{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T10:00:19Z","timestamp":1777716019762,"version":"3.51.4"},"reference-count":37,"publisher":"SAGE Publications","issue":"6","license":[{"start":{"date-parts":[[2004,6,1]],"date-time":"2004-06-01T00:00:00Z","timestamp":1086048000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["The International Journal of Robotics Research"],"published-print":{"date-parts":[[2004,6]]},"abstract":"<jats:p>In this paper we present the experimental validation of a framework for the systematic design, analysis, and performance enhancement of controllers that induce stable walking in N -link underactuated planar biped robots. Controllers designed via this framework act by enforcing virtual constraints\u2014holonomic constraints imposed via feedback\u2014on the robot\u2019s configuration, which create an attracting two-dimensional invariant set in the full walking model\u2019s state space. Stability properties of resulting walking motions are easily analyzed in terms of a two-dimensional subdynamic of the full walking model. A practical introduction to and interpretation of the framework is given. In addition, in this paper we develop the ability to regulate the average walking rate of the biped to a continuum of values by modification of within-stride and stride-boundary characteristics, such as step length.<\/jats:p>","DOI":"10.1177\/0278364904044410","type":"journal-article","created":{"date-parts":[[2004,5,29]],"date-time":"2004-05-29T03:24:04Z","timestamp":1085801044000},"page":"559-582","source":"Crossref","is-referenced-by-count":132,"title":["Experimental Validation of a Framework for the Design of Controllers that                Induce Stable Walking in Planar Bipeds"],"prefix":"10.1177","volume":"23","author":[{"given":"E. R.","family":"Westervelt","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, The Ohio State University,                        Columbus, Ohio 43210, USA,"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"G.","family":"Buche","sequence":"additional","affiliation":[{"name":"Laboratoire d\u2019Automatique de Grenoble, Ecole Nationale                        d\u2019Ing\u00e9nieurs Electriciens de Grenoble, BP 46, 38402 St                        Martin d\u2019H\u00e8res, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J. W.","family":"Grizzle","sequence":"additional","affiliation":[{"name":"Control Systems Laboratory, Electrical Engineering and Computer Science                        Department, University of Michigan, Ann Arbor, Michigan 48109-2122, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2004,6,1]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-9290(00)00101-9"},{"key":"atypb2","unstructured":"Berns, K. 2003. The walking machine catalogue. See http:\/\/www.clawar.com\/."},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1109\/9.668834"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1109\/MCS.2003.1234651"},{"key":"atypb5","doi-asserted-by":"crossref","unstructured":"Diop, S., Grizzle, J. W., Moraal, P. E., and Stefanopoulou, A. 1994. Interpolation and numerical differentiation for observer design . 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