Quaternions approach to solve the kinematic equation of rotation, A/sub a/A/sub x/=A/sub x/A/sub b/, of a sensor-mounted robotic manipulator
Why this work is in the frame
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Bibliographic record
Abstract
The problem of finding the relative orientation between the reference frames of a line-mounted sensor and the link is formulated as a kinematic equation of the form A/sub a/A/sub x/=A/sub x/A/sub b/, which has to be solved for the rotational transformation matrix A/sub x/ given the transformations A/sub a/ and A/sub b/. This equation can be transformed to its equivalent form in terms of quaternion and then simplified to a well-structured linear system of equations of the form Bx=0. Since B is rank-deficient, the solution is not unique. The generalized-inverse method using singular-value decomposition (SVD) is applied. Although the solution is reached using the analysis of SVD, the SVD is derived symbolically; therefore, the actual implementation of SVD is not required. A method for obtaining a unique solution is proposed where a system of nonlinear equations is solved using Newton-Raphson iteration. The iteration is simplified by a dimension-reduction technique that provides a set of closed-form formulas for solving the resulting linear system of equations.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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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) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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