A Smooth Distributed Feedback for Formation Control of Unicycles
Bibliographic record
Abstract
This paper investigates a formation control problem in which a group of kinematic unicycles is made to converge to a desired formation with parallel heading angles and come to a stop. A control law is presented, which solves this problem for almost all initial conditions in any given compact set. The proposed control law is local and distributed, meaning that each unicycle is only required to sense its relative displacement measured in its own body frame, and the relative heading angle with respect to each of its neighbors. No communication between the unicycles is required. The sensing graph is assumed to be connected, undirected, and time invariant. The idea used to solve the above-mentioned formation control problem is to rigidly attach to the body frame of each unicycle an appropriate fixed offset vector. Stabilizing the desired formation amounts to achieving consensus of the endpoints of the offset vectors, and simultaneously synchronizing the unicycles' heading angles. A control law achieving this goal is constructed by combining a bounded translational consensus controller with an attitude synchronizer. As a special case, the proposed solution solves the full unicycle synchronization problem, in which the unicycle positions are made to converge to each other, while the unicycle headings are made to align.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 source (direct Gemma or distilled Codex), 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".