Low-Thrust Cislunar Trajectory Optimization leveraging Neural Networks for autonomous and real time applications

In recent years the need of an augmented spacecraft autonomy has considerably increased along with the renewed interest in Lunar missions. Low-Thrust Cislunar trajectory optimization is typically achieved leveraging classical optimal control methods. These methods can be time expensive, challenging for mission analysts and they often require nontrivial computational effort, due to the non-linear nature of the three body dynamics problem. The aim of the thesis is to develop a neural network to re-compute the optimal control history of a transfer maneuver autonomously on board, in shorter time and with low computational effort. The main core of the work logic is the collection of different datasets of optimal transfer maneuvers between typical lunar orbits. A classical optimal control problem with a minimum control energy cost function is built to provide optimal solutions. Using an indirect method the OCP is reduced to a Two Point Boundary Value Problem, with initial and final states fixed on the orbits, that is solved by the Matlab bvp4c solver. A state’s discretization on both orbits is taken into account to consider different transfers. Moreover in order to cover different kind of mission plans, both time fixed and free transfer time formulations are studied. As is common knowledge one of the main drawbacks of an indirect approach is the sensitivity on the initial guesses. Therefore the implementation of an indirect method on board could be unfeasible if a real time trajectory planning is needed, because the solver may could not converge rapidly to an optimal solution without reasonable initial guesses. As a typical approach in the literature, during the data collection, random initial guesses are assigned several times and the same OCP is solved iteratively, saving the minimum energy solution. The initial random guesses that lead the method to converge are then slightly perturbated in order to check if the solution corresponds with a suitable local minimum, considering the well-known inability to find a global minimum in this chaotic dynamics. This latter solution is then used as initial guess for a similar OCP, as in a continuation method, to expedite the data collection. Finally the neural network can be trained on this data in order to map a relationship between an input vector, made of initial states and final states, and an output vector characterized by initial costates and the transfer time in the free time problem. The NN can work as a function call on board, it can be used as a fast tool to provide adequate initial guesses to bvp4c, reducing drastically the computational time of the method and making possible to plan an orbital transfer without ground station involvement.