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The term proximity operations has been widely used in recent years to describe a wide range of space missions that require a spacecraft to remain close to another space object. Such missions include, for example, the inspection, health monitoring, surveillance, servicing, and refueling of a space asset by another spacecraft. One of the biggest challenges in autonomous space proximity operations, either cooperative or uncooperative, is the need to autonomously and accurately track time-varying relative position and attitude references, i.e., pose references, with respect to a moving target, in order to avoid on-orbit collisions and achieve the overall mission goals. In addition, if the target spacecraft is uncooperative, the Guidance, Navigation, and Control (GNC) system of the chaser spacecraft must not rely on any help from the target spacecraft. In this case, vision-based sensors, such as cameras, are typically used to measure the relative pose between the spacecraft. Although vision-based sensors have several attractive properties, they introduce new challenges, such as no direct linear and angular velocity measurements, slow update rates, and high measurement noise. This dissertation investigates the problem of autonomously controlling and estimating the pose of a chaser spacecraft with respect to a moving target spacecraft, possibly uncooperative. Since this problem is inherently hard, the standard approach in the literature is to split the attitude-tracking problem from the position-tracking problem. Whereas the attitude-tracking problem is relatively simple, since the rotational motion is independent from the translational motion, the position-tracking problem is more complicated, as the translational motion depends on the rotational motion. Hence, whereas strong theoretical results exist for the attitude problem, the position problem typically requires additional assumptions. An alternative, more general approach to the pose control and estimation problems is to consider the fully coupled 6-DOF motion. However, fewer results exist that directly address this higher dimensional problem. The main contribution of this dissertation is to show that dual quaternions can be used to extend the theoretical results that exist for the attitude motion into analogous results for the combined position and attitude motion. Moreover, this dissertation shows that this can be accomplished by (almost) just replacing quaternions by dual quaternions in the original derivations. This is because dual quaternions are built on and are an extension of classical quaternions. Dual quaternions provide a compact representation of the pose of a frame with respect to another frame. Using this approach, three new results are presented in this dissertation. First, a pose-tracking controller that does not require relative linear and angular velocity measurements is derived with vision-based sensors in mind. Compared to existing literature, the proposed velocity-free pose-tracking controller guarantees that the pose of the chaser spacecraft will converge to the desired pose independently of the initial state, even if the reference motion is not sufficiently exciting. In addition, the convergence region does not depend on the gains of the controller. Second, a Dual Quaternion Multiplicative Extended Kalman Filter (DQ-MEKF) is developed from the highly successful Quaternion MEKF (Q-MEKF) as an alternative way to achieve pose-tracking without velocity measurements. Existing dual quaternion EKFs are additive, not multiplicative, and have two additional states. The DQ-MEKF is experimentally validated and compared with two conventional EKFs on the 5-DOF platform of the Autonomous Spacecraft Testing of Robotic Operations in Space (ASTROS) facility at the School of Aerospace Engineering at Georgia Tech. Finally, the velocity-free pose-tracking controller is compared qualitatively and quantitatively to a pose-tracking controller that uses the velocity estimates produced by the DQ-MEKF through a realistic proximity operations simulation. Third, a pose-tracking controller that does not require the mass and inertia matrix of the chaser satellite is suggested. This inertia-free controller takes into account the gravitational acceleration, the gravity-gradient torque, the perturbing acceleration due to Earth's oblateness, and constant -- but otherwise unknown -- disturbance forces and torques. Sufficient conditions on the reference pose are also given that guarantee the identification of the mass and inertia matrix of the satellite. Compared to the existing literature, this controller has only as many states as unknown elements and it does not require a priori known upper bounds on any states or parameters. Finally, the inertia-free pose-tracking controller and the DQ-MEKF are tested on a high-fidelity simulation of the 5-DOF platform of the ASTROS facility and also experimentally validated on the actual platform. The equations of motion of the 5-DOF platform, on which the high-fidelity simulation is based, are derived for three distinct cases: a 3-DOF case, a 5-DOF case, and a (2+1)-DOF case. Four real-time experiments were run on the platform. In the first, a sinusoidal reference attitude with respect to the inertial frame is tracked using VSCMGs. In the second, a constant reference attitude is maintained with respect to a target object using VSCMGs and measurements from a camera. In the third, the same sinusoidal reference attitude with respect to the inertial frame tracked in the first experiment is now tracked using cold-gas thrusters. Finally, in the fourth and last experiment, a time-varying 5-DOF reference pose with respect to the inertial frame is tracked using cold-gas thrusters.

This thesis focuses on decentralized deadbeat output regulation of discrete-time nonlinear plants that are composed of multiple agents. These agents interact, via scalar-valued signals, in a known structured way represented with a graph. This work is motivated by applications where it is infeasible and/or undesirable to introduce control action within each plant agent; instead, control agents are introduced to interact with certain plant agents, where each control agent focuses on regulating a specific plant agent, called its target. Then, two analyses are carried out to determine if regulation is achieved: targeting analysis is used to determine if control laws can be found to regulate all target agents, then growing analysis is used to determine the effect of those control laws on non-target plant agents. The strength of this novel approach is the intuitively-appealing notion of each control agent focusing on the regulation of just one plant agent. This work goes beyond previous research by generalizing the class of allowable plant dynamics, considering not only arbitrary propagation times through plant agents, but also allowing for non-symmetrical influence between the agents. Moreover, new necessary and sufficient algebraic conditions are derived to determine when targeting succeeds. The main contribution of this work, however, is the development of new easily-verifiable conditions necessary for targeting and/or growing to succeed. These new conditions are valuable due to their simplicity and scalability to large systems. They concern the positioning of control agents and targets as well as the propagation time of signals through the plant, and they help significantly with design decisions. Various graph structures (such as queues, grids, spiders, rings, etc.) are considered and for each, these conditions are used to develop a control scheme with the minimum number of control agents needed.

Bibliography: leaves 329-349 / xxxv, 349 leaves : ill ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, 1992

Thesis (Ph. D.)--University of Missouri--Rolla, 2007. / Vita. The entire thesis text is included in file. Title from title screen of thesis/dissertation PDF file (viewed March 26, 2008) Includes bibliographical references.

Thesis (Ph. D.)--Ohio State University, 2007. / Title from first page of PDF file. Includes bibliographical references (p. 155-158).

Thesis (M.S.)--Ohio University, August, 2001. / Title from PDF t.p.

Thesis (M.S.)--Ohio University, March, 2004. / Title from PDF t.p. Includes bibliographical references (leaves 80-81).

Thesis (Ph.D.)--Aerospace Engineering, Georgia Institute of Technology, 2009. / Committee Chair: Haddad, Wassim; Committee Member: Feron, Eric; Committee Member: JVR, Prasad; Committee Member: Taylor, David; Committee Member: Tsiotras, Panagiotis