Static Modeling and Control of Redundant Manipulators

Abstract

This paper develops unified static models for control of a redundant manipulator. We introduce the Premultiplier Diagram to describe the static behavior of a redundant manipulator. This diagram provides insight into the algebra and physics related to redundant manipulators. We derive redundancy expressions for the joint displacement, joint torque and joint stiffness matrix. These redundancy expressions are composed of a particular (net) part and a homogeneous (null) part. Based on the orthogonality property between the net and the null components, we propose an extension of the stiffness control scheme for redundant manipulators. We also show how the decomposed and decoupled static behavior of redundant manipulators can be used to derive an optimal control strategy.