Dynamic Modeling and Validation of a Notched Hollow Continuum Robot Using Cosserat Rod Theory

This article presents a novel modeling approach for a notched hollow continuum robot using Cosserat rod theory. Our modeling framework comprehensively addresses both the static and dynamic aspects of the notched continuum robot, leveraging the advantages of a cable-driven mechanism. By integrating the Cosserat rod theory with the tendon kinematic and dynamic of a cable-driven continuum robot, we derive a complete mathematical model encountering key design parameters such as the second moment of area and cross-sectional area. Additionally, we propose a nonlinear hysteresis compensator to address the friction of the tendon, tendon viscoelasticity, and the nonlinear geometric properties of the notched continuum robot. Formulated as partial differential equations (PDEs) with respect to time and arc-length, our modeling approach accurately captures the intricate static and dynamic behaviors of the robot. To effectively solve these PDEs, we utilize the backward differentiation formula-${\bm{\alpha }}$ technique. Experimental validation was conducted on small-scale notched continuum robots under various external loads, demonstrating the accuracy of the proposed approach. Furthermore, the implementation of tendon force control on the notched continuum robot validates the robustness of our modeling and control approach, even in the presence of external loads.