Allocation of Formation Control Tasks Using Delaunay Triangulation and Tetrahedralization
Bibliographic record
Abstract
This paper studies the task allocation for the formation control of multi-agent systems with directed graph topologies, where agents are required to form and preserve a specific geometric shape. A directed graph is said to be persistent if it is constraint-consistent and the underlying undirected graph is rigid. A formation of agents is constraint-consistent if every agent can satisfy all its distance constraints. In this context, based on Delaunay triangulation in 2-D and Delaunay tetrahedralization in 3-D space, we propose a novel task allocation algorithm applicable to distance-based formation topologies that guarantees constraint consistency of a desired formation of agents. Given the desired shape - a framework in space - the algorithm uses the Delaunay operations to build a network of rigid triangles/tetrahedrons representing the desired formation topology. The algorithm uses the shortest Euclidean distance-based task assignment to establish a desired topology in the form of directed triangulated or directed trilateral Laman graphs. The source agent of each edge is responsible for preserving the desired distance to the sink agent. The output of the proposed algorithm is a minimally persistent graph in 2-D or a minimally structurally persistent graph in 3-D. Examples are provided to demonstrate and verify the effectiveness of the proposed method.
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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 | 0.000 | 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 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".