航天器燃耗最优轨道直接/间接混合法延拓求解

针对转移时间和始末状态固定的航天器燃耗最优轨道的求解,给出了一种延拓方法:以双脉冲轨道为初值,首先求解全程推进轨道,然后逐步增加推力幅值,应用直接/间接混合法依次求解所有推力幅值下的、满足包括开关函数在内的所有必要条件的转移轨道,包括连续和脉冲推力轨道。通过基于开关函数曲线变化趋势的开关序列预设方法,以及基于已有优化结果的延拓步长自适应方案,实现了延拓方法的自动运行。为实现该延拓方法,给出了适用于改进春分点根数模型的脉冲最优转移轨道主矢量必要条件,推导了无推力轨道段改进春分点根数协态变量状态转移矩阵。通过3个算例对延拓求解会遇到的不同情况进行了具体说明。延拓方法可以看作现有直接/间接混合法的进一步完善与拓展,延拓过程和结果有助于对燃耗最优轨道与系统参数之间的关联获得更为深刻的认识。

Minimum-fuel spacecraft transfer trajectories solved bydirect/indirect hybrid continuation method

A continuation method is proposed for fixed-time minimum-fuel spacecraft trajectory optimization given initial and terminal states.The continuation method,based on the direct/indirect hybrid method,starts with a transfer solution with two impulses,followed by calculating firstly the full-propelling transfers and then the fuel-optimal transfers (including continuous and impulsive thrust ones) with continuation on thrust amplitude.All fuel-optimal solutions solved satisfy the necessary optimality conditions derived from the primer vector theory.A thrust switching presetting method based on the variational trends of switching function curves and a simple step-length adaptation rule based on the previous calculation results are proposed to enable the continuation automatic.The necessary optimality conditions for the impulsive trajectory expressed by the modified equinoctial orbit elements are given and verified,and the state transition matrix of costates of modified equinoctial orbit elements for coast arcs is derived.Three numerical examples are given to represent various transfer scenarios.Continuation can be regarded as improvement and extension of the direct/indirect hybrid trajectory optimization method.Continuation procedure and results can help to improve our understanding of the relations of the optimal control trajectories to system parameters.