Loosely displaced formation-keeping control for satellite swarm with continuous low-thrust

Aiming at a long-term formation-keeping problem for the satellite swarm, the concept of a loosely displaced formation is proposed in this article. On this basis, a continuous low-thrust control strategy for maintaining the loosely displaced formation is designed. The control objective is to reduce more fuel consumption during the formation-keeping. For achieving that, we proposed a forward-feedback control strategy by using pseudo-spectral method and sliding mode theory. To be specific, the control strategy includes two parts: a forward control and a feedback control. For the forward control, a numerical optimization with the Legendre pseudo-spectral method is attempted to convert the optimal control problem into a nonlinear programming problem and fuel consumption is selected as the optimization index. For stability issue, the feedback control via adaptive finite-time sliding mode theory is introduced as an additional control component. Finally, the numerical results demonstrate that propellant mass is effectively saved as well as the formation can be tracked accurately with this control strategy proposed in this article.