The backstepping double integral terminal sliding mode control of upper limb rehabilitation robot based on friction compensation

During repeated rehabilitation training, the friction between the omnidirectional wheel and the desktop can lead to control response delays, causing deviations in the training trajectory. To enhance the training trajectory accuracy of rehabilitation robots in the presence of friction interference, a backstepping double-integral terminal sliding mode controller (BDITSMC) based on an extended state observer is proposed. An integral term was introduced into the terminal sliding surface to eliminate the arrival phase and minimize the estimation error. Meanwhile, the switching frequency in the sliding mode phase was reduced, thereby addressing the “complexity explosion” problem in inversion design. This method provides a solution to improve the trajectory tracking accuracy of upper limb rehabilitation robot controllers. In the rehabilitation trajectory tracking control, quantified by the Mean Absolute Error (MAE), the error of the backstepping integral non-singular terminal sliding mode control (BINTSMC) method is 0.0039, while the BDITSMC proposed in this paper reduces this value to 0.003, representing a 23.1% improvement.