Validation of a Fuel-Efficient Collision Avoidance Manoeuvre Optimiser for the GRACE-FO Mission.

Abstract

In recent decades, the increasing number of objects in Earth’s orbit has raised significant safety concerns for spacecraft operations. Particularly in Low Earth Orbit (LEO), missions are experiencing a rise in manoeuvre frequency to maintain safety and operational continuity, mitigating the risk of colliding with hazardous objects. In this framework, it is crucial to design, develop and maintain tools to compute fuel-efficient collision avoidance manoeuvres (CAMs) in order to aid operators’ tasks while gradually minimizing the need for human intervention and advancing towards spacecraft autonomy. Recent research efforts by the authors have focused on computing fuel-optimal CAMs using convex optimisation. The dual objective is to minimize overall fuel consumption while respecting safety conditions based on the probability of collision (PoC) reduction. Specifically, the approach combines sequential convex programming, second-order cone programming, lossless convexification, and differential algebra to approximate the non-convex optimal control problem progressively. The aim of this study is to validate the convex CAM optimiser in the context of a real mission, incorporating operational constraints that are specifically tailored for the US-German joint close-formation mission Gravity Recovery and Climate Experiment - Follow-On (GRACE-FO), operated by the German Space Operations Center (GSOC) of DLR. The mission represents an ideal test-bench for the CAM optimiser. The previously established methodology is, in fact, improved by including constraints on the target relative orbital elements to facilitate formation re-acquisition post-manoeuvre. The convex optimiser’s output is tested and validated against actual CAMs executed throughout the mission’s duration, achieving enhanced fuel efficiency in terms of Delta-V, manoeuvre timing, and risk reduction. Moreover, the optimiser’s computational time significantly outperforms the time typically taken by operators to implement CAM strategies.