{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,24]],"date-time":"2026-08-24T21:28:07Z","timestamp":1787606887532,"version":"build-2736575974"},"reference-count":36,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2023,11,13]],"date-time":"2023-11-13T00:00:00Z","timestamp":1699833600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Joint Fund of Ministry of Education for Equipment Pre-Research","award":["8091B022134"],"award-info":[{"award-number":["8091B022134"]}]},{"name":"Joint Fund of Ministry of Education for Equipment Pre-Research","award":["62233001"],"award-info":[{"award-number":["62233001"]}]},{"name":"Joint Fund of Ministry of Education for Equipment Pre-Research","award":["T2121002"],"award-info":[{"award-number":["T2121002"]}]},{"name":"Joint Fund of Ministry of Education for Equipment Pre-Research","award":["62073196"],"award-info":[{"award-number":["62073196"]}]},{"name":"Joint Fund of Ministry of Education for Equipment Pre-Research","award":["62303021"],"award-info":[{"award-number":["62303021"]}]},{"name":"Joint Fund of Ministry of Education for Equipment Pre-Research","award":["BX20220001"],"award-info":[{"award-number":["BX20220001"]}]},{"name":"Joint Fund of Ministry of Education for Equipment Pre-Research","award":["2023M730061"],"award-info":[{"award-number":["2023M730061"]}]},{"name":"National Natural Science Foundation of China","award":["8091B022134"],"award-info":[{"award-number":["8091B022134"]}]},{"name":"National Natural Science Foundation of China","award":["62233001"],"award-info":[{"award-number":["62233001"]}]},{"name":"National Natural Science Foundation of China","award":["T2121002"],"award-info":[{"award-number":["T2121002"]}]},{"name":"National Natural Science Foundation of China","award":["62073196"],"award-info":[{"award-number":["62073196"]}]},{"name":"National Natural Science Foundation of China","award":["62303021"],"award-info":[{"award-number":["62303021"]}]},{"name":"National Natural Science Foundation of China","award":["BX20220001"],"award-info":[{"award-number":["BX20220001"]}]},{"name":"National Natural Science Foundation of China","award":["2023M730061"],"award-info":[{"award-number":["2023M730061"]}]},{"name":"Postdoctoral Innovative Talent Support Program","award":["8091B022134"],"award-info":[{"award-number":["8091B022134"]}]},{"name":"Postdoctoral Innovative Talent Support Program","award":["62233001"],"award-info":[{"award-number":["62233001"]}]},{"name":"Postdoctoral Innovative Talent Support Program","award":["T2121002"],"award-info":[{"award-number":["T2121002"]}]},{"name":"Postdoctoral Innovative Talent Support Program","award":["62073196"],"award-info":[{"award-number":["62073196"]}]},{"name":"Postdoctoral Innovative Talent Support Program","award":["62303021"],"award-info":[{"award-number":["62303021"]}]},{"name":"Postdoctoral Innovative Talent Support Program","award":["BX20220001"],"award-info":[{"award-number":["BX20220001"]}]},{"name":"Postdoctoral Innovative Talent Support Program","award":["2023M730061"],"award-info":[{"award-number":["2023M730061"]}]},{"name":"China Postdoctoral Science Foundation","award":["8091B022134"],"award-info":[{"award-number":["8091B022134"]}]},{"name":"China Postdoctoral Science Foundation","award":["62233001"],"award-info":[{"award-number":["62233001"]}]},{"name":"China Postdoctoral Science Foundation","award":["T2121002"],"award-info":[{"award-number":["T2121002"]}]},{"name":"China Postdoctoral Science Foundation","award":["62073196"],"award-info":[{"award-number":["62073196"]}]},{"name":"China Postdoctoral Science Foundation","award":["62303021"],"award-info":[{"award-number":["62303021"]}]},{"name":"China Postdoctoral Science Foundation","award":["BX20220001"],"award-info":[{"award-number":["BX20220001"]}]},{"name":"China Postdoctoral Science Foundation","award":["2023M730061"],"award-info":[{"award-number":["2023M730061"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Biomimetics"],"abstract":"<jats:p>Aquatic animals such as fish and cetaceans can actively modulate their body stiffness with muscle to achieve excellent swimming performance under different situations. However, it is still challenging for a robotic swimmer with bionic propulsion mode to dynamically adjust its body