Fast and Robust Inverse Kinematics of Serial Robots Using Halley’s Method
Why this work is in the frame
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Bibliographic record
Abstract
This paper proposes a novel numerical inverse kinematics algorithm called the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Quick Inverse Kinematics</i> or <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">QuIK</i> method. The QuIK method is a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">third-order</i> algorithm that uses both the first- and second-order derivative information to iteratively converge to a solution. Numerical inverse kinematics methods are readily implemented on any serial robot and do not rely on joint alignment. However, they typically are slower and less robust. The second-order derivative term allows the QuIK algorithm to converge more rapidly and more robustly than existing algorithms. A damped extension to the QuIK method is also proposed to increase reliability near singularities. The QuIK methods are tested in terms of evaluation speed, reliability, and singularity robustness against the Newton–Raphson method and several other modern algorithms. The proposed QuIK methods outperform all other tested algorithms in terms of speed and robustness, and have strong performance near singularities. The QuIK algorithms are proposed as faster and more robust “drop-in” replacements to the Newton–Raphson methods in inverse kinematics. C++ and MATLAB codebases are made available.
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Direct model labels (unvalidated)
Per-model category and study-design labels from the labeling rounds. They are machine output, unvalidated, and the disagreement between models ships as data. No study design here is MEDLINE-validated yet.
| Model arm | Categories | Study design | Confidence |
|---|---|---|---|
| gemma | no category Domain: not available · Genre: Methods About the Canadian research system: no · About a Canadian topic: no | Simulation or modeling | low |
| gpt | no category Domain: not available · Genre: Methods About the Canadian research system: no · About a Canadian topic: no | Simulation or modeling | low |
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