A Fast Geometric Framework for Dynamic Cosserat Rods with Discrete Actuated Joints
Bibliographic record
Abstract
Current dynamical models of Cosserat rods often use the finite element method limited by computational efficiency or the finite difference method in a Cartesian framework with a compromise to accuracy. We employ the finite difference method in a geometric framework to develop solutions that are both computationally efficient and accurate. A numerical study is conducted on various backward-differentiation discretization and Runge-Kutta-Munthe-Kaas integration schemes, focusing on their accuracy and computational efficiency. Case studies are conducted on a single-degree-of-freedom joint actuated Cosserat rod to mitigate additional sources of undesired error from the numerical analysis, e.g. multi-body interactions, moving base dynamics, etc. The proposed geometric integrators are demonstrated to improve solution accuracy compared to the published finite difference models. The presented solution is parameterization-free and also computationally efficient with the potential for use in real-time applications, e.g., model-based control of soft manipulators.
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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) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 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".