On Integrating Friction Dynamics Into Cosserat Models for Tendon-Driven Continuum Manipulators

This article presents a dynamic modeling framework for tendon-driven continuum manipulators, with a focus on cardiac catheters. Tendon compliance and tendon–sheath friction produce nonuniform tensions and motion-history-dependent dynamics (hysteresis), which, if neglected, degrade model fidelity and control. We develop a Cosserat-based formulation that integrates tendon compliance and a dynamic LuGre friction law into the governing nonlinear PDEs. This allows geometrically exact spatiotemporal computation of tendon–tension transmission without assuming initial friction states. Experiments on two clinical catheters demonstrate that incorporating friction dynamics reduces distal-tip error from$1.62\pm 1.01$mm (frictionless) to$0.99\pm 0.65$mm ($\approx 39\%$improvement), and achieves$2.31\pm 0.91$mm mean absolute error for out-of-plane spatial actuation of a four-tendon ICE catheter. Comparative analysis against a Coulomb-based capstan model highlights the significance of dynamic friction, which produces rate-dependent tension transmission and more accurate modeling of hysteresis effects.