Robust tracking control of 6-DOF parallel electrical manipulator in Joint-Task space with fast friction estimation ⋆

This paper presents a robust tracking controller equipped with a fast friction estimator for a 6-DOF parallel electrical manipulator in the joint-task space. Parallel manipulator control scheme mainly stems from two frameworks: the task space control and the joint space control. The former requires the system states obtained via costly direct measurements or time-consuming forward kinematics. The latter’s performance is subject to the inaccurate dynamic model. To minimize their weaknesses, the joint-task space framework is constructed by transforming the dynamics on the task space into the joint space. With this transformation, the desired positional data are used to calculate the nominal value of dynamics. On the other hand, the friction property depends on the uncertain load condition due to the spiral drive way of the electrical cylinders. A fast friction estimator is then designed to estimate the uncertain friction fast and effectively. The robust control scheme is proposed based on the Lyapunov design method to guarantee a practical stability under uncertainties such as inertia, modeling errors, friction, and measurement errors. Experimental results are presented to show the effectiveness of the proposed scheme.