Robust Position Control of an Exoskeleton Robot for Knee Rehabilitation Utilizing an LMI-Based Affine State-Feedback Controller

Rehabilitation exoskeleton robots are designed to assist individuals with lower limb dysfunction. This work proposes a robust control strategy to regulate the position of a rehabilitation exoskeleton system at the knee joint level, employing an LMI-based linear state-feedback controller. The methodology involves the utilization of the nonlinear dynamics that incorporates elements such as frictions and uncertainties in the system parameters. Additionally, the expanded dynamics is formulated to encapsulate the difference between the nonlinear dynamic model and its linearized approximation. Subsequently, a Lyapunov function conducive to the context is selected to formulate the LMI conditions governing the feedback gain of the proposed control law via two distinct design approaches, thereby ensuring the stabilization of the regulated dynamics at the desired position. We validate the robustness of the controller through the introduction of external disturbances. Furthermore, a comparison between the two proposed control strategies is achieved. Finally, simulation results and performance indexes show that the formulated controller effectively controls the position of the knee exoskeleton robot under the effects of uncertainties and external disturbances.