Lyapunov-based control of wheeled mobile robots

This dissertation describes the design and implementation of several Lvapunov-based control strategies for wheeled mobile robots. The first chapter presents the design of a new, differentiable kinematic control law that utilizes a dynamic oscillator with a tunable frequency of oscillation to achieve global uniformly ultimately-bounded tracking (i.e., the position/orientation tracking errors globally exponentially converge to a neighborhood about zero that can be made arbitrarily small). In contrast to many of the previously developed kinematic tracking controllers, the controller presented in Chapter 1 can be used for the regulation problem as well; hence, a unified framework is provided for both the tracking and the regulation problem. To compensate for uncertainty in the dynamic model, a robust nonlinear controller is designed based on the structure of the kinematic controller. Experimental results are presented to demonstrate the performance of the robust tracking controller.; In the second chapter, a differentiable, kinematic control law is designed that utilizes a redesigned dynamic oscillator to achieve global asymptotic tracking. Provided the reference trajectory satisfies a mild persistency of excitation condition, the kinematic controller is proven to achieve global exponential tracking. A setpoint extension is provided to illustrate how the tracking controller can be slightly modified to obtain global asymptotic regulation. A dynamic extension is also provided to illustrate how the kinematic controller can be embedded inside of an adaptive controller that fosters global asymptotic tracking despite parametric uncertainty in the mobile robot dynamic model. Experimental results are provided to illustrate the effectiveness of the adaptive tracking controller.; The third chapter considers the problem of position/orientation tracking control of wheeled mobile robots via visual servoing in the presence of parametric uncertainty associated with the mechanical dynamics and the camera system. Specifically, an adaptive controller is designed that compensates for uncertain camera and mechanical parameters and ensures global asymptotic position/orientation tracking. Simulation and experimental results are included to illustrate the performance of the control law.