采用传统欧拉角的方式描述导弹运动时,垂直发射导弹会存在奇异点的情况。基于四元数建立了垂直发射导弹的空间运动数学模型,实现了导弹发射后俯仰、偏航、滚转三通道控制器设计,并对不同的转弯策略进行了研究。最后采用先转后滚策略进行了弹道仿真,验证了建模和控制器设计的正确性,可适用于垂直发射导弹的设计与研究。

Singular points exist when using the traditional Euler Angles to describe vertical-launching missile’s movement. This article, therefore, builds a quaternion-based mathematics model to analyze the spatial movement of vertical-launching missiles, realizing the design of pitching, yawing, and rolling function of the triple-channel controller. It also discusses various turn strategies and verifies the validity of the mathematic model and the design of tripper-channel controller with the rolling-after-turning strategy in ballistic trajectory simulation.