Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 926158, 18 pages
Research Article

Modified Chebyshev-Picard Iteration Methods for Station-Keeping of Translunar Halo Orbits

Department of Aerospace Engineering, Texas A&M University, TAMU 3141, College Station, TX 77843-3141, USA

Received 15 July 2011; Revised 7 November 2011; Accepted 14 November 2011

Academic Editor: Tadashi Yokoyama

Copyright © 2012 Xiaoli Bai and John L. Junkins. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The halo orbits around the Earth-Moon L2 libration point provide a great candidate orbit for a lunar communication satellite, where the satellite remains above the horizon on the far side of the Moon being visible from the Earth at all times. Such orbits are generally unstable, and station-keeping strategies are required to control the satellite to remain close to the reference orbit. A recently developed Modified Chebyshev-Picard Iteration method is used to compute corrective maneuvers at discrete time intervals for station-keeping of halo orbit satellite, and several key parameters affecting the mission performance are analyzed through numerical simulations. Compared with previously published results, the presented method provides a computationally efficient station-keeping approach which has a simple control structure that does not require weight turning and, most importantly, does not need state transition matrix or gradient information computation. The performance of the presented approach is shown to be comparable with published methods.