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This control offers strong feedback to the desired trajectory and the generation of energy-efficient and robust limit cycle walking. However, we observed that this method disables the natural dynamics of the robot, leading to problems regarding energy efficiency during walking. This study demonstrates that the energy consumption of walking using the output-zeroing control increases significantly in a disturbed environment. To overcome this limitation, the proposed approach leverages the robot\u2019s dynamics using NMPC to achieve energy-efficient walking even in a disturbed environment. We demonstrate the practicality of the proposed method using two different simulation environments.<\/jats:p>","DOI":"10.1017\/s0263574723001522","type":"journal-article","created":{"date-parts":[[2023,11,15]],"date-time":"2023-11-15T09:05:53Z","timestamp":1700039153000},"page":"435-456","source":"Crossref","is-referenced-by-count":1,"title":["Energy-efficient limit cycle walking in disturbance based on nonlinear model predictive control"],"prefix":"10.1017","volume":"42","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1161-1101","authenticated-orcid":false,"given":"Yuta","family":"Hanazawa","sequence":"first","affiliation":[]},{"given":"Haruka","family":"Nishinami","sequence":"additional","affiliation":[]},{"given":"Shinichi","family":"Sagara","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2023,11,15]]},"reference":[{"key":"S0263574723001522_ref6","doi-asserted-by":"crossref","first-page":"1082","DOI":"10.1126\/science.1107799","article-title":"Efficient bipedal robots based on passive-dynamic walkers","volume":"307","author":"Collins","year":"2005","journal-title":"Science"},{"key":"S0263574723001522_ref20","first-page":"4333","volume-title":"Proc. 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