On the dynamics and control of the Sun-Earth L_2 tetrahedral formation

摘要

The dynamics and control of a tetrahedral spacecraft formation flying in the Sun-Earth L2 region is initiatively studied, based on the circular restricted three-body problem (CR3BP). Driven by the science goal of identifying extra-solar terrestrial planets and the requirement of imaging optics, a conceptional four-spacecraft triangular pyramid configuration has been proposed for the Multiple-spacecraft Exoplanet Aperture sYnthetic INterferometer (MEAYIN) project, China’s first mid-infrared interferometric imaging mission. Although it looked promising from an optical perspective, the configuration has not been verified dynamically. The formation is required to be virtually “rigid”, because its mutual distances and inertial pointing direction must be maintained with very high accuracy during each observation. In this study, the spatial geometrical relationship between the four spacecraft was established by introducing the parameters of lengths, angles, and a reference vector. The first contribution is that a compact set of normalized factors and critical time indices are defined, which can provide a complete description of the drift of the shape and pointing direction of the configuration, caused by the unstable dynamical environment. Five design variables are isolated and analyzed, and their individual impacts on the uncontrolled evolution of the formation are studied. The main results obtained reveal that the dimensions of the rigid configuration allow a free drift for a time period on the order of tens of hours, while the inertial pointing direction will be lost within merely tens of seconds. Therefore, to form a rigid configuration, the control challenge lies in the fact that control efforts are frequently required for each spacecraft in the fleet, owing to the diverging dynamics. As a second contribution, a simple and feasible control algorithm is proposed to maintain the rigidity of the formation configuration. The results indicate that the associated energy cost is merely 0.05 m/s per observation on average.