Fuel optimal maneuver of circular-like satellite formation based on continuous low thrust

An effective method is proposed to formulate and solve a fuel-optimal control problem of satellite formation maneuver using continuous low thrusters. To ensure long-term flying formation and to save fuel practically possible, the final satellite formation is designed as the passive and periodic relative orbits accommodating the J₂ perturbation. Based on the conditions of the passive and periodic relative trajectory and combining with the unknown final injection time, a final orbit is described by six implicit constraint equations. In order to overcome the complex and difficult computation, the nonlinear optimal control problem is converted into a nonlinear programming problem by means of the Legendre pseudospectral method. Due to the formulated problem including the free final time and the precise final constraints, the formation maneuver is very reasonable and the fuel consumption is minimized. The numerical results show that the control law works well for the optimal reconfiguration of satellite formation.