Bringing Nonlinear <inline-formula><tex-math notation="LaTeX">$\mathcal {H}_\infty$</tex-math> </inline-formula> Optimality to Robot Controllers

Abstract

This paper proposes a framework called nonlinear robust internal-loop compensator that enables us to bring nonlinear H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> optimality to robot controllers in a unified and simple way. Using the framework, a controller designed for the nominal plant can achieve additional robustness by simply adding PID-type auxiliary input to the original control law. Robust performance is guaranteed by the nonlinear 1-1 optimality and robust stability is guaranteed by proving the extended disturbance input-to-state stability. Moreover, the framework preserves the passivity property of the original controller. Finally, the performance bound can be predicted and leads to the gain tuning rules. By virtue of the tuning rules, the performance can be tuned using only a single variable. The proposed method was validated through the simulations and experiments.