{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,9]],"date-time":"2024-09-09T13:50:13Z","timestamp":1725889813557},"reference-count":34,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[2010,9,1]],"date-time":"2010-09-01T00:00:00Z","timestamp":1283299200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotica"],"published-print":{"date-parts":[[2011,9]]},"abstract":"SUMMARY<\/jats:title>This paper investigates the stable-running problem of a planar underactuated biped robot, which has two springy telescopic legs and one actuated joint in the hip. After modeling the robot as a hybrid system with multiple continuous state spaces, a natural passive limit cycle, which preserves the system energy at touchdown, is found using the method of Poincar\u00e9<\/jats:italic> shooting. It is then checked that the passive limit cycle is not stable. To stabilize the passive limit cycle, an event-based feedback control law is proposed, and also to enlarge the basin of attraction, an additive passivity-based control term is introduced only in the stance phase. The validity of our control strategies is illustrated by a series of numerical simulations.<\/jats:p>","DOI":"10.1017\/s0263574710000512","type":"journal-article","created":{"date-parts":[[2010,9,1]],"date-time":"2010-09-01T14:43:39Z","timestamp":1283352219000},"page":"657-665","source":"Crossref","is-referenced-by-count":17,"title":["Stable running of a planar underactuated biped robot"],"prefix":"10.1017","volume":"29","author":[{"given":"Yong","family":"Hu","sequence":"first","affiliation":[]},{"given":"Gangfeng","family":"Yan","sequence":"additional","affiliation":[]},{"given":"Zhiyun","family":"Lin","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2010,9,1]]},"reference":[{"key":"S0263574710000512_ref33","doi-asserted-by":"publisher","DOI":"10.1201\/9781420053739"},{"key":"S0263574710000512_ref9","doi-asserted-by":"publisher","DOI":"10.1177\/0278364905054929"},{"key":"S0263574710000512_ref6","doi-asserted-by":"publisher","DOI":"10.1109\/TRO.2008.2010366"},{"key":"S0263574710000512_ref21","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-36119-0_13"},{"key":"S0263574710000512_ref19","first-page":"107","volume-title":"Proceedings of the Royal Society of London. 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