A gauge-invariant formulation for constrained robotic systems using square-root factorization and unitary transformation
Bibliographic record
Abstract
A gauge-invariant formulation for deriving the equations of motion of constrained or unconstrained multi-body systems (MBS) in terms of (reduced) quasi-velocities is presented. We show that the square-root factorization of mass matrix and hence the quasi-velocities are not unique, rather they are related by unitary transformations. Subsequently, we show that a particular transformation leads to significant simplification of the dynamic modeling. In this formulation the equations of motion are decoupled from those of constrained force and each system has its own independent input (that is not attainable by other formulations). This allows the possibility to develop a simpler force control action that is totally independent from the motion control action. Moreover, the square-root of the mass matrix is used to transform disparate units into homogeneous units for all the reduced quasi-velocities making the formulation suitable for hybrid force/motion control of robots.
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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) | 0.000 | 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 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".