Long-Term Station Keeping of Space Station in Lunar Halo Orbits

Abstract

Optimization methods are presented for long-term station keeping of a low-thrust space station in lunar halo orbits for unstable collinear libration points. The methods use discretization of each half-revolution into segments and a set of pseudoimpulses for each segment. A matrix inequality of the sum of the characteristic velocities for the pseudoimpulses is used to transform the problem into a large-scale linear programming form. Terminal constraints are presented as a linear matrix equation using numerical partial derivatives along a reference orbit. Possible station-keeping strategies for quasi-periodic orbits in the vicinity of the Earth–moon collinear libration point are considered. An iterative shooting algorithm, based on the full ephemeris model and differential correction, is used. Preliminary simulation and comparative results of long-term station-keeping strategies for one year are presented. As application examples, two quasi-periodic orbits are considered. The first is similar to a planar Lyapunov orbit. The second is a halo orbit, with continuous visibility of the space station from the Earth. An algorithm for very low-thrust station keeping with long-duration burns is also presented. The algorithm can be used to estimate the required thrust-to-weight ratio of the space station.