{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T02:59:15Z","timestamp":1775789955530,"version":"3.50.1"},"reference-count":31,"publisher":"MDPI AG","issue":"18","license":[{"start":{"date-parts":[[2020,9,18]],"date-time":"2020-09-18T00:00:00Z","timestamp":1600387200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000781","name":"European Research Council","doi-asserted-by":"publisher","award":["850932"],"award-info":[{"award-number":["850932"]}],"id":[{"id":"10.13039\/501100000781","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["91748208"],"award-info":[{"award-number":["91748208"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100011710","name":"Shaanxi Provincial Science and Technology Department","doi-asserted-by":"publisher","award":["2017ZDL-G-3-1"],"award-info":[{"award-number":["2017ZDL-G-3-1"]}],"id":[{"id":"10.13039\/501100011710","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004543","name":"China Scholarship Council","doi-asserted-by":"publisher","award":["201806280161"],"award-info":[{"award-number":["201806280161"]}],"id":[{"id":"10.13039\/501100004543","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this work, we propose an intuitive and real-time model of the human arm active endpoint stiffness. In our model, the symmetric and positive-definite stiffness matrix is constructed through the eigendecomposition Kc=VDVT, where V is an orthonormal matrix whose columns are the normalized eigenvectors of Kc, and D is a diagonal matrix whose entries are the eigenvalues of Kc. In this formulation, we propose to construct V and D directly by exploiting the geometric information from a reduced human arm skeleton structure in 3D and from the assumption that human arm muscles work synergistically when co-contracted. Through the perturbation experiments across multiple subjects under different arm configurations and muscle activation states, we identified the model parameters and examined the modeling accuracy. In comparison to our previous models for predicting human active arm endpoint stiffness, the new model offers significant advantages such as fast identification and personalization due to its principled simplicity. The proposed model is suitable for applications such as teleoperation, human\u2013robot interaction and collaboration, and human ergonomic assessments, where a personalizable and real-time human kinodynamic model is a crucial requirement.<\/jats:p>","DOI":"10.3390\/s20185357","type":"journal-article","created":{"date-parts":[[2020,9,18]],"date-time":"2020-09-18T10:22:23Z","timestamp":1600424543000},"page":"5357","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":25,"title":["An Intuitive Formulation of the Human Arm Active Endpoint Stiffness"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2608-7840","authenticated-orcid":false,"given":"Yuqiang","family":"Wu","sequence":"first","affiliation":[{"name":"State Key Laboratory for Manufacturing System Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"},{"name":"Shaanxi Key Laboratory of Intelligent Robots and School of Mechanical Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"},{"name":"Human Robot Interfaces and physical Interaction lab (HRI<sup>2<\/sup>), Istituto Italiano di Tecnologia (IIT), 16163 Genova, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1405-5593","authenticated-orcid":false,"given":"Fei","family":"Zhao","sequence":"additional","affiliation":[{"name":"State Key Laboratory for Manufacturing System Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"},{"name":"Shaanxi Key Laboratory of Intelligent Robots and School of Mechanical Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3254-3929","authenticated-orcid":false,"given":"Wansoo","family":"Kim","sequence":"additional","affiliation":[{"name":"Human Robot Interfaces and physical Interaction lab (HRI<sup>2<\/sup>), Istituto Italiano di Tecnologia (IIT), 16163 Genova, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1261-737X","authenticated-orcid":false,"given":"Arash","family":"Ajoudani","sequence":"additional","affiliation":[{"name":"Human Robot Interfaces and physical Interaction lab (HRI<sup>2<\/sup>), Istituto Italiano di Tecnologia (IIT), 16163 Genova, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,9,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"957","DOI":"10.1007\/s10514-017-9677-2","article-title":"Progress and prospects of the human\u2013robot collaboration","volume":"42","author":"Ajoudani","year":"2018","journal-title":"Auton. 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