This work focuses on pose-following, a variant of path-following in which the goal is to steer the system's position and attitude along a path with a moving frame attached to it. Full body motion control, while accounting for the additional freedom to self-regulate the progress along the path, is an appealing trade-off. Towards this end, we extend the well-established dual quaternion-based pose-tracking method into a pose-following control law. Specifically, we derive the equations of motion for the full pose error between the geometric reference and the rigid body in the form of a dual quaternion and dual twist. Subsequently, we formulate an almost globally asymptotically stable control law. The global attractivity of the presented approach is validated in a spatial example, while its benefits over pose-tracking are showcased through a planar case-study.

翻译：本文研究位姿跟随问题，这是路径跟随的一种变体，其目标是在路径上附着运动坐标系，引导系统沿路径调整位置与姿态。在实现对路径进展进行自主调节的额外自由度基础上，全身体运动控制展现了一种具有吸引力的折衷方案。为此，我们将成熟的对偶四元数位姿跟踪方法扩展为位姿跟随控制律。具体地，我们以对偶四元数和对偶旋量形式推导了几何参考体与刚体间全位姿误差的运动方程，进而构建了一个近乎全局渐近稳定的控制律。通过空间算例验证了所提方法的全局吸引性，并通过平面案例研究展示了其相对于位姿跟踪方法的优势。