Nonlinear Dynamic Analysis and Friction Compensation of Tendon-Sheath Transmission System Based on ANCF

Tendon-driven continuum robots are widely used in medical and industrial applications due to their slender and nimble characteristics. It is helpful to control tendon-driven continuum robots more accurately to study the mechanism and laws of generating friction loss and the hysteresis phenomenon in tendon-sheath transmission systems (TSTS). This paper deduces a theoretical model of tension transmission and hysteresis in the TSTS. A dynamic model of the TSTS containing arbitrary Lagrange-Euler (ALE) nodes is proposed using the absolute nodal coordinate formulation (ANCF) to obtain the system configuration, total deformation angle, and to accurately compute the friction and hysteresis in conjunction with the theoretical model. A friction calculation method based on Hertzian contact theory is developed, and a non-fixed TSTS was used as the experimental object to verify the accuracy of the dynamic model of the TSTS. A feedforward compensation control strategy based on the model is constructed and experimentally validated. The root mean square error (RMSE) of the friction compared to the theoretical value obtained using the numerical calculation method was minimized to $0.097N$. The friction of the tendon system was compensated using a feedforward control strategy and the RMSE of the output relative to the desired value was obtained as $0.363N$. The results show that the dynamic model of the TSTS can accurately calculate the configurations and can be effectively combined with the theoretical model to realize model-predictive compensatory control.