Robust Torque-Computed Control for a Robot Manipulator With Unit Dual Quaternion

The six degrees-of-freedom (DoFs) nonsingular pose tracking is the prerequisite for the smooth task executions in many robot-assisted medical scenarios, such as laparoscopic surgery and sonography. This work develops a robust position/orientation tracking controller for a robot manipulator based on unit dual quaternion algebra. First, the dual quaternion-based robot manipulator dynamics are derived to accomplish the computationally minimalistic nonsingular end-effector motion representation. Then, an uncertainty and disturbance estimator-based controller is developed to estimate and compensate the system lumped uncertainty, which includes parameter uncertainty, external force/torque disturbance, and motor nonlinearity. The remote center of motion (RCM) constraints are formulated into the dual quaternion space to achieve the singularity free tool manipulation. The boundedness of the pose tracking error is analyzed via the Lyapunov function. Experiments of RCM operation with a seven DoFs Franka Emika robot manipulator are conducted for the performance validation, where the position root mean squared errors (RMSEs) are less than 0.002 m and the orientation RMSEs are less than 0.15°.