{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T12:36:01Z","timestamp":1778070961856,"version":"3.51.4"},"reference-count":43,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,1,13]],"date-time":"2023-01-13T00:00:00Z","timestamp":1673568000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["62166020"],"award-info":[{"award-number":["62166020"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Upper extremity exoskeleton rehabilitation robots have become a significant piece of rehabilitation equipment, and planning their motion trajectories is essential in patient rehabilitation. In this paper, a multistrategy improved whale optimization algorithm (MWOA) is proposed for trajectory planning of upper extremity exoskeleton rehabilitation robots with emphasis on isokinetic rehabilitation. First, a piecewise polynomial was used to construct a rough trajectory. To make the trajectory conform to human-like movement, a whale optimization algorithm (WOA) was employed to generate a bounded jerk trajectory with the minimum running time as the objective. The search performance of the WOA under complex constraints, including the search capability of trajectory planning symmetry, was improved by the following strategies: a dual-population search, including a new communication mechanism to prevent falling into the local optimum; a mutation centroid opposition-based learning, to improve the diversity of the population; and an adaptive inertia weight, to balance exploration and exploitation. Simulation analysis showed that the MWOA generated a trajectory with a shorter run-time and better symmetry and robustness than the WOA. Finally, a pilot rehabilitation session on a healthy volunteer using an upper extremity exoskeleton rehabilitation robot was completed safely and smoothly along the trajectory planned by the MWOA. The proposed algorithm thus provides a feasible scheme for isokinetic rehabilitation trajectory planning of upper extremity exoskeleton rehabilitation robots.<\/jats:p>","DOI":"10.3390\/sym15010232","type":"journal-article","created":{"date-parts":[[2023,1,16]],"date-time":"2023-01-16T03:10:34Z","timestamp":1673838634000},"page":"232","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Isokinetic Rehabilitation Trajectory Planning of an Upper Extremity Exoskeleton Rehabilitation Robot Based on a Multistrategy Improved Whale Optimization Algorithm"],"prefix":"10.3390","volume":"15","author":[{"given":"Fumin","family":"Guo","sequence":"first","affiliation":[{"name":"School of Advanced Manufacturing, Nanchang University, Nanchang 330031, China"}]},{"given":"Hua","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Advanced Manufacturing, Nanchang University, Nanchang 330031, China"},{"name":"School of Mechatronic Engineering, Shanghai University of Engineering Science, Shanghai 201620, China"}]},{"given":"Yilu","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Software, Jiangxi Agricultural University, Nanchang 330045, China"}]},{"given":"Genliang","family":"Xiong","sequence":"additional","affiliation":[{"name":"School of Mechatronic Engineering, Shanghai University of Engineering Science, Shanghai 201620, China"}]},{"given":"Cheng","family":"Zeng","sequence":"additional","affiliation":[{"name":"School of Advanced Manufacturing, Nanchang University, Nanchang 330031, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/S0140-6736(19)31055-4","article-title":"Robot assisted training for the upper limb after stroke (RATULS): A multicentre randomised controlled trial","volume":"394","author":"Rodgers","year":"2019","journal-title":"Lancet"},{"key":"ref_2","first-page":"767","article-title":"Efficacy of robot-assisted re-habilitation for the functional recovery of the upper limb in post-stroke patients: A randomized controlled study","volume":"52","author":"Taveggia","year":"2016","journal-title":"Eur. 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