月球探测器垂直软着陆4D轨道全局优化

提出一种包含动态规划法与共轭梯度法的组合优化算法，求解月球探测器垂直软着陆问题. 其以动态规划法中求得的次优控制变量作为共轭梯度法的初始控制变量，求得更为精确的最优控制变量和最优轨道. 月球垂直软着陆的轨道可以分为两段，即制动段与着陆段. 以燃料消耗量最小为性能指标，采用该组合优化算法分别对两段轨道进行了4D全局优化. 数值仿真结果表明，该组合算法优化精度较高，收敛速度快，稳定性好，可用于机载计算机实时生成垂直软着陆4D轨道，同时还可推广到其他终端时间自由型两点边值问题. 

Global 4D Trajectory Optimization Design for Lunar Vertical Soft Landing

A combinatorial algorithm, including dynamic programming and conjugate gradient, was proposed for 4D trajectory global optimization of the lunar probe vertical soft landing. By employing the suboptimum control variable calculated from dynamic programming as the initial control variable of conjugate gradient algorithm, the more precise optimum control variable and flight trajectories were obtained. The lunar probe vertical soft landing trajectory consists of two segments, i.e., the brake and landing segments. The performance index is to minimize fuel consumption of the lunar detector. The 4D trajectory of lunar vertical soft landing is optimized by this combinatorial optimization algorithm. Simulation results showed good accuracy, rapid convergence, and robustness with initial values for this combinatorial algorithm, which promise it to on-line generate a feasible vertical soft landing trajectory on the onboard computer. Meanwhile, the combinatorial algorithm could be extended to other two-point boundary value problems of terminal time uncontrolled type.