{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,15]],"date-time":"2026-06-15T14:40:23Z","timestamp":1781534423449,"version":"3.54.5"},"reference-count":35,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T00:00:00Z","timestamp":1776816000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["52305381"],"award-info":[{"award-number":["52305381"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"award":["52305381"],"award-info":[{"award-number":["52305381"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"crossref","award":["30924010937"],"award-info":[{"award-number":["30924010937"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotics"],"abstract":"<jats:p>In the context of Industry 5.0, human\u2013robot collaboration increasingly demands intuitive, safe, and sensorless interaction for tasks such as hand-guided teaching and concurrent manipulation. However, conventional admittance control systems are prone to instability due to abrupt changes in human arm stiffness and their reliance on accurate dynamic models. To address these challenges, this paper proposes a sensorless external force estimation and variable admittance control method that models robot dynamic uncertainties and interaction forces as normally distributed stochastic quantities. An improved particle swarm optimization algorithm is introduced to calibrate the variance parameters, enhancing estimation accuracy and robustness. Furthermore, an energy-based variable admittance control strategy is developed, which preserves system passivity by adaptively adjusting inertia and damping gains based on real-time energy variations. The proposed method was validated on a redundant robot platform. Experimental results show that the external force and torque estimation errors remain below 3 N and 3 N.m, respectively, with lower detection delays and errors than those of a first-order generalized momentum observer in collision detection. Variable admittance experiments demonstrate that the system maintains passivity and stable interaction even under sudden arm stiffness changes. The approach is well-suited for industrial applications requiring safe, sensorless, and compliant human\u2013robot collaboration.<\/jats:p>","DOI":"10.3390\/robotics15050084","type":"journal-article","created":{"date-parts":[[2026,4,23]],"date-time":"2026-04-23T08:11:14Z","timestamp":1776931874000},"page":"84","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Human\u2013Robot Interaction: External Force Estimation and Variable Admittance Control Incorporating Passivity"],"prefix":"10.3390","volume":"15","author":[{"given":"Jun","family":"Wan","sequence":"first","affiliation":[{"name":"School of Automotive and Traffic Engineering, Jiangsu University of Technology, Changzhou 213001, China"},{"name":"School of Materials Science and Engineering, Nanjing University of Science and Technology, Nanjing 210094, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zihao","family":"Zhou","sequence":"additional","affiliation":[{"name":"School of Automotive and Traffic Engineering, Jiangsu University of Technology, Changzhou 213001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nuo","family":"Yun","sequence":"additional","affiliation":[{"name":"School of Automotive and Traffic Engineering, Jiangsu University of Technology, Changzhou 213001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1520-4634","authenticated-orcid":false,"given":"Kehong","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Materials Science and Engineering, Nanjing University of Science and Technology, Nanjing 210094, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2648-3314","authenticated-orcid":false,"given":"Xiaoyong","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Materials Science and Engineering, Nanjing University of Science and Technology, Nanjing 210094, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,4,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"16","DOI":"10.3901\/JME.2020.03.016","article-title":"Research progress and development trend of the safety of human-robot interaction technology","volume":"56","author":"Jia","year":"2020","journal-title":"J. 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