Asteroid Mining: ACT&Friends' Results for the GTOC 12 Problem

In 2023, the 12th edition of Global Trajectory Competition was organised around the problem referred to as "Sustainable Asteroid Mining". This paper reports the developments that led to the solution proposed by ESA's Advanced Concepts Team. Beyond the fact that the proposed approach failed to rank higher than fourth in the final competition leader-board, several innovative fundamental methodologies were developed which have a broader application. In particular, new methods based on machine learning as well as on manipulating the fundamental laws of astrodynamics were developed and able to fill with remarkable accuracy the gap between full low-thrust trajectories and their representation as impulsive Lambert transfers. A novel technique was devised to formulate the challenge of optimal subset selection from a repository of pre-existing optimal mining trajectories as an integer linear programming problem. Finally, the fundamental problem of searching for single optimal mining trajectories (mining and collecting all resources), albeit ignoring the possibility of having intra-ship collaboration and thus sub-optimal in the case of the GTOC12 problem, was efficiently solved by means of a novel search based on a look-ahead score and thus making sure to select asteroids that had chances to be re-visited later on.

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

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.