Station-keeping of libration point orbits by means of projecting to the manifolds

Abstract

There are many different types of (quasi)periodic orbits in the vicinity of collinear libration points. These libration point orbits (LPOs) are inherently unstable and must be controlled. This paper studies general station-keeping strategies that are suitable for various types of LPOs. Two complementary methods are proposed by exploiting the hyperbolic dynamics of the collinear libration points. One main advantage of these methods is that no information of the nominal orbit is needed in order to do the station-keeping. The first is a semi-analytical projection method which is based on the high order polynomial approximation of the center manifold. After the transformation from synodic coordinates to center manifold coordinates is derived, the error state can be projected to center manifold or its stable manifold by introducing a station-keeping Delta-V, effectively eliminating the unstable component. The second is a fully numerical method. An escape time algorithm is designed to find the intersection of stable and unstable manifolds, effectively projecting the error state to the center manifold. By applying these techniques to the collinear libration points of Earth–Moon system, it has been demonstrated that these proposed methods can achieve better maneuver cost performance and they can handle station-keeping problems of various types of LPOs in a unified manner.