登月舱上升段最优轨迹设计

为了实现登月舱上升段轨迹的优化，建立了上升段登月舱动力学模型，用单位归一化技术建立了最优控制模型，并以燃料消耗为最优指标，利用Pontryagin极小值原理，将问题转化为时间自由的两点边值问题 TPBVP 。采用了一种基于初值预估方法和向前扫描法求解TPBVP，从而设计出登月舱上升段最优轨迹，并进行了数值仿真。仿真结果表明所设计的算法收敛速度快、可靠性高。

Optimal Trajectory Design for the Lunar Module in Ascent Stage

To realize the trajectory optimization of the lunar module in ascent stage, the dynamical model of the lunar module was established and nondimensionalized to construct the optimal control-oriented model. Based on Pontryagin's minimal principle and taking the fuel consumption as the optimizing index, the optimal problem was converted into a time free two-point boundary value problem ( TPBVP) . Using one of initial value hypothesizing methods, combined with the forward sweep algorithm, the TPBVP was solved and the optimized trajectory was obtained. Numerical simulation was conducted. The simulation results justify the rapid convergence rate and high reliability of the proposed method.