{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,7]],"date-time":"2026-03-07T00:30:50Z","timestamp":1772843450250,"version":"3.50.1"},"reference-count":57,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,4,17]],"date-time":"2025-04-17T00:00:00Z","timestamp":1744848000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004837","name":"Project SAMPL2D","doi-asserted-by":"publisher","award":["PDC2023-145812-I00"],"award-info":[{"award-number":["PDC2023-145812-I00"]}],"id":[{"id":"10.13039\/501100004837","id-type":"DOI","asserted-by":"publisher"}]},{"name":"MICIU\/AEI\/10.13039\/501100011033","award":["PDC2023-145812-I00"],"award-info":[{"award-number":["PDC2023-145812-I00"]}]},{"name":"Next Generation EU\/PRTR","award":["PDC2023-145812-I00"],"award-info":[{"award-number":["PDC2023-145812-I00"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotics"],"abstract":"<jats:p>Two primary challenges in controlling robotic rehabilitation devices are the uncertainties in dynamic models and, more importantly, the need for controllers capable of adapting to external disturbances due to human\u2013robot interaction. To address these issues, this paper proposes the particle swarm optimization (PSO) algorithm for the real-time gain tuning in the sliding mode controller (SMC) based on the exponential reaching law (ERL). The proposed approach was designed for a seven-degrees-of-freedom (DOF) robotic exoskeleton used in upper-limb physical rehabilitation. The optimization algorithm aims to minimize tracking errors in rehabilitation exercises through the robust ERL controller applied to nonlinear systems with external disturbances. The proposed method was validated through experimental tests conducted on two healthy subjects, and the outcomes indicated a reduction of over 20% in tracking errors compared to heuristically tuned gains. Mathematical analyses of dynamic modeling and algorithm convergence are shown.<\/jats:p>","DOI":"10.3390\/robotics14040051","type":"journal-article","created":{"date-parts":[[2025,4,17]],"date-time":"2025-04-17T20:50:46Z","timestamp":1744923046000},"page":"51","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Upper-Limb Robotic Rehabilitation: Online Sliding Mode Controller Gain Tuning Using Particle Swarm Optimization"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3290-2039","authenticated-orcid":false,"given":"Deira","family":"Sosa M\u00e9ndez","sequence":"first","affiliation":[{"name":"Escuela de Ingenier\u00eda de Fuenlabrada, Universidad Rey Juan Carlos, 28942 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8552-6842","authenticated-orcid":false,"given":"David","family":"Bedolla-Mart\u00ednez","sequence":"additional","affiliation":[{"name":"Electrical Engineering, \u00c9cole de Technologie Sup\u00e9rieure, Montreal, QC H3C 1K3, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2547-2509","authenticated-orcid":false,"given":"Maarouf","family":"Saad","sequence":"additional","affiliation":[{"name":"Electrical Engineering, \u00c9cole de Technologie Sup\u00e9rieure, Montreal, QC H3C 1K3, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7887-1584","authenticated-orcid":false,"given":"Yassine","family":"Kali","sequence":"additional","affiliation":[{"name":"DIFIA Laboratory, School of Engineering, Universit\u00e9 du Qu\u00e9bec en Abitibi-T\u00e9miscamingue, Rouyn-Noranda, QC J9X 5E4, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1067-0564","authenticated-orcid":false,"given":"Cecilia E.","family":"Garc\u00eda Cena","sequence":"additional","affiliation":[{"name":"Escuela T\u00e9cnica Superior de Ingenier\u00eda y Dise\u00f1o Industrial, Center for Automation and Robotics, UPM-CSIC, Universidad Polit\u00e9cnica de Madrid, 28012 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5355-0300","authenticated-orcid":false,"given":"\u00c1ngel L.","family":"\u00c1lvarez","sequence":"additional","affiliation":[{"name":"Escuela de Ingenier\u00eda de Fuenlabrada, Universidad Rey Juan Carlos, 28942 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2006","DOI":"10.1016\/S0140-6736(20)32340-0","article-title":"Global estimates of the need for rehabilitation based on the Global Burden of Disease study 2019: A systematic analysis for the Global Burden of Disease Study 2019","volume":"396","author":"Cieza","year":"2020","journal-title":"Lancet"},{"key":"ref_2","unstructured":"World Health Organization (2024, May 22). 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