The Optimization of Transfer Trajectory for Small Amplitude Halo Orbits

Abstract

Since the halo orbits in the vicinity of the collinear libration points have a strong hyperbolic character, it is possible to use their stable manifold for the transfer from the Earth. However, for halo orbits of small amplitude, the stable manifold could not approach the Earth, direct transfer from the parking orbit around the earth to the stable manifold is impossible. Nevertheless, with a halo orbit insertion maneuver, the perturbed manifold could approach the earth. This paper proposes a method that combines the differential correction method and the genetic algorithm to minimize the halo orbit insertion maneuver velocity. The method takes advantage of both the global convergence behavior of the genetic algorithm and the quick local convergence behavior of the differential correction method. Numerical simulation shows that the method has a good convergence behavior.