Abstract
© The Author(s), under exclusive licence to Shiraz University 2025.This paper explores the field of robotic rehabilitation exercises using a spherical parallel robot, with an emphasis on assistive control strategy which has a wide range of applications in ankle rehabilitation robotics. While early in the rehabilitation process, passive control is more common, assistive control eventually takes over as the patient’s condition improves. Precise feedback of force and torque generated by the patient is essential for the implementation of assistive control topology. Force/torque sensors and electromyography sensors are just a few of the sensors that help monitor this interaction between the robot and human. But problems like sensor compatibility, positioning, dependability, and signal processing complexity appear. To circumvent the requirement for force and torque sensors, this study proposes a robust motion controller and a sensor-less strategy that employs a nonlinear observer utilizing the dynamics of the robot for assistive ankle rehabilitation applications. By utilizing the sliding mode controller, and the nonlinear observer, the paper improves the robot’s position control and the accuracy of active torque estimations in the presence of uncertainties arising from dynamic modelling of the robot and human–robot interaction. This interaction includes the foot’s mass and the hysteresis loop-shaped resistance torque of the ankle applied to the robot’s moving platform. Stability analysis of the whole system including the controller and the observer is conducted to demonstrate the robustness of the proposed control framework in the presence of modelling uncertainties. Co-simulations have been conducted to demonstrate the efficiency of the observer-based sliding mode controller in accurately estimation of the active torque and tracking the predefined trajectories in the presence of uncertainties.