Study on Bipedal Running on Compliant Ground Using Hybrid Zero Dynamics Controller

Study on Bipedal Running on Compliant Ground Using Hybrid Zero Dynamics Controller | 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 Study on Bipedal Running on Compliant Ground Using Hybrid Zero Dynamics Controller Yinnan Luo, Philipp Arbogast, Ulrich J. Römer, Marten Zirkel, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5397303/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 01 Aug, 2025 Read the published version in Multibody System Dynamics → Version 1 posted 4 You are reading this latest preprint version Abstract This research contributes to the development of energy-efficient bipedal running gaits on compliant ground using the hybrid zero dynamics control framework, which has been predominantly applied to rigid ground in existing literature. The robot model is composed of five rigid body segments connected by four actuated revolute joints using electric motors. The periodic running gaits at a constant average velocity consist of single support and flight phases with discrete transitions between them. During the single support phase, the compliant contact between the stance foot and the ground is modeled as a nonlinear viscoelastic interaction. Feedback controllers are developed for the continuous phases to enforce holonomic virtual constraints, thereby synchronizing the joint angles with a reference trajectory on the actuated joints, resulting in reduced-order zero dynamics. A multiple shooting technique is employed to ascertain periodic solutions of the hybrid zero dynamics. The formulation of energy-efficient gaits is conceptualized as an optimization problem, wherein the parameters of the reference trajectory are optimized. The stability of the gait is evaluated a posteriori by computing the Floquet multipliers of the periodic solutions. The magnitude of these multipliers is considered as optimization constraints, enabling the generation of stable and energy-efficient running gaits on compliant ground. Comparison with rigid ground demonstrates that ground compliance does not necessarily reduce energy efficiency. In certain scenarios, the elastic properties of the ground can be harnessed to enhance overall efficiency despite the energy dissipation due to damping. Bipedal Robot Bipedal Running Compliant Ground Hybrid Zero Dynamics Control Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 01 Aug, 2025 Read the published version in Multibody System Dynamics → Version 1 posted Editorial decision: Revision requested 22 Nov, 2024 Editor assigned by journal 07 Nov, 2024 Submission checks completed at journal 07 Nov, 2024 First submitted to journal 05 Nov, 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-5397303","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":381578108,"identity":"a411ed2d-d443-4847-8575-1cb2db0a63a3","order_by":0,"name":"Yinnan Luo","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAy0lEQVRIiWNgGAWjYDACZgglA2QdZkgAMQ8QqYWHgYEtmSEhgRgtDHAtPMYMDMRoMTjOe+zBzx0MPAbHez4bPPzBIMd3I4GAlsN86Ya9Z4BazpzdnAB0mLEkYS08ZhK8bUAtN3I3HwBqSdxAjBbJv2AtOY9BWuqJ0iINsSWHGeSwBANCWiRBWmTbJHgkzxwzNkhIkzCceeYBfi1858+YSb5ts5HjO978WPKHjY0833ECtigcAFMSML4ELoUIIN9AWM0oGAWjYBSMdAAA5E9BBcziSYEAAAAASUVORK5CYII=","orcid":"","institution":"Karlsruhe Institute of Technology","correspondingAuthor":true,"prefix":"","firstName":"Yinnan","middleName":"","lastName":"Luo","suffix":""},{"id":381578109,"identity":"41edac64-aa27-4351-955e-2f061659ed29","order_by":1,"name":"Philipp Arbogast","email":"","orcid":"","institution":"Karlsruhe Institute of Technology","correspondingAuthor":false,"prefix":"","firstName":"Philipp","middleName":"","lastName":"Arbogast","suffix":""},{"id":381578110,"identity":"40f1977b-cce1-486f-a161-e20c7ba14a11","order_by":2,"name":"Ulrich J. 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