Specialization: Control Systems Degree: Doctor of Philosophy Abstract: Visual servoing uses camera feedback to control a robot's motion. In particular, Image-based Visual Servoing (IBVS) laws minimize an error signal defined in the image space. This thesis considers IBVS design for rotary-wing Unmanned Aerial Vehicles (UAVs). This is a challenging problem due to the nonlinear perspective projection of image formation and the underactuated nonlinear dynamics of the UAV. Traditional IBVS approaches calculate the six Degrees of Freedom (DoF) velocity reference and feed it into an inner velocity tracking loop. This approach cannot be directly applied to IBVS of an underactuated UAV. To address this issue, all IBVS laws developed in this thesis consider the vehicle's dynamics, and this approach is termed as Dynamic Image-based Visual Servoing (DIBVS). As compared to traditional position regulation or tracking of UAVs, the nonlinear image kinematics leads to systems structure which makes the control problem challenging. In this thesis a state transformation is proposed to eliminate the time derivative of attitude in the image kinematics. This leads to a simpler system structure for control design. The state transformation is obtained by solving a system of first-order homogeneous Partial Differential Equations (PDEs). The existence of solutions is proven and the general solution provided. Using the transformed state, image moment features for a planar target with multiple points or parallel lines are proposed. The state transformation approach requires an attitude measurement which is commonly available for UAVs. However, this measurement contains small bias which results in state-transformation error and introduces a disturbance into the translational velocity dynamics. The state-transformation error is proven to be negligible. In this thesis, a quadrotor is adopted as the UAV platform to validate the proposed DIBVS schemes. The external force or torque is assumed to be the product of an aerodynamic gain and the square of the Pulse Width Modulation (PWM) signal to the Electronic Speed Controller (ESC). This gain gradually decreases as battery voltage drops, and the resulting reduction in thrust has a noticeable effect on UAV motion in practise. The attitude bias, aerodynamic gain, and mass of the UAV are treated as unknown constants. Both Proportional-Integral-Derivative (PID) and adaptive DIBVS schemes are proposed to stabilize image feature error and are robust to this system uncertainty. Although in the transformed image state the convergence appears to remain in the camera Field of View (FoV), this may not be case for the actual camera image. To address this issue, a visual servoing scheme based on a nested saturation law is proposed to constrain the attitude of the quadrotor.