Task-Induced Symmetry and Reduction With Application to Needle Steering
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Bibliographic record
Abstract
Lie group symmetry in a mechanical system can lead to a dimensional reduction in its dynamical equations. Typically, the symmetries that one exploits are intrinsic to the mechanical system at hand, e.g. invariance of the system's Lagrangian to some group of motions. In the present work we consider symmetries that arise from an extrinsic control task, rather than the intrinsic structure of the configuration space, constraints, or system dynamics. We illustrate this technique with several examples. In the examples, the reduction enables us to design essentially global feedback controllers on the reduced systems. We also demonstrate how the proposed technique dovetails with Lagrangian reduction.We apply task-induced symmetry and reduction to a recently developed 6 DOF kinematic model of steerable bevel-tip needles. The resulting controllers cause the needle tip to track a subspace of its configuration space. We envision that the methodology presented in this paper will form the basis for a new planning and control framework for needle steering.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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 it