Optimal trajectory design and analysis for soft landing on the moon from lunar parking orbits

This article studies the optimal control solution of the Moon-Lander problem. The main purpose of this article is to investigate the optimal strategy for trajectory design to ensure the soft landing of the lander from the Lunar parking orbit to the lunar surface with minimum consumption of fuel. The trajectory design of lunar lander is studied via two cases by formulating the optimal control problems, where specific requirements of this soft landing problem are all incorporated in the problem formulation. To analyse the proposed optimal strategies for a soft landing the paper briefly illustrates the numerical simulation results and it shows that the required velocity for the soft landing is achieved with minimum fuel consumption. The investigated computational methods for the optimal solutions of the Moon-Lander problem in both two cases are conceptually simple and efficient.