{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,24]],"date-time":"2026-04-24T17:06:15Z","timestamp":1777050375465,"version":"3.51.4"},"reference-count":31,"publisher":"MDPI AG","issue":"15","license":[{"start":{"date-parts":[[2023,8,4]],"date-time":"2023-08-04T00:00:00Z","timestamp":1691107200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Project of Science and Technology of Henan Province","award":["212102310249"],"award-info":[{"award-number":["212102310249"]}]},{"name":"Project of Science and Technology of Henan Province","award":["212102310890"],"award-info":[{"award-number":["212102310890"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Passive rehabilitation training in the early poststroke period can promote the reshaping of the nervous system. The trajectory should integrate the physicians\u2019 experience and the patient\u2019s characteristics. And the training should have high accuracy on the premise of safety. Therefore, trajectory customization, optimization, and tracking control algorithms are conducted based on a new upper limb rehabilitation robot. First, joint friction and initial load were identified and compensated. The admittance algorithm was used to realize the trajectory customization. Second, the improved butterfly optimization algorithm (BOA) was used to optimize the nonuniform rational B-spline fitting curve (NURBS). Then, a variable gain control strategy is designed, which enables the robot to track the trajectory well with small human\u2013robot interaction (HRI) forces and to comply with a large HRI force to ensure safety. Regarding the return motion, an error subdivision method is designed to slow the return movement. The results showed that the customization force is less than 6 N. The trajectory tracking error is within 12 mm without a large HRI force. The control gain starts to decrease in 0.5 s periods while there is a large HRI force, thereby improving safety. With the decrease in HRI force, the real position can return to the desired trajectory slowly, which makes the patient feel comfortable.<\/jats:p>","DOI":"10.3390\/s23156953","type":"journal-article","created":{"date-parts":[[2023,8,5]],"date-time":"2023-08-05T10:25:36Z","timestamp":1691231136000},"page":"6953","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Customized Trajectory Optimization and Compliant Tracking Control for Passive Upper Limb Rehabilitation"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1558-4910","authenticated-orcid":false,"given":"Liaoyuan","family":"Li","sequence":"first","affiliation":[{"name":"School of Mechatronics Engineering, Henan University of Science and Technology, Luoyang 471023, China"},{"name":"Henan Provincial Key Laboratory of Robotics and Intelligent Systems, Luoyang 471000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianhai","family":"Han","sequence":"additional","affiliation":[{"name":"School of Mechatronics Engineering, Henan University of Science and Technology, Luoyang 471023, China"},{"name":"Henan Provincial Key Laboratory of Robotics and Intelligent Systems, Luoyang 471000, China"},{"name":"Collaborative Innovation Center of Machinery Equipment Advanced Manufacturing of Henan Province, Luoyang 471003, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiangpan","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mechatronics Engineering, Henan University of Science and Technology, Luoyang 471023, China"},{"name":"Henan Provincial Key Laboratory of Robotics and Intelligent Systems, Luoyang 471000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bingjing","family":"Guo","sequence":"additional","affiliation":[{"name":"School of Mechatronics Engineering, Henan University of Science and Technology, Luoyang 471023, China"},{"name":"Henan Provincial Key Laboratory of Robotics and Intelligent Systems, Luoyang 471000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xinjie","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mechatronics Engineering, Zhengzhou University of Light Industry, Zhengzhou 450001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"759","DOI":"10.1161\/CIRCULATIONAHA.116.025250","article-title":"Prevalence, incidence, and mortality of stroke in China clinical perspective","volume":"135","author":"Wang","year":"2017","journal-title":"Circulation"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"3107","DOI":"10.1161\/STROKEAHA.118.021359","article-title":"New directions in treatments targeting stroke recovery","volume":"49","author":"Lin","year":"2018","journal-title":"Stroke"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s12984-018-0383-x","article-title":"Rehabilitation robots for the treatment of sensorimotor deficits: A neurophysiological perspective","volume":"15","author":"Gassert","year":"2018","journal-title":"J. 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