Formation Control of Multi-agent Systems via Voronoi Tessellation and Kullback-Leibler Divergence
Why this work is in the frame
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Bibliographic record
Abstract
We present an algorithm to control the spatial distribution of kinematic multi-agent systems in two-dimensional workspace. Leveraging on the coverage control framework, we formulate the problem as a multi-objective optimization with a performance index composed of the area coverage metric and of the Kullback-Leibler (KL) divergence. The KL term drives the statistical spatial distribution of the agents to a desired, user-defined density in the workspace, whereas the coverage term drives the agents to a centroidal Voronoi configuration. The two terms are connected by setting the target distribution to be also the risk density in the area coverage term. The risk density for the coverage metric weights points in the area based on their relative importance. We prove that the proposed control law minimizes the multi-objective metric by driving the agents to a generalized centroidal Voronoi configuration along the trajectories generated by the gradient of the performance index, while minimizing the distance between the moments of the agents’ distribution and of the target distribution. The proposed control allows to use the target distribution to drive the system’s formation. Theoretical predictions are illustrated in simulation.
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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 | 0.001 | 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 | 0.001 |
| 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