Formation flying on quasi-halo orbits in restricted Sun–Earth/Moon system

Due to the strong nonlinear perturbations near the libration points, the continuous low-thrust technique has many potential applications in stationkeeping relative motions. The Hamiltonian structure-preserving (HSP) control is employed in this paper to stabilize formation flying on quasi-periodic orbits near LL₁ of the restricted Sun–Earth–Moon–spacecraft system. In the bi-circular model (BCM), a multiple shooting corrector is developed to refine quasi-periodic orbits as the chief spacecraft's reference trajectories. The linearized variation equation in BCM is used to design the stationkeeping control. A HSP controller is constructed to change the topology of the equilibrium from hyperbolic to elliptic using only relative position feedbacks consisting of stable, unstable and center manifolds. The critical control gains for transient and long-term stabilities are presented to guide the selection of control gains.