3-Dimensional lunar ascent reference trajectory optimization and analyses via Gauss Pseudospectral Method

A Gauss Pseudospectral Method for trajectory optimization is presented and applied successfully to the 3-dimensional lunar ascent problem in this paper. Firstly, the profile of lunar ascent is discussed. In order to setup the optimal control problem, 3-dimensional dynamics and kinematics equations of the lunar ascent is established, the angle of attack and bank angle are chosen as optimal control variables. Then the Gauss Pseudospectral Method is used to transform the optimal control problem into a nonlinear programming problem. At last, the optimum trajectory is attained by a NLP solver. Simulation results and analyses illustrate that GPM have good robustness, strong convergence and is almost insensitive to initial guesses, it's an effective method for pre-establishing the suboptimal lunar ascent trajectory.