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[Submitted on 19 Sep 2026] Title:Geometric Coherence via Weighted Matching for 3D Heterogeneous Multi-Agent Reach-Avoid Games View a PDF of the paper titled Geometric Coherence via Weighted Matching for 3D Heterogeneous Multi-Agent Reach-Avoid Games, by Prajwal Vijay View PDF HTML (experimental) Abstract:We study assignment quality in 3D heterogeneous multi-agent reach-avoid games and identify a recurring failure mode of cardinality-only matching in geometrically structured scenarios, which we term \emph{Geometric Sprawl}. In these cases, multiple maximum-cardinality assignments are available, but some induce spatially incoherent pairings and inefficient pursuit trajectories. Building on the evasion-space framework of Yan et al.~\cite{yan2022}, we introduce a cardinality-first weighted sequential matching method in which the Hamilton--Jacobi--Isaacs interception value $z_I(s,j)$ is used as a secondary assignment weight. Each sequential stage is solved with a min-cost max-flow backend, while the unweighted baseline uses the same solver with the weight term removed. We evaluate both methods on a deterministic 35-scenario benchmark (7 families & 5 initialization variants) under two regimes: a diagnostic stationary-unmatched setting and a hybrid saddle-point setting with goal-directed unmatched evaders. On this benchmark, the weighted method resolves 13 of 15 geometric stress-test instances that cause repeated timeouts for the unweighted baseline in the diagnostic regime, and under the hybrid regime improves mean captures from $3.20$ to $3.91$ (22\% increase) and mean interception height from $3.87$ to $5.36$ (40\% increase). We also report lower path tortuosity and lower angular-effort proxy values, suggesting smoother pursuit trajectories in this first-order simulation model. We release the simulator and benchmark suite at \href{this https URL}{this http URL} to support reproducible evaluation of assignment strategies for 3D reach-avoid games. Comments: ICRA 2026 Workshop on Multi-Agent Robotic Systems: Real-World Collaboration and Interaction Subjects: Robotics (cs.RO) Cite as: arXiv:2610.06882 [cs.RO] (or arXiv:2610.06882v1 [cs.RO] for this version) https://doi.org/10.48550/arXiv.2610.06882 arXiv-issued DOI via DataCite Submission history From: Prajwal Vijay [view email] [v1] Sat, 19 Sep 2026 10:05:37 UTC (610 KB) Full-text links: Access Paper: View a PDF of the paper titled Geometric Coherence via Weighted Matching for 3D Heterogeneous Multi-Agent Reach-Avoid Games, by Prajwal Vijay View PDF HTML (experimental) TeX Source view license Additional Features Audio Summary Current browse context: cs.RO new | recent | 2026-10 Change to browse by: cs References & Citations NASA ADS Google Scholar Semantic Scholar Loading... Data provided by: Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)