关于大角度范围内四元数与欧拉角转换的思考

Discussion on the Transformation Between Attitude Quaternion and Euler Angles in Large-angle Maneuver Scenario

在存在大角度姿态机动的场景中,航天飞行器通常采用基于姿态四元数的姿态运动模型,同时又多以欧拉角形式给定其期望姿态,因此研究四元数到欧拉角的转换关系十分必要。但是,姿态四元数与欧拉角之间并不存在一一对应的关系。以飞行器姿态为纽带,依据姿态四元数和欧拉角与飞行器姿态之间的内在关系,对各种可能出现的情形进行分析,在控制所对应的期望姿态的牵引下,确定出符合姿态控制利益的姿态四元数到欧拉角的转换关系。鉴于姿态四元数到欧拉角转换关系的复杂性,在飞行器进行大角度姿态机动控制时,建议采用基于四元数的姿态运动模型。

In large-angle attitude maneuver scenarios, quaternion-based attitude kinematic model is adopted widely to treat with spacecraft＇s attitude motion. Since the commanded attitude is specified in Euler-angle form, the transformation relationship from attitude quatemion to Euler angles has to be determined to serve to the Euler angles-based attitude control laws. However, the known fact is the mapping between attitude quatemion and Euler angles is very complex and no uniform expression has been formed to describe this mapping. In this paper, based on the inner relations between attitude quaternion, Euler angles and the spacecraft＇s attitude, and with analysis of each potential case, the proper transformation from attitude quaternion to Euler angles was specified. Due to the complexity of the transformation from attitude quatemion to Euler angles, the quatemion-based attitude motion model is recommended to treat the spacecraft＇s large-angle maneuver control.