Periodic solution to elliptical orbit nonlinear relative motion model and the application

Traditional formation keeping orbit design is based on linear relative motion model which will lead to more fuel consumption during long-term spacecraft formation flying. Firstly, the periodic condition and periodic solution were obtained by solving the elliptical orbit relative motion model considering the second-order nonlinear terms with perturbation approach. The periodic solution obtained was then used as the reference orbit of a PD control law for formation keeping based on the Lyapunov stability theory. Simulation results show that the periodic solution based on the nonlinear relative motion model of elliptical orbit is more accurate than that based on linear relative motion model of elliptical orbit. And the formation maintain control law with periodic reference orbit based on nonlinear model can save much more fuel compared with that based on the linear model.