{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,12]],"date-time":"2025-11-12T05:35:07Z","timestamp":1762925707032,"version":"3.45.0"},"reference-count":19,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2025,11,10]],"date-time":"2025-11-10T00:00:00Z","timestamp":1762732800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"nsfc","doi-asserted-by":"publisher","award":["52575012"],"award-info":[{"award-number":["52575012"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005047","name":"Liaoning Provincial Natural Science Foundation","doi-asserted-by":"crossref","award":["2025-MS-084"],"award-info":[{"award-number":["2025-MS-084"]}],"id":[{"id":"10.13039\/501100005047","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100011196","name":"Shenyang Institute of Automation","doi-asserted-by":"crossref","award":["2023JC1K11"],"award-info":[{"award-number":["2023JC1K11"]}],"id":[{"id":"10.13039\/501100011196","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Initial attitude calibration is a critical yet challenging phase in hardware-in-the-loop (HIL) testing for space docking, often hindered by cumbersome procedures, safety concerns, and reliance on external equipment. This paper introduces a human\u2013robot collaborative calibration method based on H\u221e robust control. The core objective is to achieve symmetric pose alignment between docking mechanisms by allowing the operator to manually guide the test device, thereby rapidly obtaining initial attitude calibration results. An interactive model incorporating a time delay is established. Using H\u221e synthesis, a stabilizing controller is designed to accurately track low-frequency operator commands while strongly suppressing high-frequency disturbances. Notably, the H\u221e framework reconstructs an ideal interactive symmetry in human\u2013robot collaboration by compensating for delays and disturbances. The solution to the Riccati equation within a game-theoretic framework effectively achieves symmetric optimization that balances tracking accuracy with safety constraints. Experimental results demonstrate that the method successfully compensates for system delays, enabling symmetric pose alignment while maintaining smooth and continuous motion of the docking mechanism. It also faithfully translates the operator\u2019s low-frequency traction intent into motion. By retaining contact forces\/torques within safe thresholds, the method balances interaction safety with operational precision, ultimately providing a reliable solution for initial attitude calibration in space docking HIL tests.<\/jats:p>","DOI":"10.3390\/sym17111922","type":"journal-article","created":{"date-parts":[[2025,11,10]],"date-time":"2025-11-10T11:47:27Z","timestamp":1762775247000},"page":"1922","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["H\u221e Control for Symmetric Human\u2013Robot Interaction in Initial Attitude Calibration of Space Docking Hardware-in-the-Loop Tests"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9495-2341","authenticated-orcid":false,"given":"Xiao","family":"Zhang","sequence":"first","affiliation":[{"name":"State Key Laboratory of Robotics and Systems, Harbin Institute of Technology, Harbin 150001, China"},{"name":"Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-4035-7332","authenticated-orcid":false,"given":"Yonglin","family":"Tian","sequence":"additional","affiliation":[{"name":"Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zainan","family":"Jiang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Robotics and Systems, Harbin Institute of Technology, Harbin 150001, China"},{"name":"Song Jiang Laboratory, Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yun","family":"He","sequence":"additional","affiliation":[{"name":"Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhen","family":"Zhao","sequence":"additional","affiliation":[{"name":"Aerospace System Engineering Shanghai, Shanghai 201109, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,11,10]]},"reference":[{"key":"ref_1","first-page":"16","article-title":"Application status and development trend of hardware-in-the-loop simulation system","volume":"5","author":"Wu","year":"2016","journal-title":"Ind. 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