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High-Accuracy Trajectory Optimization for a Trans-Earth Lunar Mission

机译：跨月登月任务的高精度弹道优化

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The trajectory optimization of a spacecraft subject to the gravitational effects of the moon, Earth, and sun are considered. The problem is how to achieve Earth-interface conditions from a low lunar orbit. Practical constraints of maximum thrust, fuel budget, and flight time generates a constrained, nonautonomous, nonlinear optimal control problem. Severe constraints on the fuel budget combined with high-accuracy demands on the endpoint conditions necessitate a high-accuracy solution to the trajectory optimization problem. The problem is first solved using the standard Legendre pseudospectral method. The optimality of the solution is verified by an application of the covector mapping principle. It is shown that the thrust structure consists of three finite burns with nearly linear steering-angle time histories. A singular arc is detected and is interpreted as a singular plane change maneuver. The Bellman pseudospectral method is then employed for mesh refinement to improve the accuracy of the solution.
机译：考虑了受月球，地球和太阳引力影响的航天器的轨迹优化。问题是如何从低月球轨道实现地球界面条件。最大推力，燃油预算和飞行时间的实际限制产生了一个受约束的非自治非线性最优控制问题。对燃料预算的严格限制，加上对端点条件的高精度要求，需要高精度解决方案来解决轨迹优化问题。首先使用标准Legendre伪光谱方法解决该问题。该解决方案的最优性通过应用协矢量映射原理进行了验证。结果表明，推力结构由三个有限的燃烧组成，具有近似线性的转向角时间历史。检测到奇异弧并将其解释为奇异平面改变操作。然后将Bellman伪光谱方法用于网格细化，以提高解的准确性。

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