On Mapping Stiffness and Damping in Robotic Impedance Control: a Spatial Validation of Coupling

Abstract

In order to calculate the necessary joint torques and end-effector forces in accordance with a desired dynamic behavior for assembly and manipulation tasks in the field of robotics, robotic impedance control has been extensively employed. Current complete congruent mapping equations have not been validated through actual robotic manipulators in impedance control tasks. In this paper, we show and validate from fundamental principles, with the use of a 6 DoF robotic manipulator, the transformation equations of the stiffness and damping matrices from Cartesian to joint space without losing generality. Our findings highlight the significance of the Cartesian damping coupling term, which is typically absent from the existent robotics literature, in the stiffness matrices after mapping them to the joint space.