{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T19:17:29Z","timestamp":1791400649060,"version":"4.3.3"},"reference-count":43,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,2,27]],"date-time":"2025-02-27T00:00:00Z","timestamp":1740614400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["12293000"],"award-info":[{"award-number":["12293000"]}]},{"name":"National Natural Science Foundation of China","award":["12293001"],"award-info":[{"award-number":["12293001"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Biomimetics"],"abstract":"<jats:p>Due to its exceptional terrain mobility, quadrupedal locomotion has been used in the design of many amphibious robots for broad applications including resource exploration, disaster rescue, and reconnaissance. In this work, swimming of a quadrupedal paddling model is considered, and the effects of the legs\u2019 initial swing angle, swing amplitude, and power phase duration are numerically investigated through three paddling gaits, namely, the trotting gait, the diagonal, and the lateral sequence gaits. Three different modes for drag-based thrust generation, the \u201cTrotting Mode\u201d, the \u201cHindering Mode\u201d, and the \u201cSeparate Mode\u201d, are identified. In the \u201cTrotting Mode\u201d, each pair of diagonal legs contributes equally and alternately to the thrust within the paddling cycle, and its contribution is impaired by the other pair of diagonal legs. In the \u201cHindering Mode\u201d, the thrust contribution of an individual leg is significantly undermined by the drag resulting from the preceding leg leaving its current power phase and entering the following recovery phase. In the \u201cSeparate Mode\u201d, the four legs independently contribute to the total thrust by forming a compact four-peak waveform equally distributed within one paddling cycle. At a given swing amplitude, the leg configuration at peak thrust moment is identical, regardless of initial swing angle and power phase ratio. Meanwhile, a forward-tilted leg configuration with flatter upper- and lower-limb alignment at peak thrust moment consistently indicates a lower thrust generation. Hydrodynamic moments in the diagonal and lateral sequence gaits are much larger than those in the trotting gait. In addition, enhanced thrust is typically accompanied by larger hydrodynamic moments and a higher energy expenditure.<\/jats:p>","DOI":"10.3390\/biomimetics10030148","type":"journal-article","created":{"date-parts":[[2025,2,28]],"date-time":"2025-02-28T02:48:37Z","timestamp":1740710917000},"page":"148","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Computational Study on the Hydrodynamics of Bio-Inspired Quadrupedal Paddling"],"prefix":"10.3390","volume":"10","author":[{"given":"Yihan","family":"Wang","sequence":"first","affiliation":[{"name":"Shien-Ming Wu School of Intelligent Engineering, South China University of Technology, Guangzhou 510641, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yumeng","family":"Cai","sequence":"additional","affiliation":[{"name":"Shien-Ming Wu School of Intelligent Engineering, South China University of Technology, Guangzhou 510641, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bin","family":"Xie","sequence":"additional","affiliation":[{"name":"Shien-Ming Wu School of Intelligent Engineering, South China University of Technology, Guangzhou 510641, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chi","family":"Zhu","sequence":"additional","affiliation":[{"name":"Department of Mechanics and Engineering Science, Peking University, Beijing 100871, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yunquan","family":"Li","sequence":"additional","affiliation":[{"name":"Shien-Ming Wu School of Intelligent Engineering, South China University of Technology, Guangzhou 510641, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ye","family":"Chen","sequence":"additional","affiliation":[{"name":"Shien-Ming Wu School of Intelligent Engineering, South China University of Technology, Guangzhou 510641, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1631\/jzus.A2100137","article-title":"Development of amphibious biomimetic robots","volume":"23","author":"Bai","year":"2022","journal-title":"J. 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