Abstract

A direct method for optimizing the spatial trajectories of lunar landing in the deceleration phase with a limitation along the descent profile, when the lander must remain inside a certain cone with apex at a given landing point, is presented. The model of motion is a point of variable mass moving in a uniform gravitational field. The method uses a two-level optimization of the characteristic velocity for a given distance and lateral displacement at free landing time. The upper level corresponds to one-dimensional nonlinear optimization of the landing time. The lower level corresponds to optimization for the landing times established at the upper level and the given coordinates of the landing point using discrete sets of pseudopulses and high-dimensional linear programming. Energetically accessible regions and regions when redetermining the landing point are presented as examples.

中文翻译：

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空间月球着陆轨迹的优化：可到达性域，重定向和下降轮廓约束

摘要

提出了一种直接方法，当着陆器必须在给定着陆点的顶点保持在某个圆锥体内部时，沿减速轮廓限制其在减速阶段优化月球着陆的空间轨迹。运动模型是可变质量在均匀重力场中运动的点。该方法对自由降落时给定的距离和横向位移使用了特征速度的两级优化。上层对应着陆时间的一维非线性优化。较低级别对应于使用离散脉冲组和高维线性编程对在较高级别建立的着陆时间和着陆点的给定坐标的优化。