基于欧氏范数的刚体转动误差测度的分析

ANALYSIS ON MEASURES OF ROTATIONAL ERROR FOR A RIGID BODY BASED ON EUCLIDEAN NORM

基于欧氏范数的概念，对于两个３×３的空间转动位置矩阵Ｒ１和Ｒ２，文章表明矩阵［Ｒ２－Ｒ１］和［Ｒ２（Ｒ１）Ｔ］都可以直接导出理想的转动误差测度．经过分析可知。

Based the concept of Euclidean norm, for two rotational positions represented by 3×3 matrices R 1 and R 2 ,it is shown that matrices [R 2-R 1] and [R 2(R 1) T] lead directly to desirable measures of rotational error . Under particular investigation ,it is made clear that the body's rotational error can be computed most efficiently through directly calculating the Euclidean norm of the matrix difference ΔR=R 2-R 1.