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使用李群方法设计了一种新型三维制导律。在俯仰、偏航通道之间存在强耦合关系时,基于双通道解耦的假设构造三维制导律变得困难,而基于李群方法则可以在不进行通道解耦的条件下进行制导律设计。本文首先基于矢量建立了三维制导的一般运动学模型,在给出了矢量的SO(3)群描述之后,按照SO(3)群上的广义比例-微分(PD)控制方式进行了制导律设计。所得到的三维制导律既能用于目标机动的制导,也能用于有终端约束的制导。该制导律在二维平面的简化结果与传统比例导引的结果一致。最后用典型飞行轨迹仿真验证了其可行性和良好的性能。
A new type of 3D guidance law is designed using Lie group method. When there is a strong coupling between pitch and yaw channel, it is difficult to construct 3D guidance based on dual-channel decoupling assumption. Guidance law design based on Lie group method without channel decoupling can be achieved. In this paper, a general three-dimensional guidance kinematics model is established based on vector. After the SO (3) group description of the vector is given, the guidance law design is conducted according to the generalized Proportional-Differential (PD) control method on SO (3) . The resulting three-dimensional guidance law can be used for guidance of the target maneuver, but also for the guidance of the terminal constraints. The simplified results of the guidance law in the two-dimensional plane are consistent with the results of traditional proportional guidance. Finally, the feasibility and the good performance of the simulation are verified by the typical flight path simulation.