Study of low-thrust transfer to Halo orbit with invariant manifolds

Design the low-thrust transfer trajectory to halo orbit based on the concept of invariant manifold in dynamical systems theory, First, the transfer orbit is compartmentalized as raising segment and coast segment by the difference of thruster work or not. Then, each segment is described by different dynamical model and parameterized by invariant manifold and the theory of Lyapunov feedback control. Finally, optimal transfer trajectory is obtained by utilizing parameter optimization. By chosen the coordinate compatibly, and using the Lyapunov feedback control, the difficulty of convergence is avoided, which is leaded by the non-linearity of three-body dynamical model and adjoint equation of optimal control problem; There are no iteration in any step of the process of optimization, so the algorithm is time economical. At the end of this paper, take the low-thrust transfer from a parking orbit to Sun-Earth L₂ halo orbit as an example to validate the effect of this method. This method is effective and important to the design of low-thrust libration point missions.