Transverse Formation of Sail-Assisted Spacecraft With Complex-Shaped Self-Differential Bounded Control

For ordinary binary formations, the relative baseline between satellites undergoes periodic changes, leading to limited time for interferometric imaging and resulting in poor observation quality. This article presents a sail-assisted spacecraft transverse formation and its corresponding control methods. These methods maintain a fixed long relative baseline in both low Earth orbit and high Earth orbit by leveraging the self-differential control set of drag and solar radiation pressure, which are prevalent in near-Earth space. First, the convex characteristics of the control set and the existence of a mapping from a continuous control sequence to a continuous actuator sequence are demonstrated. Consequently, a continuous actual actuator sequence can be solved. A stability analysis criterion of LP-type that considers overshoot is proposed based on positive invariance theory and convex premise. This criterion addresses the challenge of identifying stability caused by the complexity of the self-differential control set. Then, an optimal feedback control approach based on the LP-type criterion and a hybrid neural network method is employed to effectively tackle the challenges presented by the small amplitude and complex shape of the control set, allowing for precise real-time control of formation maintenance and reconfiguration, as demonstrated by simulation results. The proposed transverse formation and its self-differential control methods endow an effective solution to simplify the implementation of a fixed long relative baseline. Moreover, the aforementioned methods can be applied to ordinary formation and other formation applications with high specific impulse and low thrust.