Low-Thrust Transfer Dynamics and Control Between Halo Orbits in the Earth–Moon System by Means of Invariant Manifold

The low-thrust transfer between halo orbits in the Earth–Moon system is studied in this article. The optimization problem of low-thrust transfer is challenging in the circular restricted three-body problem. Making a reasonable use of the three-body dynamics structure can reduce the thrust required for the transfer. The invariant manifolds associated with planar Lyapunov orbits are spliced at first to create homoclinic and heteroclinic connections that can be used as trial solutions for low-thrust transfer. After that, the transfer of spatial halo orbits is addressed using the continuation methods. The Pontryagin maximum principle is used to calculate the optimal control law for the transfer process. Trajectories with various numbers of rotations around the Moon are suitable for transfer between halo orbits with different orientations, depending on the category of the manifold splicing. Finally, a typical model-predictive controller is designed to track the transfer trajectory in the presence of perturbations. Numerical simulations show the efficiency and practicability of the optimal transfer trajectory design strategy by means of an invariant manifold for future lunar exploration missions.