{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,19]],"date-time":"2025-10-19T15:49:41Z","timestamp":1760888981986},"reference-count":23,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2015,3,13]],"date-time":"2015-03-13T00:00:00Z","timestamp":1426204800000},"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":[[2017,1]]},"abstract":"<jats:title>SUMMARY<\/jats:title><jats:p>With regard to the small basin of attraction of the passive limit cycles, it is important to start from a proper initial condition for stable walking. The present study investigates the passive dynamic behaviors of two-dimensional bipedal walkers of a compass gait model with different foot shapes. In order to find proper initial conditions for stable and unstable period-one gait limit cycles, a method based on solving the nonlinear equations of motion is presented as a boundary value problem (BVP). An initial guess is required to solve the related BVP that is obtained by solving an initial value problem (IVP). For parametric analysis purposes, a continuation method is applied. Simulation results reveal two, period-one gait cycles and the effects of parameters variation for all models.<\/jats:p>","DOI":"10.1017\/s0263574715000077","type":"journal-article","created":{"date-parts":[[2015,3,13]],"date-time":"2015-03-13T07:31:46Z","timestamp":1426231906000},"page":"166-188","source":"Crossref","is-referenced-by-count":9,"title":["Determination of the initial conditions by solving boundary value problem method for period-one walking of a passive biped walking robots"],"prefix":"10.1017","volume":"35","author":[{"given":"Masoumeh","family":"Safartoobi","sequence":"first","affiliation":[]},{"given":"Morteza","family":"Dardel","sequence":"additional","affiliation":[]},{"given":"Mohammad","family":"Hassan Ghasemi","sequence":"additional","affiliation":[]},{"given":"Hamidreza","family":"Mohammadi Daniali","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2015,3,13]]},"reference":[{"key":"S0263574715000077_ref9","doi-asserted-by":"publisher","DOI":"10.1017\/S0263574704000475"},{"key":"S0263574715000077_ref21","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2007.05.008"},{"key":"S0263574715000077_ref15","unstructured":"A. Schwab and M. Wisse , \u201cBasin of Attraction of the Simplest Walking Model,\u201d Proceedings of Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Pittsburgh, Pennsylvania."},{"key":"S0263574715000077_ref16","volume-title":"Essentials of Dynamic Walking, Analysis and Design of Tow-Legged Robots","author":"Wisse","year":"2004"},{"key":"S0263574715000077_ref2","doi-asserted-by":"crossref","unstructured":"T. McGeer , \u201cPassive Walking with Knees,\u201d Proceedings of the IEEE Conference on Robotics and Automation (ICRA), Cincinnati, OH, USA; 13 May 1990 through 18 May 1990; Vol. 13 (1990), pp. 1640\u20131645.","DOI":"10.1109\/ROBOT.1990.126245"},{"key":"S0263574715000077_ref8","doi-asserted-by":"publisher","DOI":"10.1115\/1.2798313"},{"key":"S0263574715000077_ref13","unstructured":"A. Goswami , B. Thuilot and B. Espiau , \u201cCompass-like biped robot part I: Stability and bifurcation of passive gaits,\u201d Institut National de Recherche en Informatique et en Automatique (INRIA), Technical Report, (1996) p. 2996."},{"key":"S0263574715000077_ref11","doi-asserted-by":"publisher","DOI":"10.1016\/j.mechmachtheory.2006.11.001"},{"key":"S0263574715000077_ref3","doi-asserted-by":"publisher","DOI":"10.1163\/156855308X324811"},{"key":"S0263574715000077_ref10","doi-asserted-by":"publisher","DOI":"10.1017\/S0263574708005079"},{"key":"S0263574715000077_ref22","doi-asserted-by":"crossref","unstructured":"J. Li , Y. Tian and H. Chen , \u201cFoot Shape for Passive dynamic Kneed Biped Robot,\u201d Proceedings of the IEEE International Conference on Robotics and Biomimetics, Tianjin, China (December 14\u201318, 2010).","DOI":"10.1109\/ROBIO.2010.5723513"},{"key":"S0263574715000077_ref6","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2011.12.049"},{"key":"S0263574715000077_ref7","doi-asserted-by":"publisher","DOI":"10.1177\/027836499801701202"},{"key":"S0263574715000077_ref14","doi-asserted-by":"publisher","DOI":"10.1017\/S0263574708004906"},{"key":"S0263574715000077_ref12","first-page":"217","article-title":"The role of impact in the stability of bipedal locomotion","volume":"1","author":"Hurmuzlu","year":"1986","journal-title":"Int. J. Dyn. Stab. Syst."},{"key":"S0263574715000077_ref17","volume-title":"Exploring Passive-Dynamic Walking","author":"Berman","year":"2005"},{"key":"S0263574715000077_ref23","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511615542"},{"key":"S0263574715000077_ref5","doi-asserted-by":"publisher","DOI":"10.1016\/j.robot.2007.09.010"},{"key":"S0263574715000077_ref19","doi-asserted-by":"publisher","DOI":"10.5772\/55162"},{"key":"S0263574715000077_ref4","doi-asserted-by":"publisher","DOI":"10.1163\/156855308X324749"},{"key":"S0263574715000077_ref1","doi-asserted-by":"publisher","DOI":"10.1177\/027836499000900206"},{"key":"S0263574715000077_ref20","doi-asserted-by":"publisher","DOI":"10.1080\/02681110050032128"},{"key":"S0263574715000077_ref18","doi-asserted-by":"crossref","unstructured":"J. Kim , C. H. Choi and M. W. Spong , \u201cPassive Dynamic Walking with Symmetric Fixed Flat Feet,\u201d International Conference on Control and Automation, Guangzhou, China (May 30\u20131 Jun 2007).","DOI":"10.1109\/ICCA.2007.4376312"}],"container-title":["Robotica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0263574715000077","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,18]],"date-time":"2019-04-18T05:17:16Z","timestamp":1555564636000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0263574715000077\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,3,13]]},"references-count":23,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2017,1]]}},"alternative-id":["S0263574715000077"],"URL":"https:\/\/doi.org\/10.1017\/s0263574715000077","relation":{},"ISSN":["0263-5747","1469-8668"],"issn-type":[{"value":"0263-5747","type":"print"},{"value":"1469-8668","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,3,13]]}}}