Browsing by Subject "Stabilized continuation"
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Item A homotopic approach to solve the fuel optimal spacecraft proximity operations problem(2017-05) Gulino, Marco; Akella, Maruthi Ram, 1972-This report focuses on finding the low-thrust fuel optimal solution to a class of spacecraft proximity operations subject to path constraints. The mission is for a service spacecraft to perform a surveying orbit relative to a reference within a prescribed period, without violating a no fly zone represented by a sphere centered on the reference vehicle. Clohessy-Wiltshire equations are used, together with the controllability Gramian of the resulting linear system, to obtain an analytical solution to the energy optimal problem. A homotopic approach is subsequently shown to serve as an effective bridge from the energy optimal solution toward the fuel optimal solution.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 Hypersonic trajectories with control continuity constraints for adversarial games(2022-05-06) Trask, Adam Louis; Akella, Maruthi Ram, 1972-Computing optimal solutions for unpowered hypersonic glide vehicle trajectories requires high degree of numerical sophistication, making the development of fast and robust in-flight retargeting capabilities a challenging problem. Toward that end, recent efforts use neural networks that are pretrained with representative sets of target states obtained offline. The ability to characterize trajectories over an entire operating envelope and adapt in-flight for potentially changing target conditions requires significant computational resources. In this context, the use of continuation methods becomes extremely attractive. For unpowered hypersonics, stabilized continuation in particular is appealing due to its ability to obtain solutions with poor initial guesses, automatically select continuation step sizes, and attenuate accumulated numerical error over the continuation interval. In this work, the usage of stabilized continuation for both two and three degree of freedom unpowered hypersonics is expanded for maximum terminal energy trajectories in the context of a two-player pursuit-evasion game between a hypersonic vehicle and an adversarial ground target. Additional constraints are defined which provide guaranteed control continuity as maneuvers to new terminal conditions occur in-flight throughout a game, ensuring a realistic flight path is maintained. An easy to compute measure for characterizing the reachable terminal conditions at any given time using stabilized continuation is developed and some numerical convergence conditions are discussed. To generate various simulation scenarios, strategic capabilities for each player are designed; these strategies also employ stabilized continuation in various manners to determine courses of action throughout the game. Algorithms for these strategies are expressed and their efficacy is discussed in the context of performance through miss distance and final velocity