stiffness to improve the swimming speed due to the difficulties in designing an effective stiffness adjustment structure. In this paper, based on the special torque mode of a motor, we propose an active variable stiffness control method for a robotic dolphin to pursue better swimming speed. Different from a variable stiffness structure design, a torque control strategy for the caudal motor is employed to imitate the physical property of a torsion spring to act as the variable stiffness component. In addition, we also establish a dynamic model with the Lagrangian method to explore the variable stiffness mechanism. Extensive experiments have validated the dynamic model, and then the relationships between frequency and stiffness on swimming performance are presented. More importantly, through integrating the dynamic model and torque actuation mode-based variable stiffness mechanism, the online performance optimization scheme can be easily realized, providing valuable guidance in coordinating system parameters. Finally, experiments have demonstrated the stiffness adjustment capability of the caudal joint, validating the effectiveness of the proposed control method. The results also reveal that stiffness plays an essential role in swimming motion, and the active stiffness adjustment can significantly contribute to performance improvement in both speed and efficiency. Namely, with the adjustment of stiffness, the maximum speed of our robotic dolphin achieves up to 1.12 body length per second (BL\/s) at 2.88 Hz increasing by 0.44 BL\/s. Additionally, the efficiency is also improved by 37%. The conducted works will offer some new insights into the stiffness adjustment of robotic swimmers for better swimming performance.<\/jats:p>","DOI":"10.3390\/biomimetics8070545","type":"journal-article","created":{"date-parts":[[2023,11,13]],"date-time":"2023-11-13T02:46:47Z","timestamp":1699843607000},"page":"545","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Performance Optimization for Bionic Robotic Dolphin with Active Variable Stiffness Control"],"prefix":"10.3390","volume":"8","author":[{"given":"Di","family":"Chen","sequence":"first","affiliation":[{"name":"State Key Laboratory for Turbulence and Complex Systems, Department of Advanced Manufacturing and Robotics, College of Engineering, Peking University, Beijing 100871, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yan","family":"Xiong","sequence":"additional","affiliation":[{"name":"State Key Laboratory for Turbulence and Complex Systems, Department of Advanced Manufacturing and Robotics, College of Engineering, Peking University, Beijing 100871, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bo","family":"Wang","sequence":"additional","affiliation":[{"name":"State Key Laboratory for Turbulence and Complex Systems, Department of Advanced Manufacturing and Robotics, College of Engineering, Peking University, Beijing 100871, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-1849-6108","authenticated-orcid":false,"given":"Ru","family":"Tong","sequence":"additional","affiliation":[{"name":"Laboratory of Cognitive and Decision Intelligence for Complex System, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yan","family":"Meng","sequence":"additional","affiliation":[{"name":"State Key Laboratory for Turbulence and Complex Systems, Department of Advanced Manufacturing and Robotics, College of Engineering, Peking University, Beijing 100871, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6347-572X","authenticated-orcid":false,"given":"Junzhi","family":"Yu","sequence":"additional","affiliation":[{"name":"State Key Laboratory for Turbulence and Complex Systems, Department of Advanced Manufacturing and Robotics, College of Engineering, Peking University, Beijing 100871, China"},{"name":"Science and Technology on Integrated Information System Laboratory, Institute of Software, Chinese Academy of Sciences, Beijing 100190, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,11,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"37","DOI":"10.4031\/MTSJ.47.5.2","article-title":"Advantages of natural propulsive systems","volume":"47","author":"Fish","year":"2013","journal-title":"Mar. 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