Aerial recovery of autonomous micro air vehicles (MAVs) presents many unique challenges due to the difference in size and speed of the recovery vehicle and MAV. This thesis presents algorithms to enable an autonomous MAV to estimate the orbit of a recovery vehicle and track the orbit until the final docking phase. Methods for estimating ellipses that are rotated out of the x − y plane are developed and demonstrated through simulation. These algorithms are shown to be robust to noise and stable numerically. Parameter update methods that are computationally inexpensive, such as recursive least squares and Kalman filtering, are discussed and simulated. A discussion is given of orbit tracking algorithms for circular orbits, and these methods are expanded to include elliptical orbits. These algorithms enable the MAV to track the recovery vehicle's orbit, based on a vector field approach. The tracking algorithms are divided into lateral and longitudinal controllers that allow for tracking of inclined orbits. Finally, the hardware and software setup for live flight tests is discussed. Flight test results are given that validate the functionality of the orbit estimation and orbit tracking algorithms.

In this dissertation, we focus on the strategy that places and stabilizes the path of an aerial drogue, which is towed by a mothership aircraft using a long flexible cable, onto a horizontally flat orbit by maneuvering the mothership in the presence of wind. To achieve this goal, several studies for towed cable systems are conducted, which include the dynamic modeling for the cable, trajectory generation strategies for the mothership, trajectory-tracking control law design, and simulation and flight test implementations. First, a discretized approximation method based on finite element and lumped mass is employed to establish the mathematical model for the towed cable system in the simulation. Two approaches, Gauss's Principle and Newton's second law, are utilized to derive the equations of motion for inelastic and elastic cables, respectively. The preliminary studies for several key parameters of the system are conducted to learn their sensitivities to the system motion in the steady state. Flight test results are used to validate the mathematical model as well as to determine an appropriate number of cable links. Furthermore, differential flatness and model predictive control based methods are used to produce a mothership trajectory that leads the drogue onto a desired orbit. Different desired drogue orbits are utilized to generate required mothership trajectories in different wind conditions. The trajectory generation for a transitional flight in which the system flies from a straight and level flight into a circular orbit is also presented. The numerical results are presented to illustrate the required mothership orbits and its maneuverability in different wind conditions. A waypoint following based strategy for mothership to track its desired trajectory in flight test is developed. The flight test results are also presented to illustrate the effectiveness of the trajectory generation methods. In addition, a nonlinear time-varying feedback control law is developed to regulate the mothership to follow the desired trajectory in the presence of wind. Cable tensions and wind disturbance are taken into account in the design model and Lyapunov based backstepping technique is employed to develop the controller. The mothership tracking error is proved to be capable of exponentially converging to an ultimate bound, which is a function of the upper limit of the unknown component of the wind. The simulation results are presented to validate the controller. Finally, a trajectory-tracking strategy for unmanned aerial vehicles is developed where the autopilot is involved in the feedback controller design. The trajectory-tracking controller is derived based on a generalized design model using Lyapunov based backstepping. The augmentations of the design model and trajectory-tracking controller are conducted to involve the autopilot in the closed-loop system. Lyapunov stability theory is used to guarantee the augmented controller is capable of driving the vehicle to exponentially converge to and follow the desired trajectory with the other states remaining bounded. Numerical and Software-In-the-Loop simulation results are presented to validate the augmented controller. This method presents a framework of implementing the developed trajectory-tracking controllers for unmanned aerial vehicles without any modification to the autopilot.

This dissertation develops the visual pursuit method for air-to-air tracking and rendezvous of unmanned aircraft systems. It also shows the development of vector-field and proportional-integral methods for controlling UAS flight in formation with other aircraft. The visual pursuit method is a nonlinear guidance method that uses vision-based line of sight angles as inputs to the algorithm that produces pitch rate, bank angle and airspeed commands for the autopilot to use in aircraft control. The method is shown to be convergent about the center of the camera image frame and to be stable in the sense of Lyapunov. In the lateral direction, the guidance method is optimized to balance the pursuit heading with respect to the prevailing wind and the location of the target on the image plane to improve tracking performance in high winds and reduce bank angle effort. In both simulation and flight experimentation, visual pursuit is shown to be effective in providing flight guidance in strong winds. Visual pursuit is also shown to be effective in guiding the seeker while performing aerial docking with a towed aerial drogue. Flight trials demonstrated the ability to guide to within a few meters of the drogue. Further research developed a method to improve docking performance by artificially increasing the length of the line of sight vector at close range to the target to prevent flight control saturation. This improvement to visual pursuit was shown to be an effective method for providing guidance during aerial docking simulations. An analysis of the visual pursuit method is provided using the method of adjoints to evaluate the effects of airspeed, closing velocity, system time constant, sensor delay and target motion on docking performance. A method for predicting docking accuracy is developed and shown to be useful for predicting docking performance for small and large unmanned aircraft systems.