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We begin by introducing mathematical models of locomotion, from reduced-order models that capture essential walking behaviors to hybrid dynamical systems that encode the full-order continuous dynamics along with discrete foot-strike dynamics. These models form the basis for gait generation via (nonlinear) optimization problems. Finally, models and their generated gaits merge in the context of real-time control, wherein walking behaviors are translated to hardware. The concepts presented are illustrated throughout in simulation, and experimental instantiations on multiple walking platforms are highlighted to demonstrate the ability to realize dynamic walking on bipedal robots that is both agile and efficient. <\/jats:p>","DOI":"10.1146\/annurev-control-071020-045021","type":"journal-article","created":{"date-parts":[[2020,12,11]],"date-time":"2020-12-11T23:27:54Z","timestamp":1607729274000},"page":"535-572","source":"Crossref","is-referenced-by-count":76,"title":["Dynamic Walking: Toward Agile and Efficient Bipedal Robots"],"prefix":"10.1146","volume":"4","author":[{"given":"Jenna","family":"Reher","sequence":"first","affiliation":[{"name":"Department of Mechanical and Civil Engineering, California Institute of Technology, Pasadena, California 91125, USA;,"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Aaron D.","family":"Ames","sequence":"additional","affiliation":[{"name":"Control and Dynamical Systems Graduate Program, California Institute of Technology, Pasadena, California 91125, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"22","reference":[{"key":"B1","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.2006.1920"},{"key":"B2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02629836"},{"key":"B3","doi-asserted-by":"publisher","DOI":"10.1016\/0025-5564(72)90061-2"},{"key":"B4","doi-asserted-by":"publisher","DOI":"10.1142\/S0219843604000083"},{"key":"B5","doi-asserted-by":"publisher","DOI":"10.1126\/science.1107799"},{"key":"B6","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.2006.1917"},{"key":"B7","doi-asserted-by":"publisher","DOI":"10.1109\/IRDS.2002.1041632"},{"key":"B8","doi-asserted-by":"publisher","DOI":"10.1109\/ICHR.2005.1573544"},{"key":"B9","doi-asserted-by":"publisher","DOI":"10.1109\/ICRA.2014.6907353"},{"key":"B10","first-page":"321","volume-title":"5th IEEE-RAS International Conference on Humanoid Robots","author":"Park IW","year":"2005"},{"key":"B11","doi-asserted-by":"publisher","DOI":"10.1177\/027836498400300207"},{"key":"B12","doi-asserted-by":"publisher","DOI":"10.1109\/MEX.1986.4307016"},{"key":"B13","first-page":"217","volume":"1","author":"H\u00fcrm\u00fczl\u00fc Y","year":"1986","journal-title":"Dyn. 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