Joint Space Stiffness and Damping for Cartesian and Null Space Impedance Control of Redundant Robotic Manipulators

Cartesian impedance control has been widely used in controlling robotic manipulators for manipulation and assembly tasks to compute the required joint torques and/or end-effector forces. Current congruence mapping of the Cartesian stiffness and damping matrices to joint spaces are not valid for general cases. In this paper, we derive from first principles, the general form of the mapping of the stiffness and damping matrices between Cartesian and joint space, which applies to all general cases. The new results show the coupling of Cartesian damping in the stiffness after mapping to the joint space, which is not found in the literature. By applying principle of vibration analysis and including the null space tasks, we can choose the stiffness and damping matrices in order to achieve prescribed dynamic response. Such analysis also enables us to gain a deeper understanding of the responses versus the parameters of robot manipulators; for example, certain elements only affect dynamic responses in specific directions.