{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,6]],"date-time":"2026-01-06T13:49:39Z","timestamp":1767707379064,"version":"3.37.0"},"reference-count":18,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2009,3,9]],"date-time":"2009-03-09T00:00:00Z","timestamp":1236556800000},"content-version":"unspecified","delay-in-days":4695,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotica"],"published-print":{"date-parts":[[1996,5]]},"abstract":"<jats:title>SUMMARY<\/jats:title><jats:p>Many studies on control of dynamic biped walking have been done in the past two decades. While the biped dynamics is highly nonlinear, the stability analysis, if done, is usually based on a linearized model. The validity of the linearized model may become questionable if the walking involves states that are too far away from the operating point. In this paper, an approach for evaluating the robustness based on the linearized Poincare map is suggested and examined. The Poincare map is a useful tool to investigate the periodic motion of a dynamic system. Using the Poincare\u201c map, one can study an associated discrete time map instead of studying the continuous time system directly. Investigation of stability of a periodic motion can be reduced to the study of the stability of a fixed point of the Poincar\u00e9 map. The computational method that results in a measurement for evaluating the robustness of biped locomotion is developed. Our simulation study has verified that the suggested measurement is a good indicator.<\/jats:p>","DOI":"10.1017\/s0263574700019561","type":"journal-article","created":{"date-parts":[[2009,3,10]],"date-time":"2009-03-10T13:10:05Z","timestamp":1236690605000},"page":"253-259","source":"Crossref","is-referenced-by-count":14,"title":["Measurement of robustness for biped locomotion using a linearized Poincar\u00e9 map"],"prefix":"10.1017","volume":"14","author":[{"given":"M. -Y.","family":"Cheng","sequence":"first","affiliation":[]},{"given":"C. -S.","family":"Lin","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2009,3,9]]},"reference":[{"key":"S0263574700019561_ref007","doi-asserted-by":"publisher","DOI":"10.1115\/1.3143833"},{"volume-title":"Genetic Algorithms in Search, Optimization and Machine Learning","year":"1989","author":"Goldberg","key":"S0263574700019561_ref018"},{"key":"S0263574700019561_ref008","doi-asserted-by":"publisher","DOI":"10.1177\/027836499000900207"},{"key":"S0263574700019561_ref010","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-4067-7"},{"key":"S0263574700019561_ref002","doi-asserted-by":"publisher","DOI":"10.1109\/TBME.1974.324294"},{"key":"S0263574700019561_ref004","doi-asserted-by":"publisher","DOI":"10.1177\/027836498400300208"},{"key":"S0263574700019561_ref009","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1140-2"},{"key":"S0263574700019561_ref003","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1979.1102105"},{"key":"S0263574700019561_ref006","doi-asserted-by":"publisher","DOI":"10.1115\/1.3143752"},{"key":"S0263574700019561_ref015","first-page":"31","article-title":"On the Measurement of Dynamic Stability of Human Locomotion","volume":"116","author":"Huzmuzlu","year":"1994","journal-title":"J. Biomechanical Engineering, ASME"},{"key":"S0263574700019561_ref001","doi-asserted-by":"publisher","DOI":"10.1109\/TBME.1970.4502681"},{"key":"S0263574700019561_ref011","doi-asserted-by":"publisher","DOI":"10.1177\/027836499101000602"},{"volume-title":"From Equilibrium to Chaos-Practical Bifurcation and Stability Analysis","year":"1988","author":"Seydel","key":"S0263574700019561_ref017"},{"key":"S0263574700019561_ref013","doi-asserted-by":"crossref","unstructured":"13. Hmam H. M. and Lawrence D. A. , \u201cRobustness Analysis of Nonlinear Biped Control Laws via Singular Perturbation Theory\u201d Proceedings of the 31st Conference on Decision and Control. Tucson. Arizona (Dec, 1992) pp. 2656\u20132661.","DOI":"10.1109\/CDC.1992.371335"},{"key":"S0263574700019561_ref012","doi-asserted-by":"publisher","DOI":"10.1177\/027836499301200301"},{"key":"S0263574700019561_ref005","doi-asserted-by":"publisher","DOI":"10.1016\/0005-1098(84)90099-2"},{"key":"S0263574700019561_ref014","doi-asserted-by":"publisher","DOI":"10.1115\/1.2900798"},{"volume-title":"A Treatise on Analytical Dynamics","year":"1965","author":"Pars","key":"S0263574700019561_ref016"}],"container-title":["Robotica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0263574700019561","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,8]],"date-time":"2025-02-08T04:53:13Z","timestamp":1738990393000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0263574700019561\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,5]]},"references-count":18,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1996,5]]}},"alternative-id":["S0263574700019561"],"URL":"https:\/\/doi.org\/10.1017\/s0263574700019561","relation":{},"ISSN":["0263-5747","1469-8668"],"issn-type":[{"type":"print","value":"0263-5747"},{"type":"electronic","value":"1469-8668"}],"subject":[],"published":{"date-parts":[[1996,5]]}}}