Computing low-thrust transfers in the asteroid belt, a comparison between astrodynamical manipulations and a machine learning approach

TL;DR

This work addresses the challenge of planning low-thrust transfers in the asteroid belt by comparing analytical two-arc approximations built on MIMA and Lambert-based $\Delta V$ estimates against data-driven neural surrogates trained on a ground-truth set of about $3$ million time- and fuel-optimal transfers. It introduces a large, open dataset and demonstrates that a small neural network with 23 inputs and 3 hidden layers can predict the final-to-initial mass ratio with higher accuracy and far faster inference (≈$50$×) than the analytical method, especially for longer transfers, while analytical methods remain competitive at short time-of-flight. The results show final-mass errors typically within a few percent, and ML approaches generally outperform analytical ones as transfer duration increases, enabling more efficient exploration of mission opportunities in the belt. The open dataset and the demonstrated speedups provide practical benefits for preliminary mission design and combinatorial optimization of asteroid-tour sequences.

Abstract

Low-thrust trajectories play a crucial role in optimizing scientific output and cost efficiency in asteroid belt missions. Unlike high-thrust transfers, low-thrust trajectories require solving complex optimal control problems. This complexity grows exponentially with the number of asteroids visited due to orbital mechanics intricacies. In the literature, methods for approximating low-thrust transfers without full optimization have been proposed, including analytical and machine learning techniques. In this work, we propose new analytical approximations and compare their accuracy and performance to machine learning methods. While analytical approximations leverage orbit theory to estimate trajectory costs, machine learning employs a more black-box approach, utilizing neural networks to predict optimal transfers based on various attributes. We build a dataset of about 3 million transfers, found by solving the time and fuel optimal control problems, for different time of flights, which we also release open-source. Comparison between the two methods on this database reveals the superiority of machine learning, especially for longer transfers. Despite challenges such as multi revolution transfers, both approaches maintain accuracy within a few percent in the final mass errors, on a database of trajectories involving numerous asteroids. This work contributes to the efficient exploration of mission opportunities in the asteroid belt, providing insights into the strengths and limitations of different approximation strategies.

Figures (3)

• Figure 1: Schematic illustration of neural network architecture.
• Figure 2: Analytical and machine learning approximation results over $DB_1$, $DB_2$, $DB_3$, $DB_4$. The x-axis represents the number of transfers within a certain error threshold, normalized by the length of the database.
• Figure 3: Statistics of the errors of the analytical and ML approximations, over the whole database.