Adaptive Lqr-based Control of 3 Dof Spherical Articulated Robotic Manipulator

Adaptive Lqr-based Control of 3 Dof Spherical Articulated Robotic Manipulator | 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 Adaptive Lqr-based Control of 3 Dof Spherical Articulated Robotic Manipulator K Suryanarayana K Suryanarayana This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3899125/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 In this work, an Adaptive Linear Quadratic Regulator (LQR) is proposed for the tracking control of a 3 DOF articulated robotic manipulator. The main objective of this work is to drive the robotic manipulator to its equilibrium point from any initial position of the end effector of a robotic manipulator in an adaptive way even if the system dynamics consist of modelling uncertainties. The conventional LQR is able to provide a good measure of robustness against disturbances and achieve good tracking performance. However, it will give degraded tracking performance in case of the presence of model uncertainties. Therefore LQR tracking performance is enhanced by using a Model Reference Adaptive Controller (MRAC) in the literature for enabling a 2 DOF system to achieve good tracking against modelling uncertainties. But it has not been applied for a 3 DOF system till date. Therefore in this work, it is proposed to be applied for such a system for the first time to realize an adaptive control. The forward and inverse kinematics level equations are formulated using an indirect form of the Denavit Hartenberg (DH) convention. The dynamics of robotic manipulator are derived using the Euler-Lagrange formulation. The dynamics of manipulator with the LQR control are considered to be the reference dynamics for the MRAC control and the modelling uncertainty will be added to the system dynamics to test its performance. The MRAC augmented LQR provides faster convergence with improved stability against modelling uncertainties. MRAC Adaptive LQR command tracking spherical articulated manipulator 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. 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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-3899125","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":269621788,"identity":"11336e75-8029-4672-8698-e369eddc72c5","order_by":0,"name":"K Suryanarayana K Suryanarayana","email":"data:image/png;base64,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","orcid":"","institution":"","correspondingAuthor":true,"prefix":"","firstName":"K","middleName":"Suryanarayana K","lastName":"Suryanarayana","suffix":""}],"badges":[],"createdAt":"2024-01-26 05:59:15","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3899125/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3899125/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":50356012,"identity":"b7995620-c02a-49bf-ab4e-da9d57c1b489","added_by":"auto","created_at":"2024-01-30 09:09:21","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":320989,"visible":true,"origin":"","legend":"","description":"","filename":"robot.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3899125/v1_covered_4aa9bbb2-ed9e-43e4-a1be-461279abdfe6.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eAdaptive Lqr-based Control of 3 Dof Spherical Articulated Robotic Manipulator\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"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":"MRAC, Adaptive LQR, command tracking, spherical articulated manipulator","lastPublishedDoi":"10.21203/rs.3.rs-3899125/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3899125/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn this work, an Adaptive Linear Quadratic Regulator (LQR) is proposed for the tracking control of a 3 DOF articulated robotic manipulator. The main objective of this work is to drive the robotic manipulator to its equilibrium point from any initial position of the end effector of a robotic manipulator in an adaptive way even if the system dynamics consist of modelling uncertainties. The conventional LQR is able to provide a good measure of robustness against disturbances and achieve good tracking performance. However, it will give degraded tracking performance in case of the presence of model uncertainties. Therefore LQR tracking performance is enhanced by using a Model Reference Adaptive Controller (MRAC) in the literature for enabling a 2 DOF system to achieve good tracking against modelling uncertainties. But it has not been applied for a 3 DOF system till date. Therefore in this work, it is proposed to be applied for such a system for the first time to realize an adaptive control. The forward and inverse kinematics level equations are formulated using an indirect form of the Denavit Hartenberg (DH) convention. 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