关键词: 制导, 比例导引, 李群, 比例微分控制, 飞行器, 飞行控制

Abstract: This article proposes a new type of three-dimensional(3D) guidance laws using a Lie group method. When strong coupling exists between the pitching channel and swerve channel, there is difficulty in achieving a 3D guidance law with the channeldecoupling assumption. However, it is possible to design guidance laws based on a Lie group method without the decoupling of channels. First, a unified kinematic model of 3D guidance is formulated using vectors. Once a vector is given an SO(3)based description, guidance laws can then be developed from the generalized proportionalderivative(PD) control law on SO(3). The resulting guidance laws are suitable for both given impact direction requirements and maneuvering targets, and the simplified version in a two-dimensional(2D) plane is in consistence with the results of the conventional proportional navigation law. The effectiveness and efficiency of the guidance laws are shown by simulations of characteristic trajectories.

Key words: guidance, proportional navigation, Lie group, proportionalderivative control, aircraft, geometric control