{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:12:16Z","timestamp":1787325136116,"version":"build-2736575974"},"reference-count":25,"publisher":"Frontiers Media SA","license":[{"start":{"date-parts":[[2025,11,27]],"date-time":"2025-11-27T00:00:00Z","timestamp":1764201600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["frontiersin.org"],"crossmark-restriction":true},"short-container-title":["Front. Robot. AI"],"abstract":"<jats:p>Rehabilitation robots are widely recognized as vital for restoring motor function in patients with lower-limb impairments. A Modified Fractional-Order Proportional-Integral-Derivative (MFOPID) controller is proposed to improve trajectory tracking of a 2-DoF Lower Limb Rehabilitation Exoskeleton Robot (LLRER). The classical FOPID is augmented with a modified control formulation by which steady-state error is reduced and the transient response is sharpened. Controller gains and fractional orders were tuned offline using a hybrid metaheuristic Improved Elk Herd Optimization hybridized with Grey Wolf and Multi-Verse Optimization algorithms (IElk-GM) so that exploration and exploitation are balanced. Superiority over the classical FOPID was demonstrated in simulations under linear and nonlinear trajectories, with disturbances and parametric uncertainty: 0% overshoot was achieved at both hip and knee joints; settling time was reduced from 6.998 s to 0.430 s (hip) and from 7.150 s to 0.829 s (knee); ITAE was reduced from 23.39 to 2.694 (hip) and from 16.95 to 3.522 (knee); and the hip steady-state error decreased from 0.018 Rad to 0.0015 Rad, while the knee steady-state error remained within 0.011 Rad. Control torques remained bounded under linear tracking (&amp;lt;345 N\u00b7m at the hip; &amp;lt;95 N\u00b7m at the knee) and under nonlinear cosine tracking (&amp;lt;350 N\u00b7m at the hip; &amp;lt;100 N\u00b7m at the knee). These results indicate that safer, smoother, and more effective robot-assisted rehabilitation can be supported by the proposed controller.<\/jats:p>","DOI":"10.3389\/frobt.2025.1667688","type":"journal-article","created":{"date-parts":[[2025,11,27]],"date-time":"2025-11-27T11:05:32Z","timestamp":1764241532000},"update-policy":"https:\/\/doi.org\/10.3389\/crossmark-policy","source":"Crossref","is-referenced-by-count":3,"title":["Design of modified fractional-order PID controller for lower limb rehabilitation exoskeleton robot based on an improved elk herd hybridized with grey wolf and multi-verse optimization algorithms"],"prefix":"10.3389","volume":"12","author":[{"given":"Noor Sabah","family":"Mohammed Ali","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Muna Hadi","family":"Saleh","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nizar Hadi","family":"Abbas","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1965","published-online":{"date-parts":[[2025,11,27]]},"reference":[{"key":"B1","doi-asserted-by":"publisher","first-page":"188","DOI":"10.31026\/j.eng.2020.04.13","article-title":"Survey study of factional order controllers","volume":"26","author":"Abdulwahhab","year":"2020","journal-title":"J. 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