用四元数设计无奇异的机械臂末端姿态控制滑模变量
Quaternion Sliding Variables in Manipulator Control
- 基于四元数构建全局收敛的滑模变量，避免姿态控制中的奇异性
- 相比欧拉角等表示法，支持全工作空间运动且无缠绕问题
- 适合需要高精度姿态控制的机器人系统，如航天机械臂
本文提出两种基于四元数的滑模变量，用于控制机械臂末端执行器的姿态。这两种滑模变量均无奇异性，能实现全局指数收敛的误差动态，并在反馈控制中不出现缠绕现象。滑模变量的选择取决于末端执行器角速度在局部坐标系还是全局坐标系下表示，仅与使用方便性有关。采用四元数表示可使末端执行器在完整工作包络内运动，而其他表示方式（如欧拉角）会引入特定表示的奇异性。此外，所提出的稳定性结果为全局稳定，而非旋转矩阵表示时常达到的近似全局稳定。
原文摘要 · Abstract (English)
We present two quaternion-based sliding variables for controlling the orientation of a manipulator's end-effector. Both sliding variables are free of singularities and represent global exponentially convergent error dynamics that do not exhibit unwinding when used in feedback. The choice of sliding variable is dictated by whether the end-effector's angular velocity vector is expressed in a local or global frame, and is a matter of convenience. Using quaternions allows the end-effector to move in its full operational envelope, which is not possible with other representations, e.g., Euler angles, that introduce representation-specific singularities. Further, the presented stability results are global rather than almost global, where the latter is often the best one can achieve when using rotation matrices to represent orientation.
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