{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,8]],"date-time":"2026-02-08T05:30:55Z","timestamp":1770528655152,"version":"3.49.0"},"reference-count":73,"publisher":"SAGE Publications","issue":"7","license":[{"start":{"date-parts":[[2021,5,31]],"date-time":"2021-05-31T00:00:00Z","timestamp":1622419200000},"content-version":"vor","delay-in-days":365,"URL":"http:\/\/www.sagepub.com\/licence-information-for-chorus"}],"funder":[{"DOI":"10.13039\/100000185","name":"Defense Advanced Research Projects Agency","doi-asserted-by":"publisher","award":["W91CRB-11-1-000221"],"award-info":[{"award-number":["W91CRB-11-1-000221"]}],"id":[{"id":"10.13039\/100000185","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["The International Journal of Robotics Research"],"published-print":{"date-parts":[[2020,6]]},"abstract":"<jats:p> In this article, we present a new controller for stable and robust walking control of ATRIAS, an underactuated bipedal robot designed based on the spring-loaded inverted pendulum (SLIP) model. We propose a forced-oscillation scheme for control of vertical motion, which we prove to be stable and contractive. Moreover, we prove that, through some mild assumptions, the dynamics of the system can be written in a hierarchical form that decouples the stability analyses of the horizontal and vertical directions. We leverage these properties to find a stabilizing class of functions for foot placement. The torso control is also proved to be decoupled using singular perturbation theory and is stabilized through a feedback linearization controller. We also take advantage of the proposed framework\u2019s flexibility and extend it to include a new reflex-based uneven-terrain walking control scheme. We test the controller for various desired walking speeds (0 to 2.5 m\/s), for stepping up and down unexpected obstacles (15 cm), and for high-speed walking on a random uneven terrain (up to 10 cm of step-ups and step-downs and up to 1.8 m\/s). The results show successful performance of the controller and its stability and robustness against various perturbations. <\/jats:p>","DOI":"10.1177\/0278364920916777","type":"journal-article","created":{"date-parts":[[2020,6,1]],"date-time":"2020-06-01T04:31:00Z","timestamp":1590985860000},"page":"774-796","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":17,"title":["Control of ATRIAS in three dimensions: Walking as a forced-oscillation problem"],"prefix":"10.1177","volume":"39","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0312-3167","authenticated-orcid":false,"given":"Siavash","family":"Rezazadeh","sequence":"first","affiliation":[{"name":"University of Denver, Denver, CO, USA"}]},{"given":"Jonathan W","family":"Hurst","sequence":"additional","affiliation":[{"name":"Oregon State University, Corvallis, OR, USA"}]}],"member":"179","published-online":{"date-parts":[[2020,5,31]]},"reference":[{"key":"bibr1-0278364920916777","doi-asserted-by":"publisher","DOI":"10.1177\/0278364904047389"},{"key":"bibr2-0278364920916777","doi-asserted-by":"publisher","DOI":"10.1515\/9781400833344"},{"key":"bibr3-0278364920916777","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9290(89)90224-8"},{"key":"bibr4-0278364920916777","doi-asserted-by":"publisher","DOI":"10.1007\/BF00197760"},{"key":"bibr5-0278364920916777","doi-asserted-by":"publisher","DOI":"10.1523\/JNEUROSCI.3155-08.2009"},{"key":"bibr6-0278364920916777","doi-asserted-by":"publisher","DOI":"10.1115\/1.2718237"},{"key":"bibr7-0278364920916777","doi-asserted-by":"publisher","DOI":"10.1177\/0278364919859425"},{"key":"bibr8-0278364920916777","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0601473103"},{"key":"bibr9-0278364920916777","author":"De A","year":"2015","journal-title":"arXiv preprint arXiv:1502.05347"},{"key":"bibr10-0278364920916777","unstructured":"DRL (2015a) ATRIAS bipedal robot: Takes a walk in the park. Dynamic Robotics Laboratory. Available at: https:\/\/www.youtube.com\/watch?v=dl7KUUVHC-M."},{"key":"bibr11-0278364920916777","unstructured":"DRL (2015b) ATRIAS robot: 9.1 kph running speed (5.7 mph). Dynamic Robotics Laboratory. Available at: https:\/\/www.youtube.com\/watch?v=U4eBRPHYCdA."},{"key":"bibr12-0278364920916777","unstructured":"DRL (2015c) ATRIAS robot: Climbs a 15-cm obstacle. Dynamic Robotics Laboratory. Available at: https:\/\/www.youtube.com\/watch?v=dOoQTPqnLqI."},{"key":"bibr13-0278364920916777","unstructured":"DRL (2015d) ATRIAS robot: Dodgeball barrage. Dynamic Robotics Laboratory. Available at: https:\/\/www.youtube.com\/watch?v=yYvrTc3-uVU."},{"key":"bibr14-0278364920916777","unstructured":"DRL (2015e) ATRIAS robot: Gets kicked. Dynamic Robotics Laboratory. Available at: https:\/\/www.youtube.com\/watch?v=5BF3uzXWfDY."},{"key":"bibr15-0278364920916777","unstructured":"DRL (2015f) ATRIAS robot: Runs to the end zone. Dynamic Robotics Laboratory. Available at: https:\/\/www.youtube.com\/watch?v=KeSkAPYAJc4."},{"key":"bibr16-0278364920916777","unstructured":"DRL (2015g) ATRIAS robot: Sidestepping. Dynamic Robotics Laboratory. Available at: https:\/\/www.youtube.com\/watch?v=yd4zTfjd0LI."},{"key":"bibr17-0278364920916777","unstructured":"DRL (2015h) ATRIAS robot: Traverses rough terrain at 6.6 kph (4.1 mph). Dynamic Robotics Laboratory. Available at: https:\/\/www.youtube.com\/watch?v=VBDysRlrfcY."},{"key":"bibr18-0278364920916777","unstructured":"DRL (2015i) Stand to walk (testing) 2015-01-15. Dynamic Robotics Laboratory. 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