On Efficient Computation of Shortest Dubins Paths Through Three\n Consecutive Points
Bibliographic record
Abstract
In this paper, we address the problem of computing optimal paths through\nthree consecutive points for the curvature-constrained forward moving Dubins\nvehicle. Given initial and final configurations of the Dubins vehicle, and a\nmidpoint with an unconstrained heading, the objective is to compute the\nmidpoint heading that minimizes the total Dubins path length. We provide a\nnovel geometrical analysis of the optimal path, and establish new properties of\nthe optimal Dubins' path through three points. We then show how our method can\nbe used to quickly refine Dubins TSP tours produced using state-of-the-art\ntechniques. We also provide extensive simulation results showing the\nimprovement of the proposed approach in both runtime and solution quality over\nthe conventional method of uniform discretization of the heading at the\nmid-point, followed by solving the minimum Dubins path for each discrete\nheading.\n
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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) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.001 |
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".