多体引力场真实推力模式月地转移轨道间接优化

The third stage of China’s lunar exploration project will need to design Moon-Earth transfer orbit, and the abort return flight from the Moon must be considered for human lunar mission. Aiming to improve the capability of designing flyable optimal trajectories, the restricted multi-body model with precise ephemeris and the practical thrust model are considered, and the key techniques induced by applying optimal control in complex dynamics are studied. The main content of this research include analyzing the optimality necessary conditions for the perturbation force based on precise ephemeris as well as practical thrust control, estimating the initial adjoints without obvious physical meaning by means of a new analytic homotopic approach, and applying the optimal control theory to obtain the optimal as well as accurate solutions. A typical trajectory optimization problem in multi-body gravitational field on Moon-Earth abort return maneuvers with lunar gravity assist is studied. The achievements of this research not only extend the scope of the study on deep-space trajectory design but also lay a theoretical foundation for China's future flight of lunar exploration and the tentative human lunar mission.

我国的探月工程三期将会设计月地转移轨道，而载人登月任务则需要重点考虑月地应急返回机动。为了提高实际任务轨道的设计水平，本项目将在限制性多体系统（地-月-日-航天器）轨道机动中考虑实际的精密星历动力学模型和姿控受限推力控制模型，系统开展在多天体引力场连续推力最优控制问题中应用极大值原理的关键技术研究，包括精密星历天体摄动和受限推力控制的最优性必要条件确立，奇异弧存在性的机理分析，提出解析同伦方法解决物理意义不明确的协变量初值猜测难题，力求充分应用最优控制理论获得确保满足最优性必要条件的高精度解。我们将设计典型的多天体引力场连续推力最优转移轨道，即利用月球引力辅助的月地应急返回轨道。研究成果一方面将拓展深空轨道设计的研究范畴，另一方面可为我国探月三期及载人登月提供理论支持。

本项目应用极大值原理以及先进计算方法设计精密星历限制性多体问题中的最优飞行轨道，在考虑精密星历多体摄动和真实推力控制模式的前提下，研究了限制性多体问题中连续推力轨道最优性条件确立的理论和方法，从机理上解释了多天体引力场轨道奇异弧不存在的原因。针对复杂问题多点边值问题初值猜测的典型困难问题，我们提出了解析同伦法的求解策略，这种策略对于脉冲轨道最优控制问题具有一定的普适性，能够为工程实践中保证精确设计最优轨道提供重要的理论支撑，为我国载人登月任务提供技术支持。