Evaluating the Normalized Coprime Factor-based Stability Metric for Rigid Systems

Abstract

Abstract The introduction of flexibility into rigid-body manipulator systems generally complicates the use of simple end-point feedback control. These flexibilities induce an unmodeled oscillation that cannot be necessarily compensated through end-point feedback control. The normalized coprime factor (NCF) based robustness metric ($\varepsilon_{max}$) has been well established in the realm of optimal control and can be applied to a rigid system with flexible modes in order to determine postures that will be robust to the flexibilities. This work illustrates that for rigid (double integrator) systems there is a fixed normalized coprime-factor robustness and, that for the special case of SISO systems, deviation from rigidity yields a similar change in NCF robustness.