Spacecraft formation flying near sun-earth L ₂ lagrange point: Trajectory generation and adaptive output feedback control

In this paper, we present a trajectory generation and an adaptive, output feedback control design methodology to facilitate spacecraft formation flying near the Sun-Earth L ₂ Lagrange point. Specifically, we create a spacecraft formation by placing a leader spacecraft on a desired Halo orbit and a follower spacecraft on a desired quasi-periodic orbit surrounding the Halo orbit. We develop the nonlinear dynamics of the follower spacecraft relative to the leader spacecraft, wherein the leader spacecraft is assumed to be on a desired Halo orbit trajectory. In addition, we design a formation maintenance controller such that the follower spacecraft tracks a desired trajectory. Specifically, we design an adaptive, output feedback position tracking controller, which provides a filtered velocity measurement and an adaptive compensation for the unknown mass of the follower spacecraft. The proposed control law is simulated for the case of the leader and follower spacecraft pair and is shown to yield semi-global, asymptotic convergence of the relative position tracking errors.