Based on the idea of indirect method, an implicit shooting method is derived to solve the optimal Lunar soft landing trajectory. Firstly, a normalization system model of Lunar soft landing trajectory is established. Secondly, based on the Pontryagin's maximum principle, the optimization of Lunar soft landing trajectory is converted into a Two-Point Boundary Value Problem (TPBVP) of satisfying the necessary conditions for optimality. A new time variable is adopted, and then the terminal time-free TPBVP is changed into terminal time-fixed TPBVP. Moreover, the terminal time is considered as state variable and the value of the Hamiltonian function in terminal time is introduced as an implicit terminal condition. Finally, an implicit shooting method is proposed to solve the TPBVP with implicit terminal condition. The simulation results show that the proposed method has better convergence speed and higher optimization precision than the direct method and the hybrid method, achieving the goal of optimal fuel consumption in Lunar soft landing process. Meanwhile, the optimal Lunar soft landing trajectory with different engine thrusts is studied by this method, obtaining the optimal thrust-weight ratio with lowest fuel consumption. This can provide references for the engine selection of Lunar lander descent stage.
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