发表机构
IIT Madras（印度理工学院马德拉斯分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对三维异构多智能体到达-规避博弈中基数匹配导致的几何蔓延问题，提出基数优先加权顺序匹配方法，利用拦截值加权，提升捕获数和拦截高度，降低轨迹曲折度。
AI 中文摘要
我们研究了三维异构多智能体到达-规避博弈中的分配质量，并识别出在几何结构化场景中仅基于基数的匹配反复出现的一种失败模式，我们将其称为“几何蔓延”。在这些情况下，存在多个最大基数分配，但其中一些会导致空间上不连贯的配对和低效的追击轨迹。基于Yan等人（2022）的规避空间框架，我们引入了一种基数优先的加权顺序匹配方法，其中Hamilton-Jacobi-Isaacs拦截值z_I(s,j)被用作次要分配权重。每个顺序阶段通过最小费用最大流后端求解，而无加权基线使用相同的求解器但移除权重项。我们在一个确定性的35场景基准（7个家族和5种初始化变体）上评估了两种方法，在两种机制下：诊断性静态未匹配设置和具有目标导向未匹配逃避者的混合鞍点设置。在该基准上，加权方法解决了诊断机制中导致无加权基线重复超时的15个几何压力测试实例中的13个，并在混合机制下将平均捕获数从3.20提高到3.91（增加22%），平均拦截高度从3.87提高到5.36（增加40%）。我们还报告了较低的路径曲折度和较低的角努力代理值，表明在该一阶仿真模型中追击轨迹更平滑。我们在https://this https URL上发布了仿真器和基准套件，以支持对三维到达-规避博弈分配策略的可重复评估。
英文摘要
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{https://github.com/Prajwal-Vijay/geometric-coherence-weighted-matching}{github.com/Prajwal-Vijay/geometric-coherence-weighted-matching} to support reproducible evaluation of assignment strategies for 3D reach-avoid games.
CommentsICRA 2026 Workshop on Multi-Agent Robotic Systems: Real-World Collaboration and Interaction
