Description: According to the problem of trajectory optimization for the lunar module in ascent stage, firstly, the dynamical model of the module is established, as well as the non-dimensional optimal control-oriented model, secondly, to realize the minimal fuel consumption, the optimal problem is converted into a time free Two-Point Boundary Value Problem (TPBVP) based on the Pontrjagin’s minimal principle, finally, TPBVP is solved and the optimal trajectory is obtained using an initial value hypothesizing method along with the Forward Sweep Algorithm. The simulation results show that this method has advantages of rapid convergence velocity and high reliability, and can provide reference for the practical application of the module returning from moon
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