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

Pejman Kheradmand, Behnam Moradkhani, Raghavasimhan Sankaranarayanan, Kent K. Yamamoto, Tanner J. Zachem, Patrick J. Codd, Yash Chitalia, Pierre E. Dupont

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.

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

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 concentric tubes, each actuated by tendons, where . 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 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 of the total length. This model provides a foundation for accurate shape estimation and control of advanced tendon-actuated concentric tube robots.

Paper Structure

This paper contains 20 sections, 65 equations, 11 figures.

Table of Contents

  1. Introduction
  2. Mechanics-based Model
  3. Tube Kinematics, Relative Twist and Variable Dilation
  4. Compatibility Constraints
  5. Equilibrium Equations
  6. Constitutive Model
  7. Distributed Forces and Moments
  8. Model Equations
  9. Numerical solution
  10. Experimental Model Validation
  11. Two-Tube Configuration
  12. Helical Tendon Routing
  13. Hysteresis Effects
  14. Three-Tube Configuration
  15. Evaluation of Tendon Assignment Methods
  16. ...and 5 more sections

Figures (11)

  • Figure 1: Various examples of tendon-actuated concentric tube (TACT) robot architectures: (a) Tendon-Assisted Magnetically Steered (TAMS) robotic stylet for brachytherapykheradmand2024tams, (b) Tendon-actuated Concentric Tube Endonasal Robot (TACTER) yamamoto2025tacter, (c) Tendon-actuated concentric tube robot for lateral and ventral spinal cord stimulationmoradkhani2025exonav, and (d) Telescoping two-tube tendon-actuated catheter for transseptal navigationchitalia2023modeling.
  • Figure 2: Variable twist and elongation in concentric tubes. (a) A single tube undergoing axial elongation and twist, resulting in a local material frame that dilates and rotates along the arc length. (b) Cross-section of nested concentric tubes illustrating the relative twist ($\theta_i$) and dilation ($e_i$) of an inner tube ($i_{th}$ tube) with respect to the outermost tube, shown through the misalignment of local material frames.
  • Figure 3: CAD model of the experimental setup used for model validation. (a) Overall system configuration, including the tendon pulling unit and tube assembly. (b) Close-up view of the disks mounted on each tube (outer, middle, and inner), each featuring optical markers on their sides for shape tracking.
  • Figure 4: Comparison between model-predicted robot shape and experimental results for the two-tube configuration. Black circles represent the midpoints of tracked marker pairs. The blue tube corresponds to the outer tube and the red tube to the inner tube. (a) Tendons routed in the same direction ($0\degree$ angle between tendons path), causing both tubes to bend along the global Y-axis, (b) tendon paths are oriented at a $90\degree$ angle to each other, resulting in orthogonal bending, (c) tendons are routed $180\degree$ apart, producing opposing bending directions.
  • Figure 5: Comparison between model-predicted and experimentally observed shape for a two-tube configuration with helical tendon routing. (a) Isometric view, (b) top view.
  • ...and 6 more figures