{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,30]],"date-time":"2026-01-30T00:55:36Z","timestamp":1769734536356,"version":"3.49.0"},"reference-count":47,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2023,3,3]],"date-time":"2023-03-03T00:00:00Z","timestamp":1677801600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100008530","name":"Fondo Europeo de Desarrollo Regional","doi-asserted-by":"publisher","award":["PID2021-125694OB-I00"],"award-info":[{"award-number":["PID2021-125694OB-I00"]}],"id":[{"id":"10.13039\/501100008530","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100008530","name":"Fondo Europeo de Desarrollo Regional","doi-asserted-by":"publisher","award":["PAID-11-21"],"award-info":[{"award-number":["PAID-11-21"]}],"id":[{"id":"10.13039\/501100008530","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100008530","name":"Fondo Europeo de Desarrollo Regional","doi-asserted-by":"publisher","award":["FPU18\/05105"],"award-info":[{"award-number":["FPU18\/05105"]}],"id":[{"id":"10.13039\/501100008530","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Vicerrectorado de Investigaci\u00f3n de la Universitat Polit\u00e8cnica de Val\u00e8ncia","award":["PID2021-125694OB-I00"],"award-info":[{"award-number":["PID2021-125694OB-I00"]}]},{"name":"Vicerrectorado de Investigaci\u00f3n de la Universitat Polit\u00e8cnica de Val\u00e8ncia","award":["PAID-11-21"],"award-info":[{"award-number":["PAID-11-21"]}]},{"name":"Vicerrectorado de Investigaci\u00f3n de la Universitat Polit\u00e8cnica de Val\u00e8ncia","award":["FPU18\/05105"],"award-info":[{"award-number":["FPU18\/05105"]}]},{"name":"Ministerio de Universidades, Gobierno de Espa\u00f1a","award":["PID2021-125694OB-I00"],"award-info":[{"award-number":["PID2021-125694OB-I00"]}]},{"name":"Ministerio de Universidades, Gobierno de Espa\u00f1a","award":["PAID-11-21"],"award-info":[{"award-number":["PAID-11-21"]}]},{"name":"Ministerio de Universidades, Gobierno de Espa\u00f1a","award":["FPU18\/05105"],"award-info":[{"award-number":["FPU18\/05105"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Parallel robots are being increasingly used as a fundamental component of lower-limb rehabilitation systems. During rehabilitation therapies, the parallel robot must interact with the patient, which raises several challenges to the control system: (1) The weight supported by the robot can vary from patient to patient, and even for the same patient, making standard model-based controllers unsuitable for those tasks since they rely on constant dynamic models and parameters. (2) The identification techniques usually consider the estimation of all dynamic parameters, bringing about challenges concerning robustness and complexity. This paper proposes the design and experimental validation of a model-based controller comprising a proportional-derivative controller with gravity compensation applied to a 4-DOF parallel robot for knee rehabilitation, where the gravitational forces are expressed in terms of relevant dynamic parameters. The identification of such parameters is possible by means of least squares methods. The proposed controller has been experimentally validated, holding the error stable following significant payload changes in terms of the weight of the patient\u2019s leg. This novel controller allows us to perform both identification and control simultaneously and is easy to tune. Moreover, its parameters have an intuitive interpretation, contrary to a conventional adaptive controller. The performance of a conventional adaptive controller and the proposed one are compared experimentally.<\/jats:p>","DOI":"10.3390\/s23052790","type":"journal-article","created":{"date-parts":[[2023,3,6]],"date-time":"2023-03-06T02:28:34Z","timestamp":1678069714000},"page":"2790","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Model-Based Control of a 4-DOF Rehabilitation Parallel Robot with Online Identification of the Gravitational Term"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6535-9098","authenticated-orcid":false,"given":"Rafael J.","family":"Escarabajal","sequence":"first","affiliation":[{"name":"Departamento de Ingenier\u00eda de Sistemas y Autom\u00e1tica, Instituto de Autom\u00e1tica e Inform\u00e1tica Industrial, Camino de Vera s\/n, 46022 Valencia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0403-4593","authenticated-orcid":false,"given":"Jos\u00e9 L.","family":"Pulloquinga","sequence":"additional","affiliation":[{"name":"Departamento de Ingenier\u00eda de Sistemas y Autom\u00e1tica, Instituto de Autom\u00e1tica e Inform\u00e1tica Industrial, Camino de Vera s\/n, 46022 Valencia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2255-0567","authenticated-orcid":false,"given":"Vicente","family":"Mata","sequence":"additional","affiliation":[{"name":"Centro de Investigaci\u00f3n en Ingenier\u00eda Mec\u00e1nica, Departamento de Ingenier\u00eda Mec\u00e1nica y de Materiales, Universitat Polit\u00e8cnica de Val\u00e8ncia, Camino de Vera s\/n, 46022 Valencia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6843-6394","authenticated-orcid":false,"given":"\u00c1ngel","family":"Valera","sequence":"additional","affiliation":[{"name":"Departamento de Ingenier\u00eda de Sistemas y Autom\u00e1tica, Instituto de Autom\u00e1tica e Inform\u00e1tica Industrial, Camino de Vera s\/n, 46022 Valencia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7243-4957","authenticated-orcid":false,"given":"Miguel","family":"D\u00edaz-Rodr\u00edguez","sequence":"additional","affiliation":[{"name":"Departamento de Tecnolog\u00eda y Dise\u00f1o, Facultad de Ingenier\u00eda, N\u00facleo la Hechicera, Universidad de los Andes, Merida 5101, Venezuela"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"57","DOI":"10.4236\/mme.2012.23008","article-title":"Parallel Manipulators Applications\u2014A Survey","volume":"2","author":"Patel","year":"2012","journal-title":"Mod. 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