Based on the mixed-solving ideas, the fuel optimal lunar soft landing problem can be solved withGauss pseudospectral method(GPM) and the indirect shooting method. Based on the Pontryagin'smaximal principle, the fuel optimal lunar soft landing problem can be simplified as a two pointboundary value problem with variable final time. Gauss pseudospectral method could solve theproblem successfully and get the initial adjoint variables at the same time. And then the two pointboundary value problem was solved by the indirect shooting method with the employment of thecombinational algorithm. The hybrid method combines the advantages of the direct method andindirect method. It avoided guessing the initial value of the adjoint variables and the optimalityconditions were satisfied and the convergence range was wider. The simulation results show that theHybrid Method used for designing the soft landing trajectory gives good performance on steady,efficiency and accuracy, even some practical constraints are under considered.
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