[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
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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)
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