Nonlinear Dynamics and Control of Spacecraft Relative Motion
Type of DegreePhD Dissertation
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The description and control of the relative motion of spacecraft has attracted a great deal of attention over the last five decades. This is as a result of its numerous applications in rendezvous and proximity operations, spacecraft formation flying, distributed spacecraft missions etc. Generally, the linearized, simplified model of the relative motion is described using time-invariant, Hill-Clohessy-Wiltshire (HCW) equations developed in 1960s. This model was based on the assumptions that, the chief and deputy spacecraft are in close proximity and the chief spacecraft is in a near circular orbit. The HCW equations have the disadvantage of not being able to capture the relative dynamics over a long period of time or large separations. Hence, several new models and equations of motion have been developed. In this work, two new linearized models of the relative motion based on the harmonic balance and averaging methods are developed. Numerical solutions show that the models can provide better approximations to the relative motion than the HCW model. Another innovative contribution of this dissertation is the development of closed-form solutions of Riccati-type and Abel-type nonlinear spacecraft relative motion arising from the second and third order approximation of the variation of the true latitude rate. The results are new, closed-form analytical solutions of the true anomaly variation with time which give a better understanding of the relative motion than using Cartesian coordinates. Feedback controllers are designed for the relative motion via State Dependent Riccati Equation (SDRE) control strategy. The key interest in the use of SDRE strategy is its ability to provide an effective algorithm for synthesizing nonlinear feedback controls by allowing for nonlinearities in the system states, while offering design flexibility through state dependent weighting matrices.