Manifold-to-manifold transfers using low-thrust acceleration

This paper considers manifold-to-manifold transfers in the circular-restricted three-body problem enabled by low-thrust acceleration where an initial and target states lie on invariant manifolds associated to libration point orbits with different Jacobi constant. The basic idea is to utilize a family of stable and center manifolds that lie arbitrarily close to the target invariant manifold to reduce the cost of transfer. The linear quadratic regulator is used to design feedback control to transfer to the target manifold. Time invariant and time periodic controlleres are derived based on the linearized motion around the equilibrium point and periodic orbit respectively. The results show that the feedback controller can shape the linearized motion around manifold to be that around the equilibrium point or a periodic orbit. As a demonstration, transfer trajectories are designed to target the unstable manifold associated with an unstable Lyapunov orbit in the Earth-Moon system.