Disturbance-Resilient Flatness-Based Control for End-Effector Rehabilitation Robotics

Robotic-assisted therapy is an increasingly vital approach for upper-limb rehabilitation, offering consistent, high-intensity training critical to neuroplastic recovery. However, current control strategies often lack robustness against uncertainties and external disturbances, limiting their efficacy in dynamic, real-world settings. Addressing this gap, this study proposes a novel control framework for the iTbot—a 2-DoF end-effector rehabilitation robot—by integrating differential flatness theory with a derivative-free Kalman filter (DFK). The objective is to achieve accurate and adaptive trajectory tracking in the presence of unmeasured dynamics and human-robot interaction forces. The control design reformulates the nonlinear joint-space dynamics into a 0-flat canonical form, enabling real-time computation of feedforward control laws based solely on flat outputs and their derivatives. Simultaneously, the DFK-based observer estimates external perturbations and unmeasured states without requiring derivative calculations, allowing for online disturbance compensation. Extensive simulations across nominal and disturbed conditions demonstrate that the proposed controller significantly outperforms conventional flatness-based control in tracking accuracy and robustness, as measured by reduced mean absolute error and standard deviation. Experimental validation under both simple and repetitive physiotherapy tasks confirms the system's ability to maintain sub-millimeter Cartesian accuracy and sub-degree joint errors even amid dynamic perturbations. These results underscore the controller’s effectiveness in enabling compliant, safe, and disturbance-resilient rehabilitation, paving the way for broader deployment of robotic therapy in clinical and home-based environments.