Asymptotically Optimal Solutions for 3D Reach-Avoid Games with Exclusion Zones Using Informed-Expansive-Spaces-Tree
Bibliographic record
Abstract
This paper addresses the reach-avoid game in 3D, where a pursuer attempts to capture an evader while avoiding danger zones, and the evader seeks to reach a target without being captured. Traditional control-based methods struggle with complex scenarios or lack the solution’s guarantees. This paper casts the reach-avoid problem as a planning task, enabling probabilistic complete and asymptotically optimal open-loop solutions assuming the worst-case of the evader in more complex scenarios (i.e., optimal control). To solve this planning problem, this paper proposes the Informed-Expansive-Spaces-Tree (Informed-EST) to restrict the search space after an initial path is found, reducing computational overhead compared with other sampling-based planning algorithms while maintaining the asymptotically optimal guarantees. Evaluations against Rapidly-exploring random tree (RRT), EST and RRT<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">*</sup> in reach-avoid scenarios with static and moving exclusion zones highlight improvements in computational efficiency and performance. Additionally, critical limitations of RRT<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">*</sup> in reach-avoid scenarios are identified and discussed.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| 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 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".