Simultaneous Calibration of Multicoordinates for a Dual-Robot System by Solving the AXB = YCZ Problem
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Bibliographic record
Abstract
Multirobot systems have shown great potential in dealing with complicated tasks that are impossible for a single robot to achieve. One essential problem encountered in cooperatively working of the multirobot systems is the unknown initial transformation relationships from hand to eye, base to base, and flange to tool. In this article, the problem of multicoordinates calibration for a dual-robot system is formulated to a matrix equation AXB = YCZ. A novel approach for simultaneously solving the unknowns in equation AXB = YCZ is proposed, which is composed of a closed form method based on the Kronecker product and an iterative method which converts the calculation of a nonlinear problem to an optimization problem of a strictly convex function. The closed form method is used to quickly obtain an initial estimation for the iterative method to improve the efficiency and accuracy of iteration. In addition, a series of conditions on the solvability of the problem are proposed to guide the operators to select appropriate robot attitudes during the calibration process. To show the feasibility and superiority of the proposed iterative method, two other calibration methods are chosen to be compared to the proposed method through simulation and practical experiments. The comparison results verify the superiority of the proposed method in accuracy, efficiency, and stability.
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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