Impedance Space Method: Time-Independent Parametric Ellipses for Robot Compliant Control

This paper proposes a novel 3D graphical representation for impedance control, called the impedance space, to foster the analysis of the dynamic behavior of robotic compliant controllers. The method overcomes limitations of existing 2D graphical approaches by incorporating mass, stiffness, and damping dynamics, and associates the impedance control parameters with linear transformations to plot a parametric 3D ellipse and its projections in 2D for a mass-spring-damper impedance under sinusoidal reference. Experimental evaluation demonstrates the effectiveness of the proposed representation for analysis of impedance control. The method applies to various compliant control topologies and can be extended to other model-based control approaches.