Single-Averaged Models for Low-Thrust Collision Avoidance Under Uncertainties

This work presents a framework for the analysis of low-thrust collision avoidance activities and the design of collision avoidance manoeuvres (CAMs) under the effect of uncertainties, based on single-averaged dynamical models over the eccentric anomaly. It builds up on previous results for the tangential thrust case in the MISS (Manoeuvre Intelligence for Space Safety) software developed by Politecnico di Milano. The new models allow for the design of non-tangential manoeuvres through the superposition of analytical solutions for the tangential and normal directions. Furthermore, CAM design for probability of collision minimisation is dealt with, leveraging analytical solutions for the impulsive CAM case, and modelling the effect of uncertainties as a Gaussian distribution. A quasi-optimal, piecewise constant control profile is constructed by dividing the thrust arc into segments and assigning to each segment the thrust orientation obtained from the impulsive model. The impulsive solution, based on an eigenproblem, also provides a proxy parameter for the relative efficiency of thrusting at each segment, which can be leveraged to define the length of the thrust arc. For cases where uncertainties cannot be adequately described through a single Gaussian distribution, the use of a Gaussian Mixture Model is proposed. The performance of the models is assessed through test cases, with particular focus in analysing their range of validity depending on CAM time and total displacement. These low-thrust CAM models have applications for Space Traffic Management systems in increasingly congested scenarios and are currently being applied to a project funded by the European Space Agency for the advancement of tools for low-thrust CAM design.