Computationally Efficient Approaches for Low-Thrust Collision Avoidance Activities

The continuous evolution of low-thrust propulsion technologies, both in performance and the range of platforms that can equip them, provides increasing advantages in propellant efficiency and enables new kinds of missions. However, their smaller control authority compared to impulsive thrusters makes it more challenging to react to unforeseen situations such as collision avoidance activities. Whereas impulsive propulsion allows for efficient Collision Avoidance Manoeuvres (CAMs) performed just a few orbits before the predicted close approach, low thrust CAMs can require a longer acting time. Moreover, low-thrust CAM models are more computationally costly to perform parametric analyses and optimisations to inform the decision-making process. To tackle some of these issues, we propose analytical and semi-analytical models for low-thrust CAMs, based on averaging techniques and with focus on computational efficiency. They are part of the latest iteration of the Manoeuvre Intelligence for Space Safety (MISS) software tool for CAM design. The main goal in this work is to improve the characterisation of the phasing change at the predicted close approach, as this is the leading contribution to collision probability reduction. To this end, the fully analytical model for constant, tangential low-thrust CAMs introduced in previous works is updated to use a differential time law in eccentric anomaly including first-order terms in thrust acceleration, replacing the previous time law derived from Kepler's equation. Numerical tests show that the new approach significantly improves the accuracy with no additional model complexity, except for quasi-circular orbits. For this case, the zeroth-order time law with a correction for the displacement of the apse line deals better with the singularity of Gauss equations at zero eccentricity. The computational efficiency of the model is leveraged to perform sensitivity analyses for representative test cases, highlight their qualitative characteristics. Finally, two future improvements and applications are introduced. First, the inclusion of normal thrust acceleration components is treated. Although an analytical result can be obtained, its complexity prevents from using it for efficient CAM computation in its current form. Then, the synergies with machine learning techniques for achieving on-board CAM autonomy are briefly discussed.