| Over the past few decades, the two-wheeled driven cart, also known as the unicycle wheeled mobile robot or wheeled mobile robot with independently driven wheels, has been a favorite case study in the literature on nonholonomic control. This dissertation shows how the control of a cart can be leveraged for a novel and practical application: closed-loop control of a differentialdrive sheet registration device. The current state of the art for control of such a device, typically found in xerographic engines like printers and copiers, is open-loop motion planning. Typical works on nonholonomic control address stabilization to a point or posture. Sheet registration, however, is not concerned with stabilization to a point, but rather with stabilization to a straight-line trajectory.; This dissertation presents two closed-loop methods that achieve full-state trajectory tracking to a straight-line trajectory, one based on input-output feedback linearization and a second based on conventional linearization. For both approaches, it is shown that the intuitive formulation is not amenable to control, but the cart formulation is. The one-to-one correspondence between the motion of a sheet within a differential-drive registration system and the motion of a cart rolling on a plane makes it possible to use the cart formulation to solve the registration problem. Therefore, the control methods are developed based on a kinematic model of the cart system, and acceleration is treated as the control input. The stability of the resulting closed-loop systems is demonstrated. Elementary gain scheduling is then applied to achieve rapid closed-loop convergence while satisfying acceleration constraints. Lastly, a velocity tracking controller and an open-loop estimator are added to form overall closed-loop control schemes that are realizable.; To validate the control strategies, each scheme (developed and simulated in continuous-time) is converted to discrete-time (for implementation in a digital control system) and used to perform closed-loop registration. Simulation results based on a dynamic model of the system and experimental results from a real physical system demonstrate the effectiveness of the discrete-time implementations, and the experimental results show the schemes to be robust to real world disturbances and noise. |
