Task-space PD Control of Robot Manipulators: Unified Analysis and Duality Property

Abstract

Task-space regulation of robots is classified into two basic approaches, namely transpose Jacobian regulation and inverse Jacobian regulation. This paper shows that, despite the distinct differences between inverse Jacobian and transpose Jacobian regulation problems, there is a unified approach for the analysis and design of the transpose Jacobian and inverse Jacobian PD controllers for non-redundant robots. Based on the unified analysis, we show that there is a fundamental property in the task-space regulation problem, namely the duality property. The results on the duality property show that the transpose Jacobian matrix can be replaced by the inverse Jacobian matrix and vice versa. The two basic transformations, the transpose Jacobian and the inverse Jacobian, are said to be dual. The task-space PD controllers are implemented on an industrial robot and experiment results are presented.