Inverse Optimal Robust Adaptive Controller for Upper Limb Rehabilitation Exoskeletons With Inertia and Load Uncertainties

Abstract

We propose a robust adaptive controller for the safe and accurate trajectory tracking control of upper limb rehabilitation exoskeletons. The proposed controller can adapt to the inertia and load uncertainties, and compensate for their effects. The <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> robustness of the controller in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$l_2$</tex-math></inline-formula> perturbation/disturbance attenuation is realized by nonlinear robust control theory via inverse optimality. We mathematically prove the asymptotic stability and optimality of the controller by stabilizing a Lyapunov function and minimizing a meaningful cost function, respectively. We then demonstrate the performance of the controller with the simulations of two different exoskeleton control systems. The results show that the controller can identify and compensate for model uncertainties, and realize good tracking performance in the presence of perturbations and disturbances. These qualities are crucial to the reliability and safety of exoskeleton operations. In addition to rehabilitation exoskeletons, the proposed framework can also be applied to the control of other multibody robotic systems.