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

2025-10-27

AI Summary

Tendon-driven concentric tube robots lack a general, comprehensive mechanical model. Method: This paper establishes the first scalable, unified dynamic modeling framework based on Cosserat rod theory—supporting arbitrary configurations of *n* concentric tubes, each actuated by *mᵢ* tendons, with independent torsional and axial deformation while sharing a common centerline curvature. The model integrates geometric constraints and mechanical equilibrium equations, accommodates complex tendon routing, and achieves high-fidelity 3D deformation prediction via experimental calibration and numerical solving. Results: On two- and three-tube prototypes, end-effector positioning error is <4% of total length; when transferred to diverse existing robot configurations, maximum deviation is ≈5%. These results demonstrate the model’s high accuracy, strong generalizability, and practical reusability in engineering applications.

Technology Category

• Intelligent Robots: Multimodal Perception & Sensor Fusion
• Machine Learning: Learning with Manifolds
• Planning, Routing, and Scheduling: Model-Based Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

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 snapping instability 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 $i = {1, ldots, n}$. 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.

Problem

• Develops a general mechanical model for tendon-actuated concentric tube robots
• Addresses limited degrees of freedom in tendon-driven continuum robot designs
• Solves snapping instability problems in conventional concentric tube robots

Innovation

• Cosserat rod-based framework for multi-tube modeling
• Shared centerline enforced for bending and elongation
• Validated with tip prediction errors under 4% length