Minimizing The Maximum Distance Traveled To Form Patterns With Systems\n of Mobile Robots
Bibliographic record
Abstract
In the pattern formation problem, robots in a system must self-coordinate to\nform a given pattern, regardless of translation, rotation, uniform-scaling,\nand/or reflection. In other words, a valid final configuration of the system is\na formation that is \\textit{similar} to the desired pattern. While there has\nbeen no shortage of research in the pattern formation problem under a variety\nof assumptions, models, and contexts, we consider the additional constraint\nthat the maximum distance traveled among all robots in the system is minimum.\nExisting work in pattern formation and closely related problems are typically\napplication-specific or not concerned with optimality (but rather feasibility).\nWe show the necessary conditions any optimal solution must satisfy and present\na solution for systems of three robots. Our work also led to an interesting\nresult that has applications beyond pattern formation. Namely, a metric for\ncomparing two triangles where a distance of $0$ indicates the triangles are\nsimilar, and $1$ indicates they are \\emph{fully dissimilar}.\n
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.005 | 0.003 |
| Research integrity | 0.000 | 0.001 |
| 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".