Formation Control at the Sun-Earth L2 Libration Point Using Solar Radiation Pressure

In this paper the use of solar radiation pressure for spacecraft formation flying at the L-2 sun-Earth/moon collinear libration point is presented. The system consisting of a leader and a follower satellite is considered. The leader satellite is assumed to he in a fixed halo trajectory and the follower satellite position relative to the leader satellite is controlled using two angles and area; these are varied based on a higher-order sliding-mode control technique to achieve the desired formation control. The stability of the proposed controller is established using Lyapunov theory. The performance of the proposed controller is tested through numerical simulation of the governing nonlinear equations of motion and is applied for both formationkeeping and formation reconfiguration in the elliptical restricted three-body problem. The effects of initial state errors, nonnatural formations and optical solar sail material degradation are considered. The numerical results demonstrate the effectiveness of the proposed control technique for precise satellite formation flying using solar radiation pressure at the L-2 libration point. Furthermore, control inputs on the order of 10 deg and 4 m(2) for area change are sufficient to control formation reconfiguration changes as large as 25 km.