|Abstract:||Leveraging dynamical structures found in the three-body problem provides opportunities to explore transfers that utilize considerably less fuel, thus gaining the moniker of low-energy transfers. Typically, these transfers are constructed by analyzing intersections of these dynamical structures at certain planes of interest in the form of Poincaré surfaces of section. Initial guesses gained from these maps are then used in differential correctors to obtain feasible solutions, or transcribed as non-linear problems and solved using an NLP solver to obtain locally optimal solutions at best. This process is time consuming and requires human input for seeding initial guesses. It also does not guarantee convergence or the existence of feasible or locally optimal solutions; and if successful, it generates a single trajectory of interest. A change in initial conditions or spacecraft parameters would require repeating the entire process.
Multi-phase trajectories are defined for this study as trajectories that have multiple arcs that require propulsive maneuvers to complete. As this study analyzes low-energy transfers, each of these phases incorporates the use of dynamical structures to some extent. Solving these multi-phase transfers using the same methodology described requires linking and analyzing multiple chains of Poincaré surfaces and using intuition to search the space to find a good initial guess. This becomes increasingly taxing and challenging for a mission design engineer to process and keep track of the best solutions with such a large problem space, and constantly evolving mission parameters. To add to the onus, the combinatorial space also expands dramatically as different kinds of dynamical structures are incorporated, such as patch three-body systems, resonances, and perturbed variants.
The study conducted in this thesis aims to present a framework that enables automated generation of trajectories utilizing low-energy transfers for multi-body regimes. The goal of the framework is to alleviate the effort required in creating low-energy trajectories by incorporating human intuition and numerical optimization methods in a Hybrid Optimal Control framework to rapidly produce a solution front of trajectories trading in multiple objectives that are of interest to mission design engineers. The Hybrid Optimal Control framework uses a dual-loop architecture, with an outer loop using a genertic algorithm for global search and an inner loop using a non-linear problem solver for local optimization. The outer loop uses a variable chromosome transcription to select the phase itinerary for different number of phases. The inner loop uses Monotonic Basin Hopping to seed initial guesses for the non-linear problem solver. Solutions are presented in the form of Pareto fronts trading multiple-objectives.
The work described here presents the motivation for such a tool, the mathematical models that form the foundation of the analysis, generation of relevant dynamical structures, the numerical optimization tools which formulate the search and optimization aspect of the framework, and the application of this framework to common mission concepts for impulsive and low-thrust propulsion types. Analysis of multi-phase trajectories and their impact on the quality of the solution space is conducted, and suggestions of improvements and desired features are given.