REAL-TIME AUTONOMOUS TRAJECTORY OPTIMIZATION IN CISLUNAR SPACE USING NEURAL NETWORKS

The cislunar space is a dynamically rich environment, in which the classical two-body assumption falls, and trajectories are significantly impacted by multi-body effects. Due to these considerations, trajectory optimization for cislunar applications presents major challenges due to increased computational effort, and thereby presenting a bottleneck for autonomous on-board implementations. Neural networks have been extensively proved to be excellent function approximators, even when the underlying mathematics is extremely complex. In this work, the aim is to explore the development and implementation of a simple and computationally inexpensive feedforward neural network that can serve as an on-board tool for the estimation of optimal trajectories between any two points (i.e., prescribed boundary conditions) within the cislunar space. For this purpose, a first phase of data collection has been performed, during which several optimal control problems between two repeating natural orbits have been transcribed into two-point boundary value problems, according to the so-called indirect method, and then solved using off-the-shelf numerical optimization packages such as MATLAB built-in function bvp4c. The data gathered have then been used to train and validate a neural network that can map the relationship between the boundary states and the initial costates (or adjoints) of the indirect formulation, considering a transfer time both fixed and left free. The results obtained show that a simple network can approximate the initial costates with a high degree of accuracy. From those predictions, the control history can also be easily obtained; however, in some cases, the prediction on just the initial adjoints is not sufficient to reconstruct the entire optimal control vector because of error propagation: some possible solutions to this problem, without incurring too much penalty upon the computational speed, are then discussed.