Rodrigues参数与四元数间的关系分析

Analysis of Relationship between Rodrigues Parameters and Quaternion

介绍了Rodrigues参数,从投影的角度,详细阐述了四元数与经典Rodrigues参数及改进型Rodrigues参数的关系,推导了Rodrigues参数微分方程以及与姿态阵的关系,建立了等效旋转时避免奇异值出现的方法。以典型圆锥运动为背景,对以Rodrigues参数描述的导弹捷联姿态算法和以四元数描述的姿态算法在计算量和计算精度上做了详细的比较。

The paper gives a discussion on Rodrigues parameters and a detail discussion on relationship between quaternion and the classical Rodrigues parameters and the modified Rodrigues parameters in term of projection. The differential equation and attitude matrix based on Rodrigues parameters are induced. A method based on modified Rodrigues parameters which can avoid singular value during equivalent rotation is built. On the basis of the classical conical motion, this paper gives a detailed comparison on the computational complexity and computing accuracy of strap-down attitude algorithm of missile based on Rodrigues and attitude algorithm based on quaternion.