Input-to-state stable cooperative attitude regulation of spacecraft formation flying

In this paper, the problem of cooperative attitude control under the concept of input-to-state stability for spacecraft formation flying is discussed in the presence of external disturbances. More specifically, the relative attitude quaternion and relative angular velocity are firstly introduced to describe the relative attitude motion between different formation agents. A novel proportional-derivative type controller is then developed including bounded cooperative attitude control term composed of relative quaternion and angular velocity. Associated Lyapunov stability analysis shows that the closed-loop system is proved to be semi-globally input-to-state stable from the generalized disturbance (i.e. cooperative attitude control term and external disturbance) to system states. Besides, the selecting constraint on control parameters is given in the sense of input-to-state stability as one of the main contributions of this paper. Numerical simulation results are also presented which not only highlight the ensuring closed-loop performance benefits from the control law derived here but also shows a rapid transient process and high accuracy.