With the rapid growth of space activities and advancement of aerospace science and technology, many autonomous space missions have been proliferating in recent decades. Control of spacecraft in proximity operations is of great importance to accomplish these missions. The research in this dissertation aims to provide a precise, efficient, optimal, and robust controller to ensure successful spacecraft proximity operations. This is a challenging control task since the problem involves highly nonlinear dynamics including translational motion, rotational motion, and flexible structure deformation and vibration. In addition, uncertainties in the system modeling parameters and disturbances make the precise control more difficult. Four control design approaches are integrated to solve this challenging problem. The first approach is to consider the spacecraft rigid body translational and rotational dynamics together with the flexible motion in one unified optimal control framework so that the overall system performance and constraints can be addressed in one optimization process. The second approach is to formulate the robust control objectives into the optimal control cost function and prove the equivalency between the robust stabilization problem and the transformed optimal control problem. The third approach is to employ the è-D technique, a novel optimal control method that is based on a perturbation solution to the Hamilton-Jacobi-Bellman equation, to solve the nonlinear optimal control problem obtained from the indirect robust control formulation. The resultant optimal control law can be obtained in closedorm, and thus facilitates the onboard implementation. The integration of these three approaches is called the integrated indirect robust control scheme. The fourth approach is to use the inverse optimal adaptive control method combined with the indirect robust control scheme to alleviate the conservativeness of the indirect robust control scheme by using online parameter estimation such that adaptive, robust, and optimal properties can all be achieved. To show the effectiveness of the proposed control approaches, six degree-offreedom spacecraft proximity operation simulation is conducted and demonstrates satisfying performance under various uncertainties and disturbances.

