Multi-objective optimization of interplanetary Halo-to-Halo orbit transfers

In this paper, the multi-objective optimization of Halo-to-Halo transfer trajectory between different Sun-planet systems is discussed by considering the ephemeris constraints. The direct and indirect transfers that employ the different sets of the invariant manifolds are analyzed, respectively. The pseudo-manifolds, along which the spacecraft can depart and approach Halo orbit quickly, is introduced to replace the traditional invariant manifolds. Then, the multi-objective optimization models are built for two transfer schemes. In the direct transfer scheme, the outer branches of the pseudo-manifolds are connected under the heliocentric two-body model. In the indirect transfer, the inner branches of the pseudo-manifolds and the interplanetary transfer trajectory are connected by combining the periapsis Poincare map with a matching algorithm. Further, a polynomial spline method is utilized to estimate the pseudo-manifolds. The computational efficiency is improved for avoiding the numerical integration. For each transfer scheme, the trajectory design can be considered as a multi-variable unconstrained optimization problem. The NSGA-II (Non-domination Sort Genetic Algorithm) is adopted to solve the problems taking total velocity increment and flying time as optimization objects. The efficiency of the proposed approach is verified by the simulation example of Earth-Mars Halo-to-Halo transfer trajectory.