Controller Design for a Force-Reflecting Teleoperator System With Kinematically Dissimilar Master and Slave

Abstract

The purpose of this paper is to develop a controller for a force-reflecting teleoperator system having kinematically dissimilar master and slave. The controller is a stiffness controller for both the master and the slave. A mathematical problem associated with representing orientations using Euler angles is described, and Euler parameters are proposed as a solution. The basic properties of Euler parameters are presented, specifically those pertaining to stiffness control. The stiffness controller for both the master and the slave is formulated using Euler parameters to represent orientation and a Liapunov stability proof is presented for the controller. The master portion of the control scheme is implemented on a six-degree-of-freedom master.

Derivation of three closed loop kinematic velocity models using normalized quaternion feedback for an autonomous redundant manipulator with application to inverse kinematics

“…The procedure described in steps (i) and (ii) results in the determination of J°as a function of J and [a, 8,7]T . [10], and in Appendix A it is shown that the singularities of this function are identical to those in step (ii). It is evident that modeling the manipulator system using eq.…”

“…Interestingly, 8o = 1 and 8v = 03×1 when the desired and actual orientations of the end effector are identical. 8, was proposed to be an appropriate representation of the orientation error for tracking control purposes in [7] and has been demonstrated on robotic hardware in [8,10]. A rigorous derivation of the orientation error leading to eq.…”

“…It was argued in [7] that the desired and actual normalized quaternions are an appropriate set of generalized coordinates to form the orientation error needed for control purposes. A mathematical model of the orientation error was derived in [7] which has served as the basis for i recent work on this problem in robotics [8,9,10]. Another approach to formulating the error between the desired and actual end effector orientations using orthogonal " rotation matrices or the Euler rotation angle and unit vector is suggested in [11].…”

Remote Manipulation Systems

“…Currently, many masters are provided by force reflecting, which significantly decreases task completion time (Jansen et al, 1992;Matsuhira et al, 1993;Yokokohji and Yoshikawa, 1994). The FM permits a master-slave regime to be achieved for such manipulators.…”

“…In MSSs, the slightest alteration in the construction of a slave arm demands a corresponding alteration in the construction of a master, or additional kinematic transformations (Jansen et al, 1992), because of control quality aggravation. In addition, it is common knowledge that a master-slave regime application for multi-joint redundant manipulators is impossible (Asano, 1984).…”