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

TL;DR

This paper introduces a comprehensive Cosserat rod-based model for tendon-actuated concentric tube robots with multiple tubes and tendons, enabling accurate shape estimation and control, validated through experiments with low tip prediction errors.

Contribution

It presents the first general mechanical model for multi-tube, multi-tendon concentric tube robots, addressing previous limitations and enabling better control and shape prediction.

Findings

Tip prediction errors less than 4% of total length in experiments.

Model successfully applied to existing robots with around 5% tip deviation.

Validated across various configurations with high accuracy.

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.