Browsing by Subject "Optimal control theory"
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Item Autonomous time-optimal spacecraft rendezvous and proximity operations using stabilized continuation(2016-05) Kollin, Emily Margaret; Akella, Maruthi Ram, 1972-; Bakolas, EfstathiosThis 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.Item Optimal lunar orbit insertion from a free return trajectory(2012-05) Jesick, Mark Christopher; Ocampo, Cesar; Fowler, Wallace; Hull, David; Marchand, Belinda; Russell, RyanWith the discovery of water ice at the moon's south pole, future human lunar exploration will likely occur at polar sites and, therefore, require high inclination orbits. Also of importance for human missions is the capability to abort if unfavorable circumstances arise. This dissertation addresses both of these concerns by creating an automated, systematic architecture for constructing minimum propellant lunar orbit insertion sequences while ensuring crew safety by maintaining a ballistic Earth return trajectory. To ensure a maneuver-free abort option, the spacecraft is required to depart Earth on a free return trajectory, which is a ballistic Earth-moon-Earth segment that requires no propulsive maneuvers after translunar injection. Because of the need for global lunar access, the required spacecraft plane change at the moon may be large enough that a multi-maneuver sequence offers cost savings. The combination of this orbit insertion sequence with the free return orbit increases the likelihood of a safe Earth return for crew while not compromising the ability to achieve any lunar orbit. A procedure for free return trajectory generation in a simplified Earth-moon system is presented first. With two-body and circular restricted three-body models, the algorithm constructs an initial guess of the translunar injection state and time of flight. Once the initial trajectory is found, a square system of nonlinear equations is solved numerically to target Earth entry interface conditions leading to feasible free return trajectories. No trial and error is required to generate the initial estimate. The automated algorithm is used to generate families of free return orbits for analysis. A targeting and optimization procedure is developed to transfer a spacecraft from a free return trajectory to a closed lunar orbit through a multi-maneuver sequence in the circular restricted three-body model. The initial estimate procedure is automated, and analytical gradients are implemented to facilitate optimization. Cases are examined with minimum time, variable symmetric, and general free returns. The algorithm is then upgraded to include a more realistic solar system model with ephemeris-level dynamics. An impulsive engine model is used before conversion to a finite thrust model. Optimal control theory is applied and the results are compared with the linearly steered thrust model. Trends in the flight time and propellant for various orbit insertion sequences are analyzed.