Lyapunov-based control for mechanical and vision-based systems

This Ph.D. dissertation describes the design and implementation of various control strategies centered around the following applications: (i) Global Output Feedback Control of Dynamically Positioned Surface Vessels: An Adaptive Control Approach, (ii) Nonlinear Coupling Control Laws for an Underactuated Overhead Crane System, (iii) Adaptive 2.5D Visual Servoing of Kinematically Redundant Robot Manipulators, and (iv) Robust 2.5D Visual Servoing for Robot Manipulators. The theory found in each of these sections is demonstrated through simulation or experimental results. An introduction to each of these four primary chapters can be found in chapter one.; In Chapter 2, we presented an adaptive output feedback tracking controller for dynamically positioned ship systems. The proposed control law achieves global asymptotic position tracking and does not require velocity measurements nor knowledge of the ship parameters. The global stability result is based on a stability analysis that involves the use of a non-quadratic Lyapunov function and exploits several properties inherent to the ship dynamic model. Simulation results were also given to illustrate the performance of the proposed control system.; In Chapter 3, we presented three controllers for an overhead crane system. By utilizing a Lyapunov-based stability analysis along with LaSalle's Invariance Theorem, we proved asymptotic regulation of the gantry and payload position for a PD controller and two nonlinear controllers. Experimental results were utilized to demonstrate that the increased coupling between the gantry and payload that results from the additional nonlinear feedback terms in the nonlinear coupling control laws, resulted in improved transient response.; In Chapter 4, a kinematic visual servoing controller is developed that ensures asymptotic regulation of the camera translation and rotation error systems while simultaneously compensating for uncertainty in the distance from the desired camera position to the stationary target plane. Specifically, by decomposing the homography into separate translation and rotation components, we were able to exploit both 2D image-space and projected 3D task-space (i.e., 2.5D visual servoing) information to construct the kinematic controller. Based on the desire to enhance the robustness of the control design, the integrator backstepping approach was utilized to incorporate the robot kinematic and dynamic models. Specifically, a joint torque control input was developed to ensure asymptotic regulation of the position and orientation of the camera held by the robot end-effector (camera-in-hand problem) of a kinematically redundant robot manipulator, despite parametric uncertainty in the dynamic model of the robot.; In Chapter 5, the 3-Dimensional (3D) position and orientation of a camera held by the end-effector of a robot manipulator is regulated to a constant desired position and orientation despite (i) the lack of depth information of the actual or desired camera position from a target, (ii) the lack of a geometric model of the target object, and (iii) uncertainty regarding both the angle and axis of rotation of the camera with respect to the robot end-effector (i.e., the orientation extrinsic camera parameters). By fusing 2D image-space and projected 3D task-space information (i.e., 2.5D visual servoing), a robust controller is developed that ensures exponential regulation of the position and orientation of the camera. The stability of the controller is proven through a Lyapunov-based analysis, and the performance of the controller is validated by numerical simulation results.