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

TL;DR

The paper tackles the Sustainable Asteroid Mining challenge of GTOC12 by combining large-scale departure and return trajectory databases with fast low-thrust to Lambert approximations, ML surrogates, and ILP-based ship subset selection. It introduces maximum initial mass (MIM), minimum time-of-flight (MINT), and two analytical approximations (MIMA and MIMA2), augmented by machine learning to predict propellant costs, to efficiently navigate a vast combinatorial search space. A pair of self-sufficient ship search strategies, trajectory scaffolding and time-looking beam search, generate a pool of candidate ships, which is then optimized via an ILP to form an assembled solution of 28 ships mining 18,475 kg from 249 asteroids (score 15,728 with bonuses). The work demonstrates a scalable framework that exploits fast approximations and data-driven models to design high-performing multi-asteroid missions while preserving computational tractability, with implications for future mission planning in asteroid resource utilization.

Abstract

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.

Figures (14)

• Figure 1: Spatial density of GTOC12 asteroids $x$-$y$ plane (left) and in the radius-$z$ plane (right), calculated by computing the asteroid positions at epochs 69807, 70107, and 70407 MJD corresponding to early mid and late mission epochs, and binning the Cartesian space with cubes of $0.1$ AU size. Red lines show circular bounds between 2.7 and 2.9 AU.
• Figure 2: Visualization of the low-thrust transfers included in the departure database $\mathcal{D}_{\text{dep}}$. A total of 91,135 non-dominated transfers to 18,504 asteroids were included. The 665 transfers making use of a Mars fly-by are marked. The transfers hitting the bounds on $t_{f\max}$ are clearly visible as vertical lines.
• Figure 3: Departure epoch vs semi-major axes for all entries in the return database $D_{\text{ret}}$, consisting of 190,976 transfers to 59,993 asteroids.
• Figure 4: Maximum initial mass curve as a function of time from the start of the mission for different asteroid hops. In the legend, we display the database ID of the departing and arriving asteroids.
• Figure 5: To approximate the maximum initial mass (MIM) we find an analytical representation for a low-thrust transfer that employs a piecewise constant thrust. All variables $\mathbf a_1, \mathbf a_2, t_1$ can be found expanding the solution around the corresponding Lambert problem (i.e. a ballistic transfer from $\mathbf r_s$ to $\mathbf r_f$ in $T$).

Theorems & Definitions (4)

• Lemma 1
• proof
• Theorem 2
• proof