Enhancing Knee Rehabilitation Exoskeleton Control via a Robust LMI-Based Strategy and by Considering State Constraints

This study introduces a robust control strategy to regulate the position of knee rehabilitation exoskeleton robot. A description of this particular robotic system and its nonlinear dynamic model are outlined first. The system faces challenges such as state constraints, external disruptions, and parameter uncertainties, all of which are meticulously addressed in the control design. Subsequently, we define the affine state-feedback controller and its design based on the LMI approach, aimed at ensuring the stabilization of the active exoskeleton robotic system at the knee joint level and hence its stability at the desired position. To achieve this, our proposed method utilizes a quadratic Lyapunov function and leverages mathematical tools such as the S-procedure Lemma, the Schur complement, the matrix inversion Lemma, and the Young inequality to derive finally two LMI conditions that guarantee the stability of the controlled knee exoskeleton system. Finally, the simulation studies validate the effectiveness of the proposed approach in the design of the LMI stability condition and hence the efficiency of the controller in the robust control of the knee exoskeleton robot.