Using Euler Curves to Model Continuum Robots
Bibliographic record
Abstract
Due to the continuous and flexible nature of continuum robot backbones and the infinite number of parameters required to represent them in configuration space, modeling them accurately and in real-time is challenging. While the constant curvature assumption provides a simple alternative, it is limited in its capabilities as it cannot account for external tip forces. In cases where the backbone deviates from the constant curvature backbone, Euler curves are an interesting alternative for modeling continuum robots. In this paper, we show that a linear approximation of the backbone curvature is sufficiently accurate for estimating the shape of a robot subject to external tip forces. Next, we propose a numerical static model for tendon-driven continuum robots experiencing in-plane external tip forces. In this model, we use Euler arc splines to circumvent the limitations of standard numerical integration schemes required to calculate these curves. The system reduces to solving two nonlinear equations, allowing fast approximation of the backbone shape. The proposed model is validated experimentally on a robot prototype. Average tip error of 3.07% of the robot length is obtained for an average computation time of 0.51 ms.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".