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

Abstract-- T endon-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 snapping instability associated with concentric tube robots. However, a complete and general mechanical model for these systems remains an open problem. 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. Minimally invasive surgical interventions have revolutionized modern medicine by reducing patient trauma, shortening recovery times, and improving procedural outcomes. However, accessing deep-seated anatomical targets, such as the spine, brain, or vasculature, poses significant challenges due to the confined, and deformable nature of biological tissues. While highly accurate in structured environments, traditional rigid-link robotic systems often lack the flexibility and compliance required to safely navigate these constrained anatomical spaces.