Low-thrust under-actuated satellite formation guidance and control strategies

This study presents autonomous guidance and control strategies for reconfiguring close-range multi-satellite formations. The formation consists of $N$ under-actuated deputy satellites and an uncontrolled virtual or physical chief spacecraft. Each deputy is equipped with a single throttleable but ungimbaled low-thrust nozzle, requiring a combination of thrust and coast arcs, during the latter attitude adjustments redirect the nozzle to the desired thrust direction. The guidance problem is formulated as a trajectory optimization task incorporating dynamical and physical constraints, along with a minimum acceleration threshold imposed by typical electric thrusters. Two frameworks are considered: centralized and distributed. The centralized approach ensures fuel-optimal solutions but is feasible only for small formations, with all calculations performed on a physical chief satellite. The distributed approach, while sub-optimal, scales better by treating the chief as a virtual point mass and allowing each deputy to handle its own computations. This study focuses on spaceborne closed-loop control implementation, ensuring reliability and automation in solving the optimal control problem. To mitigate infeasibility risks, constraints that pose potential threats are identified and softened. Two Model Predictive Control architectures, shrinking-horizon and fixed-horizon, are implemented and compared in terms of fuel consumption and control accuracy. Their performance is analyzed for typical close-range reconfigurations required in Earth observation missions and benchmarked against existing approaches in the literature.