Scale-free coordinates for multi-robot systems with bearing-only sensors
Bibliographic record
Abstract
We propose scale-free coordinates as an alternative coordinate system for multi-robot systems with large robot populations. Scale-free coordinates allow each robot to know, up to scaling, the relative position and orientation of other robots in the network. We consider a weak sensing model where each robot is only capable of measuring the angle, relative to its own heading, to each of its neighbors. Our contributions are three-fold. First, we derive a precise mathematical characterization of the computability of scale-free coordinates using only bearing measurements, and we describe an efficient algorithm to obtain them. Second, through simulations we show that even in graphs with low average vertex degree, most robots are able to compute the scale-free coordinates of their neighbors using only two-hop bearing measurements. Finally, we present an algorithm to compute scale-free coordinates that is tailored to low-cost systems with limited communication bandwidth and sensor resolution. Our algorithm mitigates the impact of sensing errors through a simple yet effective noise sensitivity model. We validate our implementation with real-world robot experiments using static accuracy measurements and a simple scale-free motion controller.
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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) | 0.000 | 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 | 0.001 | 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".