arXiv cs.MA· Jitian Liu, Subhrajit Bhattacharya·· 6 天前AI 评分12
平面机器人集群中用于空洞闭合的分布式调和协方差反馈
Distributed Harmonic-Covariance Feedback for Hole Closure in Planar Robot Swarms
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针对感知圆盘构成时变 Čech 复形的平面多智能体系统，研究者提出一种调和协方差反馈：用调和边信号定位空洞并转化为智能体力，通过正则化 Hodge Laplacian 的固定次数多项式在本地算子应用中分布式求值。闭环从每个安全初始状态都有唯一全局轨迹，离线有限计算可给出累积空洞面积的理性下界且收敛于该面积；15 秒数值演示中所有空洞在 9.9s 前闭合并保持闭合。
正文 · 原文
Abstract:We consider hole closure in a planar multi-agent system whose sensing disks form a time-varying Čech complex. We propose a harmonic-covariance feedback that uses harmonic edge signals to locate holes and converts those signals into agent forces. For distributed evaluation, we use a fixed-degree polynomial of the regularized Hodge Laplacian. This polynomial is evaluated through local operator applications. The closed loop has a unique global trajectory from every safe initial state. The model data and initial state are supplied with procedures for approximation to any requested accuracy with explicit error bounds. We assume that hole area is measurable and bounded, holes evolve continuously without splitting or merging, and only finitely many temporary new holes appear. Under these conditions, offline finite calculations produce rational lower bounds for the cumulative hole area on the time horizon without querying trajectory data. These bounds converge to that cumulative area, whether finite or infinite. If it is finite, holes close in the time-averaged sense: the average normalized hole area over every fixed-length time window tends to zero as time tends to infinity. In a 15-second numerical demo, all holes close by 9.9s and remain closed through the end.
| Subjects: | Robotics (cs.RO); Multiagent Systems (cs.MA); Systems and Control (eess.SY) |
| Cite as: | arXiv:2610.12637 [cs.RO] |
| (or arXiv:2610.12637v1 [cs.RO] for this version) | |
| https://doi.org/10.48550/arXiv.2610.12637 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Jitian Liu [view email]
[v1]
Thu, 8 Oct 2026 18:59:52 UTC (218 KB)
来源：arXiv cs.MA · arxiv.org