This thesis models and analyzes an in-situ method for measuring the density of the thermosphere at low Earth orbit (LEO) altitudes in real time. As satellites orbit in the thermosphere, the sparse yet present air perturbs their orbits via the drag force. The drag force is poorly characterized and has a significant effect at LEO altitudes relative to other forces, making this perturbation force one of the greatest uncertainties in LEO orbit propagation. A steadily increasing number of satellites orbit at LEO altitudes, so for safety, it is critical to accurately track these satellites to avoid collisions. Therefore, better knowledge of the drag force is required. The drag force depends directly on the air mass density in the thermosphere, and current knowledge of the thermospheric density is limited. Models exist to describe the variations in density over time, but due to the many unpredictable factors which affect the thermosphere, the best of these models are only accurate to within 10%. Also, currently available techniques to measure the thermospheric density can only return time-averaged measurements, which causes inaccuracies in orbit propagation due to local density variations. Some planned in-situ density measurement missions rely on measuring acceleration caused by the drag force, but this requires a highly accurate accelerometer to be able to separate the drag force from other stronger forces acting on a satellite. The Satellite Producing Aerodynamic Torque to Understand LEO Atmosphere (SPATULA) concept was introduced as an alternative method, which infers density based on measurements of the drag torque. In the rotational regime, drag produces the strongest torque at LEO altitudes by far, making it possible to acquire accurate density measurements with inexpensive, commercially available sensors and actuators on a SPATULA spacecraft. This thesis expands upon a preliminary study of the SPATULA concept. A SPATULA spacecraft's dynamics are modeled in three dimensions, and a novel method is introduced for modeling the dependence of external torques on the geometry and attitude of the spacecraft. In addition to the dynamics model, discrete-time algorithms for guidance, system state filtering, attitude control, and density estimation are developed for the six degrees of freedom case. The MathWorks tools MATLAB and Simulink are used to simulate the physics and system models. The simulations are used to evaluate the performance of the SPATULA system's density measurements and compare them to conventional methods. It is found that the accuracy and bandwidth of the SPATULA system have a significant dependence on the assumed accuracy of the torque models in the system's filter. When the bandwidth is set to avoid significant phase shift errors, the SPATULA system can produce real-time measurements of density accurate over a minimum time scale of about 60 seconds, and the density error has a standard deviation of about 2 x 10^-14 kg/m^3. This accuracy is about 6 times better than the best thermospheric models, and it is also better than reported accuracies of most other density measurement methods. If bandwidth is sacrificed, the density error standard deviation can be decreased by a factor of 4. This introduces additional error due to phase shift delays, but these can be corrected with signal processing techniques. With the higher accuracy, the SPATULA system loses its real-time ability, but the data it produces would still provide excellent insight for improving thermospheric models. With high accuracy and low cost, the SPATULA concept is a promising path to pursue toward improving thermospheric density knowledge. / Master of Science / This thesis models and analyzes a method for measuring the density of the upper atmosphere in real time directly onboard a satellite. As low Earth orbit (LEO) satellites orbit at low altitudes, the sparse yet present atmosphere changes their orbits via the drag force. The drag force is poorly characterized and has a significant effect at LEO altitudes relative to other forces, making this perturbation force one of the greatest uncertainties in LEO orbit prediction. A steadily increasing number of satellites orbit at LEO altitudes, so for safety, it is critical to accurately track and predict the orbits of these satellites to avoid collisions. Therefore, better knowledge of the drag force is required. The drag force depends directly on air density, and current knowledge of the upper atmospheric density is limited. Models exist to describe the variations in density over time, but due to the many unpredictable factors which affect the atmosphere, the best of these models are only accurate to within 10%. Also, currently available techniques to measure the upper atmospheric density can only return time-averaged measurements, which causes inaccuracies in orbit prediction due to local density variations. Some planned density measurement missions rely on measuring acceleration caused by the drag force, but this requires a highly accurate accelerometer to be able to separate the drag force from other stronger forces acting on a satellite. The Satellite Producing Aerodynamic Torque to Understand LEO Atmosphere (SPATULA) concept was introduced as an alternative method, which infers density based on measurements of the drag torque. Drag produces the strongest torque at LEO altitudes by far, making it possible to acquire accurate density measurements with inexpensive, commercially available parts on a SPATULA spacecraft. This thesis expands upon a preliminary study of the SPATULA concept. A SPATULA spacecraft's motion and rotation is modeled in three dimensions, and a novel method is introduced for modeling the dependence of external torques on the geometry and orientation of the spacecraft. In addition to the dynamics model, algorithms that could be implemented on a satellite's computer are developed for determining the best orientation, estimating the state of the system, controlling the orientation, and estimating density. The MathWorks tools MATLAB and Simulink are used to simulate the physics and system models. The simulations are used to evaluate the performance of the SPATULA system's density measurements and compare them to conventional methods. It is found that the accuracy and bandwidth of the SPATULA system have a significant dependence on the assumed accuracy of the torque models used by the system. When a high bandwidth is used to avoid problems associated with low bandwidth, the SPATULA system can produce real-time measurements of density accurate over a minimum time scale of about 60 seconds, and the density error has a standard deviation of about 2 x 10^-14 kg/m^2. This accuracy is about 6 times better than the best upper atmospheric models, and it is also better than reported accuracies of most other density measurement methods. If bandwidth is sacrificed, the density error standard deviation can be decreased by a factor of 4. This introduces additional error due to delayed measurements of quickly varying components of the density, but these can be corrected with signal processing techniques. With the higher accuracy, the SPATULA system loses its real-time ability, but the data it produces would still provide excellent insight for improving atmospheric density models. With high accuracy and low cost, the SPATULA concept is a promising path to pursue toward improving density knowledge.

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CubeSats have become popular among universities, research organizations, and government agencies due to their low cost, small size, and light weight. Their standardized configurations further reduce the development time and ensure more frequent launch opportunities. Early cubesat missions focused on hardware validation and simple communication missions, with little requirement for pointing accuracy. Most of these used magnetic torque rods or coils for attitude stabilization. However, the intrinsic problems associated with magnetic torque systems, such as the lack of three-axis control and low pointing accuracy, make them unsuitable for more advanced missions such as detailed imaging and on-orbit inspection. Threeaxis control in a cubesat can be achieved by combining magnetic torque coils with other devices such as thrusters, but the lifetime is limited by the fuel source onboard. To maximize the mission lifetime, a fast attitude control management algorithm that could optimally manage the usage of the magnetic and thruster torques is desirable. Therefore, a recently developed method, the BSpline-augmented virtual motion camouflage, is presented in this defense to solve the problem. This approach provides results which are very close to those obtained through other popular nonlinear constrained optimal control methods with a significantly reduced computational time. Simulation results are presented to validate the capabilities of the method in this application

