{"paper_id":"1d8c5db1-3408-4d22-b2aa-99acfdcc89fd","body_text":"Adaptive Fuzzy Sliding Mode Trajectory Tracking Control Using Hexagonal Fuzzy Numbers | 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 Adaptive Fuzzy Sliding Mode Trajectory Tracking Control Using Hexagonal Fuzzy Numbers Amir Ali Mokhtarzadeh, Israel Ntumba Mbala, DeYe Wang, Ahmed N. Abdalla, and 4 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7627606/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 13 You are reading this latest preprint version Abstract This paper presents an adaptive fuzzy sliding mode controller (AFSMC) designed for precise trajectory tracking of an omnidirectional mobile robot operating within dynamic and uncertain environments. The control strategy integrates a sigmoid-based sliding mode switching function with an integral component to enhance system convergence speed and effectively mitigate chattering. A novel fuzzy gain adaptation mechanism employs a hexagonal fuzzy number (HFN) representation, facilitating more flexible and nonlinear shaping of membership functions. This methodology enables multi-objective gain tuning, assisting the controller in balancing robustness, responsiveness, and smoothness of control signals. The AFSMC architecture combines both equivalent and switching control laws to ensure robust resilience against model uncertainties, parameter variations, sensor noise, and external disturbances. Extensive simulations under diverse conditions, including disturbance injection, payload variations, and external force application, demonstrate that the proposed HFN-based AFSMC consistently attains lower root mean square error (RMSE), reduced overshoot, and significantly diminished chattering relative to conventional fuzzy sliding mode controllers employing triangular and trapezoidal membership functions. These findings affirm that the integration of HFN-based fuzzy adaptation within the sliding mode framework provides a robust and efficient solution for the accurate trajectory tracking of omnidirectional mobile robots in real-world and unpredictable scenarios. Impact : The method offers a practical framework for precision mobile robotics control, with potential extensions to autonomous navigation under soft-sensing and unstructured terrain conditions. fuzzy multi-objective function sliding mode control adaptive sliding mode mobile robot trajectory tracking Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 22 Oct, 2025 Reviews received at journal 21 Oct, 2025 Reviews received at journal 16 Oct, 2025 Reviews received at journal 12 Oct, 2025 Reviewers agreed at journal 10 Oct, 2025 Reviewers agreed at journal 09 Oct, 2025 Reviewers agreed at journal 09 Oct, 2025 Reviewers agreed at journal 07 Oct, 2025 Reviewers invited by journal 30 Sep, 2025 Editor assigned by journal 30 Sep, 2025 Editor invited by journal 28 Sep, 2025 Submission checks completed at journal 26 Sep, 2025 First submitted to journal 26 Sep, 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. 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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-7627606\",\"acceptedTermsAndConditions\":true,\"allowDirectSubmit\":false,\"archivedVersions\":[],\"articleType\":\"Research Article\",\"associatedPublications\":[],\"authors\":[{\"id\":528232576,\"identity\":\"2c2dd761-cf0d-428d-aaef-062bbf155a8a\",\"order_by\":0,\"name\":\"Amir Ali Mokhtarzadeh\",\"email\":\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAp0lEQVRIiWNgGAWjYFACxgaGDwheAnFaGGeQqIWBgZmHJC380w63fbbdYyMn38D88AFjWxphLRK3E5tn5zxLM2ZsYDM2YGzLIcJVQC3MOQcOJzYz8LBJMLZVENYhD9JiAdTSRrQWA5AWBqCWHogWIhxmCNTC2HMgzViCGeiXhHNEeF/udvpjhh8HgCHW3vzwwYeyZMJaEICZgeiIHAWjYBSMglFACAAATmsxu4VRalUAAAAASUVORK5CYII=\",\"orcid\":\"\",\"institution\":\"Huaiyin Institute of Technology\",\"correspondingAuthor\":true,\"prefix\":\"\",\"firstName\":\"Amir\",\"middleName\":\"Ali\",\"lastName\":\"Mokhtarzadeh\",\"suffix\":\"\"},{\"id\":528232577,\"identity\":\"7f2b678b-b680-47ef-b972-9cce801a32db\",\"order_by\":1,\"name\":\"Israel Ntumba Mbala\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"Huaiyin Institute of Technology\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Israel\",\"middleName\":\"Ntumba\",\"lastName\":\"Mbala\",\"suffix\":\"\"},{\"id\":528232578,\"identity\":\"8182a036-0a8a-4efa-9837-cbe67769b490\",\"order_by\":2,\"name\":\"DeYe Wang\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"Huaiyin Institute of Technology\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"DeYe\",\"middleName\":\"\",\"lastName\":\"Wang\",\"suffix\":\"\"},{\"id\":528232579,\"identity\":\"7ff7e660-36f8-470b-b6b2-5b468641be81\",\"order_by\":3,\"name\":\"Ahmed N. 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The control strategy integrates a sigmoid-based sliding mode switching function with an integral component to enhance system convergence speed and effectively mitigate chattering. A novel fuzzy gain adaptation mechanism employs a hexagonal fuzzy number (HFN) representation, facilitating more flexible and nonlinear shaping of membership functions. This methodology enables multi-objective gain tuning, assisting the controller in balancing robustness, responsiveness, and smoothness of control signals. The AFSMC architecture combines both equivalent and switching control laws to ensure robust resilience against model uncertainties, parameter variations, sensor noise, and external disturbances. Extensive simulations under diverse conditions, including disturbance injection, payload variations, and external force application, demonstrate that the proposed HFN-based AFSMC consistently attains lower root mean square error (RMSE), reduced overshoot, and significantly diminished chattering relative to conventional fuzzy sliding mode controllers employing triangular and trapezoidal membership functions. 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