基于四元数的导弹反步控制及全方位算法应用

Omnidirectional Quaternion Algorithm and Missile Attitude Control Based on Backstepping Method in Quaternion

针对传统四元数适应范围小,分析误差困难问题,基于误差四元数的概念深入研究了姿态误差形式和姿态角和四元数全方位转换问题,提出了姿态角和四元数的全方位转换算法。该算法实现了姿态角和四元数的-1800到1800全空间转换,并且具有抗扰动的能力,同时将四元数与非线性反步(backstepping)方法结合,进行了导弹姿态控制。仿真表明了全角度算法的正确性,以及基于文中的四元数姿态误差方程可有效进行导弹全方位姿态控制。

To solve applied field small and error analysis difficult in traditional quaternion method, problems of attitude error and omnidirectional transformation between quaternion and Euler angle were deeply studied using error quaternion, Based on above analysis, a new algorithm was proposed to realize omnidirectional transformation from 180°to -180°, and the algorithm will guarantee right transforming result even when external disturbance causes quaternion errors. In addition, nonlinear backstepping method in quaternion is used to control missile attitude, for attitude error is always nonlinear. Simulation shows the algorithm validity and the attitude motion equation in error quaternion are effective to omnidirectional attitude control.