Station-keeping for quasi-periodic orbits

The shallow gravity gradient in the libration point regions enables manoeuvring at low ∆v expenses, but implicates a sensitivity to small perturbations. A variety of bounded orbits can be determined around each libration point and station-keeping is required to maintain them for multiple revolutions. In this paper, a station-keeping algorithm based on the orbital lifetime expectancy is proposed for so-called quasi-periodic solutions. The method introduced is based on the identification of a manoeuvre maximising the lifetime of an orbit within defined boundaries. The manoeuvre direction and magnitude is finally optimised with a differential evolution algorithm. The novelty of the method presented here is the identification of the downstream centre manifold by the lifetime analysis to preserve the orbit with its properties forward in time. The study shows that the manoeuvre direction is directly correlated to stability information that is provided by the Floquet modal theory. Finally, numerical calculations were carried out for trajectories around the far-side libration point in the Earth-Moon system to show the effectiveness of this station-keeping approach. The robustness is proven by the introduction of errors and the evaluation of their impact