Feature Engineering for Low-Thrust Trajectory Optimization

Abstract

Using low-thrust propulsion for interplanetary space missions has the potential to allow for more payload for the same mass put into orbit compared to what impulsive propulsion would allow for. The disadvantages are found in mission planning, however, as the continuous nature of the thrust yields a more complex problem. One potential solution to help in the early planning and discovery phase of mission design is to employ artificial neural networks (ANNs). This has been done in the past, yet only in a limited capacity. Specifically, the engineering of the feature space used with the neural network has never been investigated. This thesis attempts to provide a first look at the influence of different feature space compositions. This includes the use of nine different state representations but also an analysis of additional values in the feature space. Additionally, the effect of extraneous variables, one of them notably being the target of interest, on the neural network performance is analyzed. The dataset used is generated using indirect optimization, and the case investigated is a set of minimum fuel Earth-Mars transfer trajectories. Low-thrust spacecraft trajectories are for space exploration what neural networks are for computer science: The vanguard of current trends with a lot of potential. Only recently have the two ideas, trajectory optimization and machine learning, been combined. In all the publications making use of machine learning for low-thrust optimization, a clear gap exists, however: Feature engineering has never been investigated. This thesis attempts to provide a first patch for that gap, limiting itself in scope to interplanetary Earth-Mars trajectories and feedforward neural networks. The data used as the basis to evaluate the performance of a number of factors having a potential influence on the choice of feature is obtained through indirect optimization. A novel method to generate those trajectories is implemented. The data is then used to investigate the effect different targets and network parameters have on the choice of features. On the feature side, a significant number of state representations are analyzed, both in dimensional and nondimensionalized form. Additionally, the feature space is expanded by additional variables, and various transformations are attempted. Over the course of this work, the importance of properly scaled data has been demonstrated. It is also shown that using Keplerian state and costate as feature and target, respectively, reliably yields good results. When mass is estimated, fuel mass is preferable over total spacecraft mass. Finally, none of the additional parameters or transformations (besides nondimensionalization) attempted resulted in reliable improvements and are thus best avoided.