Dynamic Modelling and Optimal Sliding Mode Control of the Wearable Rehabilitative Bipedal Cable Robot with 7 Degrees of Freedom

Abstract

Although robot-assisted physiotherapy has gained increasing attention in recent years, the use of wearable rehabilitation robots for lower limbs has shown reduced efficiency due to additional equipment and motors located at the center of the joint, increasing complexity and load on disabled patients. This paper proposes a novel rehabilitation approach by eliminating motors and equipment from the center of joints and placing them on a fixed platform using cable-based power transmission. A proposed model of a 14 cable-driven bipedal robot with 7 degrees of freedom has been used to model a lower limb rehabilitation robot corresponding to it. The dynamic equations of the robot are derived using the Euler-Lagrange method. The sliding mode control technique is utilized to offer accurate control for tracking desired trajectories, ensuring smoothness despite disturbances, and reducing tracking errors. This approach is employed to help prevent patients from falling and support them in maintaining balance during rehabilitative exercises. To ensure that cables exert positive tension, the sliding mode controller was combined with quadratic programming optimization, minimizing path error while constraining the controller input torque to be non-negative. The performance of the proposed controller was assessed by considering several control gains resulting in K = 10 identified as the most effective one. The feasibility of this approach to rehabilitation is demonstrated by the numerical results in MATLAB simulation, which show that the RMSE amount of the right and left hip and thigh angles are 0.29, 0.37, 0.31, and 0.44, respectively which verified an improved rehabilitation process. Also, the correlation coefficient between the Adams and MATLAB simulation results for motor torque was found to be 0.98, indicating a high degree of correlation between the two simulation results.