Formation Tracking of Nonholonomic Systems on the Special Euclidean Group under Fixed and Switching Topologies: An Affine Formation Strategy
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Bibliographic record
Abstract
An affine formation tracking problem of multiple mobile agents is studied in this work. Each agent in the system is modeled as an underactuated kinematic rigid body with nonholonomic constraints, maneuvering on the special Euclidean group $(SE(3))$. A controller is designed for each agent directly on the corresponding Lie algebra of $SE(3)$. Moreover, only local information accessible to each agent in its body-fixed frame is involved. The proposed control protocol can be implemented under both directed and undirected topologies. In addition, for directed graphs, an algorithm is proposed to realize the formation under switching topologies. Finally, numerical simulations are given to illustrate the efficiency and feasibility of the proposed results.
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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 | 0.001 | 0.002 |
| 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