Browsing by Subject "Continuation"
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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 Initial guess and optimization strategies for multi-body space trajectories with application to free return trajectories to near-Earth asteroids(2014-08) Bradley, Nicholas Ethan; Russell, Ryan Paul, 1976-; Ocampo, CesarThis concept of calculating, optimizing, and utilizing a trajectory known as a ``Free Return Trajectory" to facilitate spacecraft rendezvous with Near-Earth Asteroids is presented in this dissertation. A Free Return Trajectory may be defined as a trajectory that begins and ends near the same point, relative to some central body, without performing any deterministic velocity maneuvers (i.e., no maneuvers are planned in a theoretical sense for the nominal mission to proceed). Free Return Trajectories have been utilized previously for other purposes in astrodynamics, but they have not been previously applied to the problem of Near-Earth Asteroid rendezvous. Presented here is a series of descriptions, algorithms, and results related to trajectory initial guess calculation and optimal trajectory convergence. First, Earth-centered Free Return Trajectories are described in a general manner, and these trajectories are classified into several families based on common characteristics. Next, these trajectories are used to automatically generate initial conditions in the three-body problem for the purpose of Near-Earth Asteroid rendezvous. For several bodies of interest, example initial conditions are automatically generated, and are subsequently converged, resulting in feasible, locally-optimal, round-trip trajectories to Near-Earth Asteroids utilizing Free Return Trajectories. Subsequently, a study is performed on using an unpowered flyby of the Moon to lower the overall DV cost for a nominal round-trip voyage to a Near-Earth Asteroid. Using the Moon is shown to appreciably decrease the overall mission cost. In creating the formulation and algorithms for the Lunar flyby problem, an initial guess routine for generic planetary and lunar flyby tours was developed. This continuation algorithm is presented next, and details a novel process by which ballistic trajectories in a simplistic two-body force model may be iteratively converged in progressively more realistic dynamical models until a final converged ballistic trajectory is found in a full-ephemeris, full-dynamics model. This procedure is useful for constructing interplanetary transfers and moon tours in a realistic dynamical framework; an interplanetary and an inter-moon example are both shown. To summarize, the material in this dissertation consists of: novel algorithms to compute Free Return Trajectories, and application of the concept to Near-Earth Asteroid rendezvous; demonstration of cost-savings by using a Lunar flyby; and a novel routine to transfer trajectories from a simplistic model to a more realistic dynamical representation.Item Nonlinear aeroelastic analysis of high aspect-ratio wings using the method of numerical continuation(Texas A&M University, 2006-08-16) Nichkawde, ChetanThis research explores the impact of kinematic structural nonlinearities on the dynamics of a highly deformable cantilevered wing. Two different theoretical formulations are presented and analysed for nonlinear behavior. The first formulation, which is more conventional, assumes zero equilibrias and structural nonlinearities occur as terms up to third order in the Taylor series expansion of structural nonlinearities. In the second approach, no prior assumption about equilibria states of the wing is made. Kinematic nonlinearities due to curvature and inertia were retained in their exact form. Thus, the former becomes a special case of the latter. This nonlinear formulation permits the analysis of dynamics about nonzero trims. Nonzero trim states are computed as a system parameter is varied using a continuation software tool. The stability characteristics of these trim states are also ascertained. Various bifurcation points of the system are determined. Limit-cycle oscillations are also investigated for and are characterized in terms of amplitude of vibration. The research in particular examines the impact of in-plane degree of freedom on the stability of nonzero trim states. The effect of variation of system parameters such as stiffness ratio, aspect ratio and root angle of attack is also studied. The method of direct eigenanalysis of nonzero equilibria is novel and new for an aeroelastic system.