Hovering Formation Design and Control Based on Relative Orbit Elements

In the final approaching stage of an on-orbit servicing mission, hovering technology is widely applied to maintain the chasing satellite at a specified position relative to the reference satellite. Applicability of the conventional continuous-thrust control approach is limited because of its high requirements for the engine. In this study, a "teardrop" hovering formation is obtained by designing the chasing-satellite absolute orbit, and a set of relative orbit elements is introduced to describe the hovering formation. Explicit geometric meaning makes it convenient to apply the proposed hovering formation in practical engineering problems on on-orbit servicing missions of the chasing satellite. Moreover, based on relative orbit elements, a new impulsive control strategy is proposed to keep the chasing satellite in the hovering pattern for a long time. The effect of hovering formation on the required impulse is exhaustively analyzed. The control method for hovering formation movement is also derived. Furthermore, to control the chasing satellite from any configuration to the designated hovering formation, a strategy based on Lambert's problem is established. Considering the impact of measurement errors and perturbations, a closed-loop impulsive feedback control law is derived as well. Numerical simulations are conducted to demonstrate the efficacy of these proposed methods.