A numerical SC approach for a teleoperated 7-DOF manipulator

To tackle the singularity problem, the SC (singularity-consistent) approach was introduced. It achieves very stable control at and around a singularity with feasible joint velocities and no directional error in the end-effector velocity. This approach is very suited for a direct manual teleoperation system because of its errorless character for the direction. Until now, it was applied for the teleoperation of a nonredundant manipulator. In this paper, the SC approach for a 7-DOF manipulator will be addressed. To derive the whole properties of the SC approach, analytical studies for both the adjoint and the determinant of the Jacobian are necessary. However, it is very difficult to realize this goal, since the kinematics of a 7-DOF manipulator is quite complicated. Therefore, here, we establish a method to apply the SC approach to a 7-DOF manipulator numerically without analyzing the kinematic properties. This method, though, cannot realize the whole properties of the SC approach but a stable control at and around the singularities is achieved which is the most important and demanded property of the SC approach. Moreover, this method can also be applied for any type of articulated manipulator if its Jacobian can be defined. The results of our approach have been confirmed by experiments with graphics model.