Recursive Method for Efficient Collision Avoidance Manoeuvres with Multiple Polynomial Constraints

The increasing number of satellites and debris in low Earth orbit poses a growing risk of collision for operational spacecraft, requiring efficient collision avoidance manoeuvres (CAMs) that can handle short warning times while minimising impact on the mission. Conventional approaches rely on propulsive manoeuvres, but alternative methods are required for satellites without active propulsion or those on a stringent propellant budget. Aerodynamic CAMs provide a propellant-less alternative, and their development has been identified by the Zero Debris Community as a key enabling factor in improving spacecraft manoeuvrability. Previous research has employed drag-based CAMs that are initiated several orbits prior to a projected collision. However, challenges remain in managing short warning times and complex conjunction scenarios. Our work explores the potential of out-of-plane aerodynamic forces, or lift, as a means to improve control authority and the ability to reduce orbital decay. Starting from the conjunction point, the spacecraft performing the manoeuvre is propagated back in time. The spacecraft’s constrained aerodynamic control authority can then be related to an effect on the conjunction geometry and the collision risk through differential algebra. A fast heuristic method for finding an initial guess to the optimal control problem is computed by iterative back-stepping from the conjunction and finding the local optimal controls using the boundary of the reachable set. We demonstrate that Very Low Earth Orbit satellites, operating at altitudes of 450 km and below, can effectively use aerodynamic forces for collision avoidance with lift-based manoeuvres being more efficient in short warning time scenarios.