Optimal path planning under defferent norms in continuous state spaces
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Bibliographic record
Abstract
Optimal path planning under full state and map knowledge is often accomplished using some variant of Dijkstra's algorithm, despite the fact that it represents the path domain as a discrete graph rather than as a continuous space. In this paper we compare Dijkstra's discrete algorithm with a variant (often called the fast marching method) which more accurately treats the underlying continuous space. Analytically, both generate a value function free of local minima, so that optimal path generation merely requires gradient descent. We also investigate the use of optimality metrics other than Euclidean distance for both algorithms. These different norms better represent optimal paths for some types of problems, as demonstrated by planning optimal collision-free paths for a multiple robot scenario. When considering approximations consistent with the underlying state space, our conclusion is that fast marching places fewer constraints upon grid connectivity, and that it achieves better accuracy than Dijkstra's discrete algorithm in many but not all cases
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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 | 0.000 | 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 | 0.001 | 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