Nonlinear Station-Keeping Control in the Vicinity of the Sun-Earth L2 Point Using Solar Radiation Pressure

Abstract

The use of solar radiation pressure for station-keeping at a sub-L2 Sun-Earth/Moon collinear libration point is presented. Numerical halo and Lissajous reference trajectories are generated for the sub-L2 libration point. Owing to the instability of these orbits, active station-keeping is required to prevent spacecraft escape after orbit insertion. The control inputs for solar sail control include area variation and solar sail pitch and roll angle variations. A nonlinear higher order control method is developed to utilize solar radiation pressure to minimize the trajectory tracking error. The stability of the proposed controllers is established using the Lyapunov theory. The performance of the proposed controllers is tested through numerical simulation of the governing nonlinear equations of motion and is applied for station-keeping in the elliptical restricted three-body problem. It is shown that underactuated control is able to keep the spacecraft motion bounded, but the tracking error remains high. The fully actuated control is able to provide accurate station-keeping for both halo and Lissajous trajectories. The numerical results demonstrate the effectiveness of the proposed control technique for precise station-keeping using solar radiation pressure at a sub-L2 libration point.