Cluster-based search space pruning in single leg low-thrust trajectory optimisation problems

Abstract

Many contemporary interplanetary missions use efficient low-thrust engines to reach the far corners of our Solar System. Their trajectories, however, have proven to be complicated to optimise due to the non-impulsive manoeuvres involved in low-thrust spaceflight. Even though shaping methods have been used extensively to reduce the computational burden, multiple-gravity assists and the presence of constraints create significant computational hurdles. Reducing the number of fitness evaluations during optimisation is one way of speeding up the search and can be done by `pruning away' regions of infeasible trajectories. In this research, we approach this by applying clustering, an unsupervised machine learning approach, to single leg trajectory optimisation problems based on a hodographic shaping trajectory model in combination with restricted two-body dynamics. Through clustering, groups of promising trajectories can be isolated so that unwanted regions can be discarded. Earth --- Mars, Earth --- Venus, and Earth --- 9P/Tempel 1 trajectories are used as test cases and are shown to exhibit periodic behaviour (related to the synodic periods of the departure and target bodies), which enables clustering on grid search-generated datasets. Different clustering algorithms were compared using the Silhouette, Davies-Bouldin, and Calinski-Harabasz internal validation indices. However, traditional clustering algorithms such as (H)DBSCAN, OPTICS, KMeans, and Gaussian Mixture Models, failed to robustly provide clusterings that can be used for pruning, because of the oblong shape of the clusters and the absence of data/noise density differences due to the artificial nature of the problem. Instead, a multimodality-based clustering model called SkinnyDip was found to be much more promising for this task. This algorithm comes with the additional advantage of having very few hyperparameters, eliminating the need for extensive parameter tuning.