Satellite Formation Keeping Based on Legendre Pseudospectral Method

This paper presents a model predictive controller based on the leader-follower control mode for fuel consumption optimization and thrust saturation problem in satellite formation keeping. The controller performs rolling optimization with closed-loop feed-back and a finite predictive horizon. To achieve higher computational capability in online optimization, the Legendre pseudospectral method is used to fit the online optimization within the predictive horizon. The optimal control force is obtained by solving the optimization problem through the quadratic programming method. A simulation environment for orbital propagation affected by multiple perturbations is built to verify the proposed formation keeping method. The simulation results show that the designed controller outperforms the traditional LQR controller in terms of fuel consumption and state-error convergence rate in a multi-perturbation environment.