Research on the model predictive control approach for satellite formation keeping

In this paper, a coordinative control approach based on model predictive control method is proposed aiming at the formation keeping problem of multiple satellites formation. First, the linearized relative motion dynamics based on relative orbital elements is given and based on which, a linear programming mathematical model is set up to optimally determine the reference center for multiple satellites formation keeping and to determine the desired correction value for each satellite. Then, on basis of the established discrete states equation and measurement equation, A mixed-integer linear programming model considering many constraints is proposed to get the formation keeping control law. So, by solving the two mathematical programming model mentioned above, a coordinative formation keeping control law based on model predictive control is derived. In the end, mathematical simulation results show the effectiveness and superiority of the given algorithm.