The Extended Kalman Filter for Constraint Enforcement in the Forward Dynamics of Multibody Systems

The Extended Kalman Filter for Constraint Enforcement in the Forward Dynamics of 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 The Extended Kalman Filter for Constraint Enforcement in the Forward Dynamics of Multibody Systems Dario Richiedei, Iacopo Tamellin, Alberto Trevisani This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6589073/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The forward dynamics of multibody systems is widely exploited in engineering applications to simulate the behavior of complex mechanical systems undergoing kinematic constraints. It relies on the integration of the equations of motion of the system. However, the numerical integration error causes the simulation to violate the position and velocity kinematic constraint. In this paper a novel Constraint Enforcement method based on the application of the prediction-correction scheme of the Extended Kalman Filter is proposed and it will be denoted (CE-EKF). First, the equations of motion of the system are integrated to provide thesimulation output estimate, i.e., the prediction. Then, the Kalman Filter computes the correction to ensure that the corrected simulation output is consistent with respect to the constraint equations. Besides proposing such the novel theoretical framework for the application of the Extended Kalman Filter in the suppression of constraints violation. In this work the numerical application of the method is provided for a redundant mechanism. The provided results highlight the effectiveness of the proposed method in comparison with other methodsproposed in the literature. multibody dynamics forward dynamics constraint violation constraint enforcement kalman filter Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted 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. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-6589073","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":454234961,"identity":"f69fa7d6-18c3-4ef1-bc28-a851573db584","order_by":0,"name":"Dario Richiedei","email":"","orcid":"","institution":"University of Padua","correspondingAuthor":false,"prefix":"","firstName":"Dario","middleName":"","lastName":"Richiedei","suffix":""},{"id":454234962,"identity":"a55580ab-2574-415c-a9b9-07adb62d36c9","order_by":1,"name":"Iacopo Tamellin","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA7ElEQVRIiWNgGAWjYBACNiQ244EHBgxyQLoByJEgqAWs4kCCAYMxTAtuPahaGBgSG5BFsAE+9sMPHxdUMNTxTzt84EBCwZ30Dbeb26QrGCzqcDqMJ83YeMYZoDtupyUAHfYsd8Odg22SZ/A4jI0hh02atw3ojNs5BkAth3M33EhsNmzAp4X/DUSL/O38DyAt6QYEtUhAbTG4nQMKscMJQC2ND/FreQbyi4TkxttpYIcZzgRrMZCQbMChRb4/GRRiNvxyt5MfPvjw57A83430BwcbKur4cdkCAsxYIsEAnwawllEwCkbBKBgFeAAAUkJT4kpHrJcAAAAASUVORK5CYII=","orcid":"","institution":"University of Verona","correspondingAuthor":true,"prefix":"","firstName":"Iacopo","middleName":"","lastName":"Tamellin","suffix":""},{"id":454234963,"identity":"11736f23-0a9d-461f-bacc-72ce75b1c965","order_by":2,"name":"Alberto Trevisani","email":"","orcid":"","institution":"University of Padua","correspondingAuthor":false,"prefix":"","firstName":"Alberto","middleName":"","lastName":"Trevisani","suffix":""}],"badges":[],"createdAt":"2025-05-04 15:08:14","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6589073/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6589073/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":100594697,"identity":"c7b10765-4613-46dc-89ff-8ba1b1d6a1a7","added_by":"auto","created_at":"2026-01-19 13:43:57","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1371509,"visible":true,"origin":"","legend":"","description":"","filename":"EKFConstraintenhancement.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6589073/v1_covered_b9b9b7de-9a46-4b6f-8409-ec65f337134f.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"The Extended Kalman Filter for Constraint Enforcement in the Forward Dynamics of Multibody Systems","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"multibody dynamics, forward dynamics, constraint violation, constraint enforcement, kalman filter","lastPublishedDoi":"10.21203/rs.3.rs-6589073/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6589073/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"The forward dynamics of multibody systems is widely exploited in engineering applications to simulate the behavior of complex mechanical systems undergoing kinematic constraints. 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