Analysis and control of a kinematically redundant manipulator

Abstract

To study space applications of telerobotics, Goddard Space Flight Center (NASA) has recently built a testbed composed mainly of a pair of redundant slave arms having 7 degrees-of-freedom and a master hand controller system. This paper presents the mathematical developments required for the computer simulation study and motion control of the slave arms. First the slave arm forward kinematic transformation is derived using the Denavit-Hartenberg notation and is then reduced to its most simplified form suitable for real-time control applications. The vector cross product method is then applied to obtain the slave arm Jacobian matrix. Using the developed forward kinematic transformation and quaternion representation of the slave arm end-effector orientation, computer simulation is conducted to evaluate the efficiency of the Jacobian in converting joint velocities into Cartesian velocities and to investigate the accuracy of the Jacobian pseudo-inverse for various sampling times. In addition, the equivalence between Cartesian velocities and quaternion is also verified using computer simulation. Finally three control schemes, the joint-space adaptive control scheme, the Cartesian adaptive control scheme and the hybrid position/force control scheme are proposed for controlling the motion of the slave arm end-effector and some preliminary results of the proposed control schemes are presented and discussed.