On Integrating Friction Dynamics Into Cosserat Models for Tendon-Driven Continuum Manipulators
Bibliographic record
Abstract
This article presents a dynamic modeling framework for tendon-driven continuum manipulators, with a focus on cardiac catheters. Tendon compliance and tendon–sheath friction produce nonuniform tensions and motion-history-dependent dynamics (hysteresis), which, if neglected, degrade model fidelity and control. We develop a Cosserat-based formulation that integrates tendon compliance and a dynamic LuGre friction law into the governing nonlinear PDEs. This allows geometrically exact spatiotemporal computation of tendon–tension transmission without assuming initial friction states. Experiments on two clinical catheters demonstrate that incorporating friction dynamics reduces distal-tip error from$1.62\pm 1.01$mm (frictionless) to$0.99\pm 0.65$mm ($\approx 39\%$improvement), and achieves$2.31\pm 0.91$mm mean absolute error for out-of-plane spatial actuation of a four-tendon ICE catheter. Comparative analysis against a Coulomb-based capstan model highlights the significance of dynamic friction, which produces rate-dependent tension transmission and more accurate modeling of hysteresis effects.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".