Precise halo orbit design and optimal transfer to halo orbits from earth using differential evolution

Abstract

The mission design to a halo orbit around the libration points from Earth involves two important steps. In the first step, we design a halo orbit for a specified size and in the second step, we obtain an optimal transfer trajectory design to the halo orbit from an Earth parking orbit. Conventionally, the preliminary design for these steps is obtained using higher order analytical solution and the dynamical systems theory respectively. Refinements of the design are carried out using gradient based methods such as differential correction and pseudo arc length continuation method under the of circular restricted three body model. In this paper, alternative single level schemes are developed for both of these steps based on differential evolution, an evolutionary optimization technique. The differential evolution based scheme for halo orbit design produces precise halo orbit design avoiding the refinement steps. Further, in this approach, prior knowledge of higher order analytical solutions for the halo orbit design is not needed. The differential evolution based scheme for the transfer trajectory, identifies the precise location on the halo orbit that needs minimum energy for insertion and avoids exploration of multiple points. The need of a close guess is removed because the present scheme operates on a set of bounds for the unknowns. The constraint on the closest approach altitude from Earth is handled through objective function. The use of these schemes as the design and analysis tools within the of circular restricted three body model is demonstrated through case studies for missions to the first libration point of Sun–Earth system.