Autonomous time-optimal spacecraft rendezvous and proximity operations using stabilized continuation
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This thesis addresses the minimum-time rendezvous optimal control problem by implementing continuation with a stabilizing input. The rendezvous problem is first formulated as an optimal control problem which is then parameterized to enable the inclusion of the continuation parameter. A stabilizing input is then applied to attenuate the errors accumulated during the process of numerical integration. In this work, a state feedback stabilizing term with an additive open-loop control stabilizing term is implemented. By applying stabilized continuation to a rendezvous scenario in which two spacecraft are initialized in the same planar, circular orbit separated by some phase angle, a family of minimum-time rendezvous solutions is obtained for variable levels of thrust, mass flow rate, or initial phase angle separation. The approach is first demonstrated on a linear harmonic oscillator problem, and then applied to the Keplerian two-body motion model, with and without the inclusion of atmospheric drag perturbations. In addition to rendezvous trajectories, the approach is also applied to generate kinetic impact trajectories. This work considers only translational dynamics in two-dimensional space, however, the scope is not limited strictly to circular orbits. The effectiveness of the stabilized continuation scheme when used to generate minimum-time rendezvous and kinetic impact trajectories is demonstrated through simulations. The optimality of the solutions is verified with the Hamiltonian. The performance of the stabilized continuation scheme is compared against that of a direct shooting method, and the results obtained in this thesis are compared to other results from similar applications in the literature.