 .

[13]  O. Egeland,et al.  A Lyapunov approach to exponential stabilization of nonholonomic systems in power form , 1997, IEEE Trans. Autom. Control..

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

[15]  Wei Huo,et al.  Adaptive stabilization of dynamic nonholonomic chained systems with uncertainty , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[16]  Darren M. Dawson,et al.  QMotor 2.0-A PC based real-time multitasking graphical control environment , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[17]  S. Sastry,et al.  Adaptive Control: Stability, Convergence and Robustness , 1989 .

[18]  Fumio Miyazaki,et al.  A stable tracking control method for an autonomous mobile robot , 1990, Proceedings., IEEE International Conference on Robotics and Automation.

[19]  Darren M. Dawson,et al.  An adaptive controller for a class of induction motor systems , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[20]  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.

[21]  Anuradha M. Annaswamy,et al.  Robust Adaptive Control , 1984, 1984 American Control Conference.

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

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

[24]  Zhong-Ping Jiang,et al.  A recursive technique for tracking control of nonholonomic systems in chained form , 1999, IEEE Trans. Autom. Control..

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

[26]  S. Sastry,et al.  Stabilization of trajectories for systems with nonholonomic constraints , 1994 .