Deep-Koopman-ehnanced Kalman Filter for multibody systems

Deep-Koopman-ehnanced Kalman Filter for multibody systems | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Deep-Koopman-ehnanced Kalman Filter for multibody systems Paolo Boscariol, Domenico Dona', Dario Richiedei, Alberto Trevisani This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6566900/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 23 Sep, 2025 Read the published version in Multibody System Dynamics → Version 1 posted 9 You are reading this latest preprint version Abstract State estimation is a key requirement for the control of multibody systems, yet full state measurements are rarely available in practice. This necessitates the use of observers. While extended Kalman filters (eKFs) are widely used for nonlinear systems, their reliance on local linearizations often results in approximation errors. The Koopman operator framework offers an alternative by transforming nonlinear dynamics into a higher-dimensional linear representation, theoretically valid over the entire state space. In this work, we propose a Koopman-based observer that integrates a Kalman filter for state estimation in nonlinear multibody systems. The Koopman operator is approximated using a deep neural network trained on system trajectories. We evaluate the method in simulation on two representative systems: a cable-driven parallel robot and a planar parallel robot. Results show that our Koopman-based observer consistently achieves lower estimation errors than a conventional eKF, demonstrating its potential for accurate and robust state estimation in nonlinear control applications. Koopman Operator Kalman Filter Deep Learning Cable-Driven-Parallel-Robot Multibody Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 23 Sep, 2025 Read the published version in Multibody System Dynamics → Version 1 posted Editorial decision: Revision requested 11 Jul, 2025 Reviews received at journal 09 Jul, 2025 Reviewers agreed at journal 17 Jun, 2025 Reviews received at journal 06 Jun, 2025 Reviewers agreed at journal 12 May, 2025 Reviewers invited by journal 07 May, 2025 Editor assigned by journal 05 May, 2025 Submission checks completed at journal 01 May, 2025 First submitted to journal 30 Apr, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6566900","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":453275161,"identity":"afb6937c-6e45-43dc-bf4d-fc4f2f4434dd","order_by":0,"name":"Paolo Boscariol","email":"","orcid":"","institution":"University of Padua","correspondingAuthor":false,"prefix":"","firstName":"Paolo","middleName":"","lastName":"Boscariol","suffix":""},{"id":453275162,"identity":"32db66d1-8c33-4cec-9af1-bc24ed5ee506","order_by":1,"name":"Domenico Dona'","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA30lEQVRIiWNgGAWjYDCCAyDCAEQkAHEFAwMbiJtAvJYzMC349ByAs4CqGNsYoCbg0cJ3vDvxcUGBnRwDe/KxBz/nHc7jk27ewPDwB24tkmfObjaeYZBszMDzLN2wd9vhYjaZYwV4HWZwI3ebNI/BgcQGiRwzCd5thxPbJHLw+wWoZftvmBbJv3OI07KNGaZFmreBCC0gvwAdlmzMxvMsTVrmWHpiG9AvBxLScGvhO9678TPPHzs5fmCISb6psU6cP7t548MfNri1wAEbnCWBHFnEAQkS1Y+CUTAKRsGwBwCdWFCnvFDF1AAAAABJRU5ErkJggg==","orcid":"","institution":"University of Padua","correspondingAuthor":true,"prefix":"","firstName":"Domenico","middleName":"","lastName":"Dona'","suffix":""},{"id":453275163,"identity":"c142a746-a965-4854-b529-24c72afea865","order_by":2,"name":"Dario Richiedei","email":"","orcid":"","institution":"University of Padua","correspondingAuthor":false,"prefix":"","firstName":"Dario","middleName":"","lastName":"Richiedei","suffix":""},{"id":453275164,"identity":"39a443df-c57e-41bf-9364-c19f19fc9eec","order_by":3,"name":"Alberto Trevisani","email":"","orcid":"","institution":"University of Padua","correspondingAuthor":false,"prefix":"","firstName":"Alberto","middleName":"","lastName":"Trevisani","suffix":""}],"badges":[],"createdAt":"2025-04-30 17:08:09","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6566900/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6566900/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s11044-025-10108-7","type":"published","date":"2025-09-23T15:57:18+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":92431550,"identity":"9ab8ed62-9550-4d3c-adce-8cacf48f954a","added_by":"auto","created_at":"2025-09-29 16:09:54","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2222126,"visible":true,"origin":"","legend":"","description":"","filename":"MSDDeepKeKFforCDPRs.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6566900/v1_covered_55cd476f-e37c-468b-866d-188e78f5f48a.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Deep-Koopman-ehnanced Kalman Filter for multibody systems","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"multibody-system-dynamics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"mubo","sideBox":"Learn more about [Multibody System Dynamics](http://link.springer.com/journal/11044)","snPcode":"11044","submissionUrl":"https://submission.nature.com/new-submission/11044/3","title":"Multibody System Dynamics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Koopman Operator, Kalman Filter, Deep Learning, Cable-Driven-Parallel-Robot, Multibody","lastPublishedDoi":"10.21203/rs.3.rs-6566900/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6566900/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"State estimation is a key requirement for the control of multibody systems, yet full state measurements are rarely available in practice. 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