Redundant Manipulators and Kinematic Singularities The Operational Space Approach

Abstract

The operational space formulation has provided a fundamental tool for the description of the dynamic behavior and control of manipulator end-effectors. In this paper, we present the extension of this formulation to redundant manipulator systems. The end-effector equations of motion in operational space of a redundant manipulator are established, and its behavior with respect to generalized joint forces is described. The end-effector is controlled by an operational space control system based on these equations of motion. Asymptotic stabilization of the mechanism is achieved by the use of dissipative joint forces selected from the null space of the Jacobian transpose matrix, consistent with the manipulator dynamics. This allows the elimination of any effects of these additional forces on the end-effector behavior and maintains its dynamic decoupling. We also present a new and systematic approach for dealing with the problems araising at kinematic singularities. The basic philosophy behind this approach is the treatment of the manipulator, at singular configuration, as a mechanism that is redundant with respect to the motion of the end-effector in the subspace of operational space orthogonal to the singular direction.