Hovering formation control based on two-stage constant thrust

Hovering technology, applied to maintain a chasing spacecraft at a specified position relative to a reference orbit, has received widespread attention in recent years. Conventional impulsive or continuous-thrust control approaches require high demand for the engine and have limited applicability in practice. In this study, a new hovering formation controlled by two-stage constant thrust is proposed. The mathematical model of the two-stage constant-thrust control problem is first formulated, and a rapid method using sensitivity matrix is presented to solve the problem. Then, based on relative orbital elements, the strategy of hovering formation by two-stage constant control in the two-body case is obtained. To avoid the drift of hovering formation caused by J₂ perturbation, an improved strategy is presented to guarantee periodic revisits to the specified relative position. Numerical simulations are conducted to demonstrate the efficiency of the proposed method.