Discovering Dominant Dynamics for Nonlinear Continuum Robot Control

Discovering Dominant Dynamics for Nonlinear Continuum Robot Control | 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 Article Discovering Dominant Dynamics for Nonlinear Continuum Robot Control John Irvin Alora, Mattia Cenedese, George Haller, Marco Pavone This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4716136/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 11 You are reading this latest preprint version Abstract Continuum robots, which emulate biological organisms’ dexterity and flexibility, hold transformative potential for terrestrial and extraterrestrial applications. While these capabilities present significant modeling and control challenges, these robots’ highly dissipative nature allows their behavior to be explained by low-dimensional, dominant dynamics. Despite extensive research to uncover these dynamics, existing methodologies often fail to produce models that accurately capture them, hindering precise control in diverse and safety-critical tasks. This work addresses this gap by discovering these dynamics and leveraging them in a control methodology that substantially outperforms existing methods. Our approach, grounded in Spectral Submanifold theory, enhances accuracy up to sixfold and improves tracking performance by up to 150 times across a diverse set of control tasks, achieving Pareto dominance in precision and computational efficiency. These advances enable the development of simple yet robust models suitable for real-time control, moving us closer to deploying highly adaptive, efficient, and safe continuum robots. Continuum Robotics Spectral Submanifold Model Predictive Control Nonlinear Dynamics Machine Learning Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 13 Sep, 2024 Reviews received at journal 02 Sep, 2024 Reviews received at journal 31 Aug, 2024 Reviewers agreed at journal 05 Aug, 2024 Reviewers agreed at journal 02 Aug, 2024 Reviewers agreed at journal 02 Aug, 2024 Reviewers agreed at journal 23 Jul, 2024 Reviewers invited by journal 23 Jul, 2024 Editor assigned by journal 13 Jul, 2024 Submission checks completed at journal 11 Jul, 2024 First submitted to journal 10 Jul, 2024 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-4716136","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":335818535,"identity":"4323297d-97ec-4152-b8da-88b71c90d430","order_by":0,"name":"John Irvin Alora","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA50lEQVRIie3OsQqCQBjA8YtAl4PWg6h7BUOwpp5FCXJRCIIQGroQXFvdegVbnBo+Ec7FB2gKJ6eGWprzamvwHIPuP9xxH/fjDiGV6gfrMehBs4/fp0AMEDJkBAliIq1Zyy5EJIjDOpP+Pq/gcZ67x2NYVxBcR0wPU9L+MW5kcb3wE65NDSjXJsN8IyFg5Bj6fqIha/iIbIcRz5KQ4t6QnUsj/UkyQehNRkrxSm4jjq0PIVhKVlkMxSTh3oZAaZsRXq5nbWQSF6fqDltKwyIlENijg56fLu0EviZa23URHTDZFZVKpfr7XivKVXMZONAAAAAAAElFTkSuQmCC","orcid":"","institution":"Stanford University","correspondingAuthor":true,"prefix":"","firstName":"John","middleName":"Irvin","lastName":"Alora","suffix":""},{"id":335818537,"identity":"d6bdf464-6496-47d4-9449-625db9b37445","order_by":1,"name":"Mattia Cenedese","email":"","orcid":"","institution":"ETH Zürich","correspondingAuthor":false,"prefix":"","firstName":"Mattia","middleName":"","lastName":"Cenedese","suffix":""},{"id":335818538,"identity":"3d2da7b3-cc7a-4566-912e-585b8761e960","order_by":2,"name":"George Haller","email":"","orcid":"","institution":"ETH Zürich","correspondingAuthor":false,"prefix":"","firstName":"George","middleName":"","lastName":"Haller","suffix":""},{"id":335818539,"identity":"2518672e-6f4f-42f9-9011-5fdcc1f1f08b","order_by":3,"name":"Marco Pavone","email":"","orcid":"","institution":"Stanford University","correspondingAuthor":false,"prefix":"","firstName":"Marco","middleName":"","lastName":"Pavone","suffix":""}],"badges":[],"createdAt":"2024-07-10 06:52:45","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4716136/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4716136/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":61803864,"identity":"661ece70-ba15-4087-9cec-9de7ace8deb8","added_by":"auto","created_at":"2024-08-05 18:29:19","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":10205388,"visible":true,"origin":"","legend":"","description":"","filename":"DiscoveringDominantDynamicsforNonlinearContinuumRobotControl.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4716136/v1_covered_062c5e0a-aaf5-4fd6-87cc-cba7bb847e15.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Discovering Dominant Dynamics for Nonlinear Continuum Robot Control","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":"npj-robotics","isNatureJournal":false,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"npjrobot","sideBox":"Learn more about [npj Robotics](http://www.nature.com/npjrobot/)","snPcode":"44182","submissionUrl":"https://mts-npjrobot.nature.com/cgi-bin/main.plex","title":"npj Robotics","twitterHandle":"@NaturePortfolio","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"NPJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Continuum Robotics, Spectral Submanifold, Model Predictive Control, Nonlinear Dynamics, Machine Learning","lastPublishedDoi":"10.21203/rs.3.rs-4716136/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4716136/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Continuum robots, which emulate biological organisms’ dexterity and flexibility, hold transformative potential for terrestrial and extraterrestrial applications. 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