Quasi-static modeling of a cable-driven continuum manipulator considering non-smooth cable-hole friction and experimental verification

In cable-driven continuum manipulator (CDCM) systems, the driving hysteresis effect due to non- smooth friction significantly affects motion control. In this paper, a quasi-static model of a CDCM considering non-smooth friction is proposed. The finite element method is used to discretize the backbone, neglecting the inertial effect in the driving process, and the nodal force vector for the backbone is obtained. Then, by considering the attenuation and non-smoothness of friction, the nodal force vector for the driving cables is obtained, and the tangent stiffness matrix of the nodal force vector is derived in detail. Subsequently, cable reeling/unreeling experiments were also conducted, and the hysteresis loops obtained were consistent with the theoretical model, thus verifying the validity of the non-smooth model. Finally, trajectory tracking simulations along spatial curves are conducted, and the influence of sliding friction and loading history on the evolution of driving force is studied.