单位四元数、罗德里格转换模型与欧拉角的映射关系

在大角度姿态运动场景中,运动状态通常采用单位四元数或罗德里格转换模型,但转换参数并不具有直观性和几何意义,因此研究单位四元数、罗德里格转换模型与欧拉角的映射关系十分必要。然而,单位四元数、罗德里格参数与欧拉角相互之间并不存在一一对应的关系。结合三种转换模型的特点及欧拉角、罗德里格参数存在奇异问题,本文对可能出现的情况进行推导分析,建立各模型间转换参数的映射关系,实现单位四元数、罗德里格转换模型与欧拉角大角度范围的转换。

Mapping Relationship between Unit Quaternion,Rodrigues Transform Model and Euler Angle

In the scene of large-angle attitude motion,the motion state usually adopts the unit quaternion or Rodrigues transformation model,but the conversion parameters are not intuitive and geometric,so it is necessary to study the mapping relationship between unit quaternion However,there is no one-to-one correspondence between the unit quaternion,the Rodrigues parameter and the Euler angle.Combining the characteristics of three conversion models and the singular problems of Euler angle and Rodrigues parameters,this paper deduces and analyzes the possible situations,establishes the mapping relationship between conversion parameters of each model,and realizes the conversion of unit quaternion,Rodrigues conversion model and Euler Angle in large Angle range.