Approximate Environment Decompositions for Robot Coverage Planning using Submodular Set Cover
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Bibliographic record
Abstract
In this paper, we investigate the problem of decomposing 2D environments for robot coverage path planning (CPP). CPP involves computing a cost-minimizing path so that the robot’s coverage or sensing tool visits all points in the environment. CPP is an NP-Hard problem, so existing approaches simplify the problem by decomposing the environment into the minimum number of sectors, i.e., sub-regions that can each be covered using a lawnmower path (along parallel straight-line paths) oriented at an angle. However, traditional methods either limit the coverage orientations to be axis-parallel (horizontal/vertical) or provide no guarantees on the number of sectors in the decomposition. We introduce an approach to decompose the environment into possibly overlapping rectangular sectors, with an approximation guarantee on the number of sectors computed for an environment. We do this by leveraging the submodular property of the sector coverage function, which enables us to formulate the decomposition problem as a submodular set cover (SSC) problem with wellknown approximation guarantees for the greedy algorithm. Our approach improves upon existing coverage planning methods, as verified on example maps of complex real-world environments.
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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 | 0.000 | 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