Internal dynamics of a wheeled mobile robot

Since the dynamics of a wheeled mobile robot is nonlinear, the feedback linearization technique is commonly used to linearize the input-output map. The input-output linearized system has a nonlinear internal dynamics. In this paper, the internal dynamics of the mobile robot under the look-ahead control is first characterized. The look-ahead control takes the coordinates of a reference point in front of the mobile robot as the output equation. Using a novel Lyapunov function, the stability of the internal dynamics is then analyzed. In particular, it is shown that the internal motion of the mobile robot is asymptotically stable when the reference point is commanded to move forward, whereas the internal motion is unstable when the reference point moves backward. Simulation and experimental results are provided to verify the analysis.

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

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

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

[4]  Karim Ait-Abderrahim,et al.  Mobile robot control. Part 1 : Feedback control of nonholonomic wheeled cart in cartesian space , 1990 .

[5]  Carlos Canudas de Wit,et al.  Path following of a 2-DOF wheeled mobile robot under path and input torque constraints , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[6]  W. E. Schmitendorf,et al.  Analytical dynamics of discrete systems , 1977 .

[7]  Alessandro De Luca,et al.  Zero Dynamics in Robotic Systems , 1991 .

[8]  A. Bloch,et al.  Controllability and stabilizability properties of a nonholonomic control system , 1990, 29th IEEE Conference on Decision and Control.

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

[10]  Xiaoping Yun,et al.  Coordinating locomotion and manipulation of a mobile manipulator , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[11]  Weiping Li,et al.  Applied Nonlinear Control , 1991 .

[12]  A. Isidori.  Nonlinear Control Systems: An Introduction , 1986 .

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

[14]  Georges Bastin,et al.  Dynamic feedback linearization of nonholonomic wheeled mobile robots , 1992, Proceedings 1992 IEEE International Conference on Robotics and Automation.