Model-free Control of Manipulator in Task Space Containing Mismatched Uncertainty

Model-free Control of Manipulator in Task Space Containing Mismatched Uncertainty | 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 Model-free Control of Manipulator in Task Space Containing Mismatched Uncertainty Xiaohui Yang, Zhenghong Xu, Wenjie Zhang, Wei Zhang, Peter Xiaoping Liu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-685614/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 paper, a novel trajectory tracking control method for manipulator task space containing mismatched uncertainty is proposed. This paper considers the mismatched uncertainty that exists in the signal conversion between joint space and task space in the robotic arm system. The time delay estimation is employed to approximate the dynamic and kinematic parameters of the system to achieve model-free control. The time delay estimation errors is treated as part of the system disturbances and a disturbance observer based on an auxiliary control system capable of estimating both matched and mismatched disturbances is designed, which does not require additional design of adaptive laws to compensate for disturbances or upper bounds on the derivatives of disturbances. We transform the control error by a prescribed performance function to accomplish transient control of the error, and design a fast terminal sliding surface for the virtual control variables based on the backstepping design method to improve the convergence speed of the controller. Based on the Lyapunov criterion, the closedloop stability of the whole system is demonstrated. The feasibility and superiority of the method in this paper is demonstrated by numerical simulation compared with other control methods. Applied Mathematics Computer Architecture and Engineering Robotics Prescribed performance control Backstepping design method Mismatched uncertainty Fast terminal sliding surface Model-free control Full Text 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. 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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-685614","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":38712569,"identity":"d27879f8-d3b2-4663-a19f-048372e9e0de","order_by":0,"name":"Xiaohui Yang","email":"","orcid":"","institution":"Nanchang University - Qianhu Campus: Nanchang University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Xiaohui","middleName":"","lastName":"Yang","suffix":""},{"id":38712570,"identity":"46cc304d-8a2c-45c0-9ed0-c2f24a4be029","order_by":1,"name":"Zhenghong Xu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA2ElEQVRIiWNgGAWjYBACNgnGBoYEAwZmfhAvoYAILfwSzEAtFQzskg0gLQZEaJGcwQ5Ue4aB3+AAiEuMFoPbjW0SD9sOSxufX5344YEBgzy/2AECWu4cbJNIbDtsbHbj7WYJoMMMZ85OIKDlRmKzAVBLstmNsxtAWhIMbhOppX7zjLObfxClRXJGYuODhDOHmQ34e7cRZwu/zEGglop0ZokbvNssEgwkCPuFTbr9wcEfBtbM/P1nN9/8UWEjzy9NQAsCSIBVShCrHOzEA6SoHgWjYBSMgpEEAD/SSQCYtgvrAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0002-0145-2055","institution":"Nanchang University - Qianhu Campus: Nanchang University","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Zhenghong","middleName":"","lastName":"Xu","suffix":""},{"id":38712571,"identity":"ac657f80-1d03-4641-8841-d8bcf4a03fd7","order_by":2,"name":"Wenjie Zhang","email":"","orcid":"","institution":"Nanchang University - Qianhu Campus: Nanchang University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Wenjie","middleName":"","lastName":"Zhang","suffix":""},{"id":38712572,"identity":"406ba575-4765-429c-8d60-9927ce63503c","order_by":3,"name":"Wei Zhang","email":"","orcid":"","institution":"Nanchang University - Qianhu Campus: Nanchang University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Wei","middleName":"","lastName":"Zhang","suffix":""},{"id":38712573,"identity":"af46b68b-f276-429d-8b92-d91a67824693","order_by":4,"name":"Peter Xiaoping Liu","email":"","orcid":"","institution":"Carleton College","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Peter","middleName":"Xiaoping","lastName":"Liu","suffix":""}],"badges":[],"createdAt":"2021-07-04 08:14:37","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-685614/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-685614/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[],"financialInterests":"","formattedTitle":"\u003cp\u003eModel-free Control of Manipulator in Task Space Containing Mismatched Uncertainty\u003c/p\u003e","fulltext":[{"header":"Full Text","content":"This preprint is available for \u003ca href='/article/rs-685614/latest.pdf' target='_blank'\u003edownload as a PDF\u003c/a\u003e."}],"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":false,"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":"Prescribed performance control, Backstepping design method, Mismatched uncertainty, Fast terminal sliding surface, Model-free control","lastPublishedDoi":"10.21203/rs.3.rs-685614/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-685614/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"In this paper, a novel trajectory tracking control method for manipulator task space containing mismatched uncertainty is proposed. This paper considers the mismatched uncertainty that exists in the signal conversion between joint space and task space in the robotic arm system. The time delay estimation is employed to approximate the dynamic and kinematic parameters of the system to achieve model-free control. The time delay estimation errors is treated as part of the system disturbances and a disturbance observer based on an auxiliary control system capable of estimating both matched and mismatched disturbances is designed, which does not require additional design of adaptive laws to compensate for disturbances or upper bounds on the derivatives of disturbances. We transform the control error by a prescribed performance function to accomplish transient control of the error, and design a fast terminal sliding surface for the virtual control variables based on the backstepping design method to improve the convergence speed of the controller. Based on the Lyapunov criterion, the closedloop stability of the whole system is demonstrated. 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