The Soviet Union''s Lunar 1 was the first human-made object to reach on the Moon on 13 September 1959. The first manned mission to land on the Moon on 20 July 1969. Since six manned U.S. landing, no soft landing had been happened from 1976 until 14 December 2013. Chang''e 3 was launched on 2 December 2013 aboard a Long March 3B rocket, and successfully landed on the Moon on 14 December 2013. The lunar rover named Yutu is first rover to operate there since the Soviet Lunokhod 2 ceased operation on 11 May 1973. Joseph Louis Lagrange published an "Essay on the three-body problem". In this essay, he demonstrated two special constant-pattern solutions, the collinear and the equilateral for any three masses with circular orbits. Indeed, the german astronomer Max Wolf discovered Achilles of the trojan asteroids in the L4 Lagrange point of the Sun-Jupiter system.
Orbits around Lagrange points offer advantages for performing certain spacecraft missions. For example the Sun-Earth L1 point is useful for observations of the Sun as the Sun is always visible without obstructions by the Earth or the Moon. The Sun-Earth L2 point is useful for astronomy missions using space telescope with no sun light interference. In 1968, Farquhar first suggested a spacecraft in a halo orbit on the far side of the Moon near the Earth-Moon L2 point as a communication relay station for an Apollo mission to the far side of the Moon. The Earth-Moon L2 point also used a gateway to explorer the solar system. Also Earth-Moon L2 halo orbit can be used for as an orbit of lunar space station to supply for a space explorer. And it might be needed to land on the Moon for gathering lunar resources. For this reason, a transfer strategy from earth and halo orbit and a transfer strategy halo orbit to lunar surface should be determined with taking into account fuel saving.
In this paper, in order to get the maneuver planning for the lunar soft landing via the Earth-Moon L2 halo orbit, the mission the surface of the Moon is consist of two scenario. The first scenario is orbit transfers from GTO(Geostationary Transfer Orbit) to the Earth-Moon L2 Halo orbit, performing three maneuvers in the GTO in order to make a transfer to GEO, then performing a maneuver in the GEO to leave to the Earth-Moon L2 Halo orbit, then performing an additional maneuver to become injected on Halo orbit. The lowest total burn for this type of direct transfer is a Hohmann transfer from the GEO to the Halo orbit. The second scenario is orbit transfers from the Earth-Moon L2 Halo orbit to lunar soft landing, performing Halo deorbit maneuver, the lunar orbit injection maneuver, lunar low circular orbit maneuver, powered descent maneuver, braking maneuver and soft landing maneuver. In this paper, the reference trajectory was calculated using differential corrector, and the global optimization was used in order to get orbit maneuver parameters such as maneuver time, magnitude and direction.
A spacecraft may face a collision with space debris or astroid, which result in catastrophic mission failure or a loss of human life. A global optimization algorithm such as genetic algorithm, simulated annealing, and pattern search is used to obtain the maneuver magnitude, direction and time to reach a target orbit, and to reduce the probability of collision with uncontrolled objects.
As a result, in non-linear problem, the differential corrector can lead us to the wrong answer and diverge because of initial guess values. Also sequential quadratic programming based on the derivative may go into local minimum solution. It is found that the utilization of global optimization has benefit to obtain solution for orbit maneuver in near earth orbit mission and beyond the earth orbit with constrained problem because of derivative free. But it have a disadvantage in expensive computational time.