A Comprehensive General Model of Tendon-Actuated Concentric Tube Robots with Multiple Tubes and Tendons

Tendon-actuated concentric tube mechanisms combine the advantages of tendon-driven continuum robots and concentric tube robots while addressing their respective limitations. They overcome the restricted degrees of freedom often seen in tendon-driven designs and mitigate issues such as restricted curvatures associated with concentric tube robots. However, a complete and general mechanical model for these systems remains an open problem. In this work, we propose a Cosserat rod-based framework for modeling the general case of $n$ concentric tubes, each actuated by $m_i$ tendons, where $i=\{1,\dots ,n\}$ . The model allows each tube to twist and elongate while enforcing a shared centerline for bending. We validate the proposed framework through experiments with two-tube and three-tube assemblies under various tendon routing configurations, achieving tip prediction errors < 4% of the robot's total length. We further demonstrate the model's generality by applying it to existing robots in the field, where maximum tip deviations remain around 5% of the total length. This model provides a foundation for accurate shape estimation and control of advanced tendon-actuated concentric tube robots.