Spacecraft collision avoidance procedures have become an essential part of satellite operations. Complex and constantly updated estimates of the collision risk between orbiting objects inform various operators who can then plan risk mitigation measures. Such measures can be aided by the development of suitable machine learning (ML) models that predict, for example, the evolution of the collision risk over time. In October 2019, in an attempt to study this opportunity, the European Space Agency released a large curated dataset containing information about close approach events in the form of conjunction data messages (CDMs), which was collected from 2015 to 2019. This dataset was used in the Spacecraft Collision Avoidance Challenge, which was an ML competition where participants had to build models to predict the final collision risk between orbiting objects. This paper describes the design and results of the competition and discusses the challenges and lessons learned when applying ML methods to this problem domain.

Imitation learning is a control design paradigm that seeks to learn a control policy reproducing demonstrations from expert agents. By substituting expert demonstrations for optimal behaviours, the same paradigm leads to the design of control policies closely approximating the optimal state-feedback. This approach requires training a machine learning algorithm (in our case deep neural networks) directly on state-control pairs originating from optimal trajectories. We have shown in previous work that, when restricted to low-dimensional state and control spaces, this approach is very successful in several deterministic, non-linear problems in continuous-time. In this work, we refine our previous studies using as a test case a simple quadcopter model with quadratic and time-optimal objective functions. We describe in detail the best learning pipeline we have developed, that is able to approximate via deep neural networks the state-feedback map to a very high accuracy. We introduce the use of the softplus activation function in the hidden units of neural networks showing that it results in a smoother control profile whilst retaining the benefits of rectifiers. We show how to evaluate the optimality of the trained state-feedback, and find that already with two layers the objective function reached and its optimal value differ by less than one percent. We later consider also an additional metric linked to the system asymptotic behaviour-time taken to converge to the policy’s fixed point. With respect to these metrics, we show that improvements in the mean absolute error do not necessarily correspond to better policies.

The preliminary mission design of spacecraft missions to asteroids often involves, in the early phases, the selection of candidate target asteroids. The final result of such an analysis is a list of asteroids, ranked with respect to the necessary propellant to be used, that the spacecraft could potentially reach. In this paper we investigate the sensitivity of the produced asteroids rank to the employed trajectory model in the specific case of a small low-thrust propelled spacecraft beginning its journey from the Sun-Earth $L_2$ Lagrangian point and heading to a rendezvous with some near-Earth asteroid. We consider five increasingly complex trajectory models: impulsive, Lambert, nuclear electric propulsion, nuclear electric propulsion including the Earth’s gravity, solar electric propulsion including the Earth’s gravity and we study the final correlation between the obtained target rankings. We find that the use of a low-thrust trajectory model is of great importance for target selection, since the use of chemical propulsion surrogates leads to favouring less attractive options 19% of times, a percentage that drops to 8% already using a simple nuclear electric propulsion model that neglects the Earth’s gravity effects and thrust dependence on the solar distance. We also find that for the study case considered, a small interplanetary CubeSat named M-ARGO, the inclusion of the Earth’s gravity in the considered dynamics does not affect the target selection significantly.