Design and control of multiple spacecraft formation flying in elliptical orbits
Spacecraft formation flying is an attractive new concept in international aeronautic fields because of its powerful functions and low cost. In this paper, the formation design and PD closed-loop control of spacecraft formation flying in elliptical orbits are discussed. Based on two-body relative dynamics, the true anomaly is applied as independent variable instead of the variable of time. Since the apogee is considered as the starting point, the six integrating constants are calculated. Therefore, the algebraic solution is obtained for the relative motion in elliptical orbits. Moreover, the formation design is presented and both circular formation and line formation are provided in terms of an algebraic solution. This paper also discusses the PD-closed loop control for precise formation control in elliptical orbits. In this part, the error-type state equation is put forward and the linear quadratic regulator (LQR) method is used to calculate PD parameters. Though the gain matrix calculated from LQR is time-variable because the error-type state equation is time variable, the PD parameters are also considered as constants because of their small changes in simulation. Finally, taking circular formation as an example, the initial orbital elements are achieved for three secondary spacecraft. And the numerical simulation is analyzed under PD formation control with initial errors and J2 perturbation. The simulation results demonstrate the validity of PD closed-loop control scheme.
作 者： WANG Peng-ji YANG Di 作者单位： Dept. of Astronautic Engineering and Mechanics, Harbin Institute of Technology, Harbin 150001, China 刊 名： 哈尔滨工业大学学报（英文版） EI 英文刊名： JOURNAL OF HARBIN INSTITUTE OF TECHNOLOGY(NEW SERIES) 年，卷(期)： 2005 12(1) 分类号： V412.4 关键词： spacecraft formation flying relative motion in elliptical orbits formation design linear quadratic regulator (LQR) PD closed-loop formation control