A Double Shooting Method for Two-Point Boundary Value Problems in Multibody Dynamics

A Double Shooting Method for Two-Point Boundary Value Problems in Multibody Dynamics | 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 A Double Shooting Method for Two-Point Boundary Value Problems in Multibody Dynamics Philipp Eichmeir, Wolfgang Steiner This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6563065/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 12 Jan, 2026 Read the published version in Multibody System Dynamics → Version 1 posted 9 You are reading this latest preprint version Abstract The solution of two-point boundary value problems (TPBVPs) in multibody system dynamics is a tough challenge. In this article, a double shooting method (DSM) tailored for TPBVPs is presented. The method builds upon the classical single shooting method while incorporating optimization strategies to overcome numerical instability and sensitivity to initial guesses. Conventional shooting methods are associated with some numerical problems: The numerical gradient computation for updating initial values causes problems in many cases, since the disturbance parameter for determining the numerical derivative must be selected appropriately in order to achieve sufficient accuracy. Moreover, integrating the initial value problem can be numerically challenging, especially when the interval is large and the differential equations have unstable modes. The DSM is designed to address these challenges. Therefore, the method incorporates a discrete costate variable approach to cope with the numerical gradient computation, which is often the Achilles' heel of classical shooting methods. Finally, the method is formulated using a discrete implicit integration scheme to determine, as a first example, a double pendulum upswing maneuver and, as a second example, the energy-optimal control of a robot multibody model. Multibody Systems Two-Point Boundary Value Problem Double Shooting Method Adjoint Method Optimal Control Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 12 Jan, 2026 Read the published version in Multibody System Dynamics → Version 1 posted Editorial decision: Revision requested 21 Jul, 2025 Reviews received at journal 19 Jun, 2025 Reviews received at journal 03 Jun, 2025 Reviewers agreed at journal 21 May, 2025 Reviewers agreed at journal 20 May, 2025 Reviewers invited by journal 05 May, 2025 Editor assigned by journal 30 Apr, 2025 Submission checks completed at journal 30 Apr, 2025 First submitted to journal 30 Apr, 2025 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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