Optimization of lunar soft landing trajectory based on combinational algorithm

Based on the Pontryagin's maximal principle, the fuel optimal lunar soft landing problem can be simplified as a two point boundary value problem with variable final time. The initial adjoint variables were listed by searching the neighborhood of guessed adjoint variables with the employment of the combinational algorithm, which is combined with particle swarm optimization (PSO) for reducing the territory of searching region and simplex method (SM) for decreasing the time of obtaining suitable results. The most valuable advantage of the combinational algorithm is that both the globe searching and local searching are utilized at the same time. The simulation results show that the combinational algorithm used for designing the soft landing trajectory gives good performance on steady, efficiency and accuracy, even some practical constraints are under considered.