This paper investigates the tracking problem of a smooth coordinate-invariant trajectory using dual quaternion algebra. The proposed architecture consists of a cascade structure in which the outer-loop MPC performs real-time smoothing of the manipulator's end-effector twist while an inner-loop kinematic controller ensures tracking of the instantaneous desired end-effector pose. Experiments on a $7$-DoF Franka Emika Panda robotic manipulator validate the proposed method demonstrating its application to constraint the robot twists, accelerations and jerks within prescribed bounds.

翻译：本文研究利用对偶四元数代数对光滑坐标不变轨迹的跟踪问题。所提出的架构采用级联结构，其中外环MPC实时平滑机械臂末端执行器的扭转，内环运动学控制器确保对瞬时期望末端执行器位姿的跟踪。在7自由度Franka Emika Panda机械臂上的实验验证了所提方法，证明其能将机器人扭转、加速度和加加速度约束在预设范围内。