There are benefits to the use of internal actuators for rotational maneuvers of small-scale underwater vehicles. Internal actuators are protected from the outside environment by the external pressure hull and will not disturb the surrounding environment during inspection tasks. Additionally, internal actuators do not rely on the relative fluid motion to exert control moments, therefore they are useful at low speed and in hover. This paper describes the design, fabrication and testing of one such autonomously controlled, internally actuated underwater vehicle. The Internally Actuated, Modular Bodied, Untethered Submersible (IAMBUS) can be used to validate non-linear control strategies using internal actuators. Vehicle attitude control is provided by three orthogonally mounted reaction wheels. The housing is a spherical glass pressure vessel, which contains all of the components, such as actuators, ballast system, power supply, on-board computer and inertial sensor. Since the housing is spherically symmetric, the hydrodynamics of IAMBUS are uncoupled (e.g. a roll maneuver does not impact pitch or yaw). This hull shape enables IAMBUS to be used as a spacecraft attitude dynamics and control simulator with full rotational freedom. / Master of Science

Thesis (MScEng)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: With CubeSats becoming popular as a cheap alternative to larger satellites, the need for advanced miniature attitude determination and control systems (ADCS) arises to meet the pointing requirements of satellite operations such as earth imaging and orbit maintenance. This thesis describes the design of a complete ADCS for use on CubeSats. A previously designed CubeSat on-board-computer, CubeComputer, and ne sun and nadir sensor, CubeSense, is incorporated in the design. The remaining requirements with regard to sensors and actuators were met by CubeControl, an additional module, the design, manufacturing and testing of which are described. CubeControl can implement magnetic control with the use of a magnetometer and three magnetorquers. It is also capable of driving three reaction wheels for accurate active 3-axis stabilization. / AFRIKAANSE OPSOMMING: Met CubeSats wat gewild raak as 'n goedkoop alternatief tot groter satelliete ontstaan die behoefte vir gevorderde miniatuur ori entasiebepaling en -beheerstelsels wat satelliet operasies soos aardwaarneming en wentelbaan korreksies moontlik maak. Hierdie tesis beskryf die ontwerp van 'n volledige ori entasiebepaling en -beheerstelsel vir CubeSats. 'n Voorheen ontwikkelde CubeSat aanboordrekenaar, CubeComputer, en 'n fyn sonsensor en nadirsensor, CubeSense, is ingesluit in die ontwerp. Die orige benodighede met verband tot sensors en aktueerders word vervul deur CubeControl, 'n addisionele module waarvan die ontwerp, vervaardiging en toetsing beskyf word. CubeControl kan magnetiese beheer implementeer deur gebruik te maak van 'n magnetometer en drie magneetstange. Dit kan ook drie reaksiewiele aandryf vir akkurate aktiewe 3-as stabilisering.

The design of an attitude control system for a flexible spacecraft using magnetic actuation is considered. The nonlinear, linear, and modal equations of motion are developed for a general flexible body. Magnetic control is shown to be instantaneously underactuated, and is only controllable in the time-varying sense. A PD-like control scheme is proposed to address the attitude control problem for the linear system. Control gain limitations are shown to exist for the purely magnetic control. A hybrid control scheme is also proposed that relaxes these restrictions by adding a minimum control effort from an alternate three-axis actuation system. Floquet and passivity theory are used to obtain gain selection criteria that ensure a stable closed-loop system, which would aid in the design of a hybrid controller for a flexible spacecraft. The ability of the linearized system to predict the stability of the corresponding nonlinear system is also investigated.

The design of an attitude control system for a flexible spacecraft using magnetic actuation is considered. The nonlinear, linear, and modal equations of motion are developed for a general flexible body. Magnetic control is shown to be instantaneously underactuated, and is only controllable in the time-varying sense. A PD-like control scheme is proposed to address the attitude control problem for the linear system. Control gain limitations are shown to exist for the purely magnetic control. A hybrid control scheme is also proposed that relaxes these restrictions by adding a minimum control effort from an alternate three-axis actuation system. Floquet and passivity theory are used to obtain gain selection criteria that ensure a stable closed-loop system, which would aid in the design of a hybrid controller for a flexible spacecraft. The ability of the linearized system to predict the stability of the corresponding nonlinear system is also investigated.