中文摘要：

在长期的航天器编队飞行中传统的基于线性相对运动模型设计编队保持轨道的方法会引起较多的燃料消耗。首先采用摄动法解析地求得了考虑二阶非线性项时椭圆轨道相对运动模型的周期性条件和周期解;然后以此周期解为参考轨道设计了基于Lyapunov稳定的PD保持控制律。仿真结果表明：基于椭圆轨道非线性相对运动模型的周期解较基于椭圆轨道线性相对运动模型的周期解,精度明显提高;以前者为参考轨道的保持控制与以后者为参考轨道的保持控制相比,燃耗明显降低。

英文摘要：

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.