Investigating Advantageous Approaches for Incorporating DAE-Based Multibody Models in Model Predictive Control Problems

Investigating Advantageous Approaches for Incorporating DAE-Based Multibody Models in Model Predictive Control Problems | 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 Investigating Advantageous Approaches for Incorporating DAE-Based Multibody Models in Model Predictive Control Problems Arnim Kargl, Henrik Ebel, Peter Eberhard This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9439249/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 7 You are reading this latest preprint version Abstract Multibody dynamics research has enabled efficient and effective simulation, design optimization, control, and identification of mechanical systems, contributing significantly to applications as diverse as simulation-driven and optimization-based engineering design, robotics, digital-twin technology, and many more. Nowadays, different formulations are in use and their properties and comparative differences are especially well understood for numerical simulation purposes. Also, software for multibody modeling often predominantly takes simulation applications into focus. However, efficiency is particularly paramount when using multibody system (MBS) models for model-based real-time control, where, in particular, model predictive control (MPC) comes to mind. This contribution investigates different ways of discretizing the higher-index differential-algebraic equations (DAEs) of motion of an MBS model when implementing the MPC's underlying optimal control problem (OCP). In contrast to the widely used reduction to an index-1 DAE in combination with an implicit integration scheme, more direct approaches are proposed, exploiting the ability of nonlinear programming solvers to efficiently handle equality constraints. The proposed OCP implementations are evaluated on a set of example MBS, revealing a superior numerical efficiency, especially with state-of-the-art structure exploiting OCP solvers. The presented approaches are chosen so that they introduce as few additional hyperparameters as possible while allowing as much flexibility as possible in OCP design, and, this way, the obtained results demonstrate that the automatic synthesis of real-time capable MPC controllers from MBS models can nowadays be feasible without arduous per-system tuning or overly specific or limited numerical approaches. However, it is also noted that a prospective, automated workflow from MBS model to MPC controller poses certain requirements for multibody modeling software, motivating a discussion of how such software should be designed to facilitate optimal control, revealing desirable characteristics exceeding what is required for simulation purposes. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviewers agreed at journal 04 May, 2026 Reviewers agreed at journal 01 May, 2026 Reviewers agreed at journal 30 Apr, 2026 Reviewers invited by journal 28 Apr, 2026 Editor assigned by journal 19 Apr, 2026 Submission checks completed at journal 17 Apr, 2026 First submitted to journal 16 Apr, 2026 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-9439249","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":625678457,"identity":"0d53232f-68fa-419e-93da-76aeb1acf1dd","order_by":0,"name":"Arnim Kargl","email":"","orcid":"","institution":"University of Stuttgart","correspondingAuthor":false,"prefix":"","firstName":"Arnim","middleName":"","lastName":"Kargl","suffix":""},{"id":625678458,"identity":"f49bcc98-6c61-4797-bce6-a855a0456ea4","order_by":1,"name":"Henrik Ebel","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAyElEQVRIiWNgGAWjYBACAxCRcADEYG588ADIYW8mXgtjs0ECkOI5TIwWBoiWNgmwlgMEtJiz9x778OAMg5w5e2NbRWLbHwYedgJaLHvOJc9IuMFgbNlzsO1GYhvQFmZCDruRY8yQ8IEhcQNQPViLPUEt99+AtdRvuP+wrYBIW3iAWm4wJBjcYGxjIE7LGZDDzkgY7uxJbJZIOGfMQ1jL8TPGjD+O2cibsx8++OFDmZwcD/8BAnogQALO4iFK/SgYBaNgFIwC/AAAoCNBQ1/W1ZsAAAAASUVORK5CYII=","orcid":"","institution":"Lappeenranta University of Technology","correspondingAuthor":true,"prefix":"","firstName":"Henrik","middleName":"","lastName":"Ebel","suffix":""},{"id":625678459,"identity":"9b2c50a6-87e4-4622-b13e-e1df2d101a8e","order_by":2,"name":"Peter Eberhard","email":"","orcid":"","institution":"University of Stuttgart","correspondingAuthor":false,"prefix":"","firstName":"Peter","middleName":"","lastName":"Eberhard","suffix":""}],"badges":[],"createdAt":"2026-04-16 14:09:01","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9439249/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9439249/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":107387620,"identity":"eeea5bf0-f8fb-430d-987d-0903c6eaf29e","added_by":"auto","created_at":"2026-04-21 04:10:56","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":936710,"visible":true,"origin":"","legend":"","description":"","filename":"KarglEbelEberhard26.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9439249/v1_covered_b7d5b471-a9a0-49a4-a1cb-4ccf57780b60.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Investigating Advantageous Approaches for Incorporating DAE-Based Multibody Models in Model Predictive Control Problems","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"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":"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":"","lastPublishedDoi":"10.21203/rs.3.rs-9439249/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9439249/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Multibody dynamics research has enabled efficient and effective simulation, design optimization, control, and identification of mechanical systems, contributing significantly to applications as diverse as simulation-driven and optimization-based engineering design, robotics, digital-twin technology, and many more. 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