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[Submitted on 8 Oct 2026] Title:Distributed Harmonic-Covariance Feedback for Hole Closure in Planar Robot Swarms View a PDF of the paper titled Distributed Harmonic-Covariance Feedback for Hole Closure in Planar Robot Swarms, by Jitian Liu and 1 other authors View PDF HTML (experimental) 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) Full-text links: Access Paper: View a PDF of the paper titled Distributed Harmonic-Covariance Feedback for Hole Closure in Planar Robot Swarms, by Jitian Liu and 1 other authors 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 cs.MA cs.SY eess eess.SY 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?)