Study on relative orbital configuration in satellite formation flying

In this paper, the relative orbital configurations of satellites in formation flying with non-perturbation and J₂ perturbation are studied, and an orbital elements method is proposed to obtain the relative orbital configurations of satellites in formation. Firstly, under the condition of non-perturbation, we obtain many shapes of relative orbital configurations when the semi-major axes of satellites are equal. These shapes can be lines, ellipses or distorted closed curves. Secondly, on the basis of the analysis of J₂ effect on relative orbital configurations, we find out that J₂ effect can induce two kinds of changes of relative orbital configurations. They are distortion and drifting, respectively. In addition, when J₂ perturbation is concerned, we also find that the semi-major axes of the leading and following satellites should not be the same exactly in order to decrease the J₂ effect. The relationship of relative orbital elements and J₂ effect is obtained through simulations. Finally, the minimum relation perturbation conditions are established in order to reduce the influence of the J₂ effect. The results show that the minimum relation perturbation conditions can reduce the J₂ effect significantly when the orbital element differences are small enough, and they can become rules for the design of satellite formation flying.The project supported by the National Natural Science Foundation of China (10202008) and Specialized Research Fund for the Doctoral Program of Higher Education (20020003024)     

Decentralized coordinated attitude control for satellite formation flying via the state-dependent Riccati equation technique

The goal of the present study is to develop a decentralized coordinated attitude control algorithm for satellite formation flying. To handle the non-linearity of the dynamic system, the problems of absolute and relative attitude dynamics are formulated for the state-dependent Riccati equation (SDRE) technique. The SDRE technique is for the first time utilized as a non-linear controller of the relative attitude control problem for satellite formation flying, and then the results are compared to those from linear control methods, mainly the PD and LQR controllers. The stability region for the SDRE-controlled system was obtained using a numerical method. This estimated stability region demonstrates that the SDRE controller developed in the present paper guarantees the globally asymptotic stability for both the absolute and relative attitude controls. Moreover, in order to complement a non-selective control strategy for relative attitude error in formation flying, a selective control strategy is suggested. This strategy guarantees not only a reduction in unnecessary calculation, but also the mission-failure safety of the attitude control algorithm for satellite formation. The attitude control algorithm of the formation flying was tested in the orbital-reference coordinate system for the sake of applying the control algorithms to Earth-observing missions. The simulation results illustrate that the attitude control algorithm based on the SDRE technique can robustly drive the attitude errors to converge to zero.