LMI-Based Robust Control Strategy for a Knee Rehabilitation Exoskeleton: Addressing State Constraints, Parameter Uncertainties and External Disturbances

Exoskeletons, or wearable robotics, are gaining popularity for assisting the elderly and individuals with limb disorders in regaining mobility. This study focuses on lower limb exoskeletons designed for physical movement assistance and rehabilitation. Our main objective is to introduce a robust control strategy tailored for a 1-DoF knee rehabilitation exoskeleton robot, with a focus on precise position control. Our approach utilizes an affine state-feedback controller to address challenges such as state constraints, parameter uncertainties, and external disturbances. We employ a quadratic Lyapunov function and utilize mathematical tools such as the Schur complement, Young’s inequality, matrix inversion lemma, and the S-procedure lemma to formulate Linear Matrix Inequality (LMI) stability conditions on the feedback gains of the adopted controller. These conditions are developed through two different design methods. They ensure robust stabilization of the 1-DoF knee exoskeleton robot, even in the presence of uncertainties and external disruptions. Furthermore, a comparison between these methods is conducted. Finally, simulation studies validate the efficiency of the proposed LMI stability conditions and demonstrate the controller’s effectiveness in achieving robust position control of the knee exoskeleton robot, providing valuable insights for the advancement of rehabilitation exoskeleton control strategies.