{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,26]],"date-time":"2025-10-26T14:15:02Z","timestamp":1761488102368},"reference-count":22,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2009,7,1]],"date-time":"2009-07-01T00:00:00Z","timestamp":1246406400000},"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":[[2009,7]]},"abstract":"<jats:title>SUMMARY<\/jats:title><jats:p>The purpose of our research is to study the effects of circular arc feet on the biped walk with a geometric tracking control. The biped studied is planar and is composed of five links and four actuators located at each hip and each knee thus the biped is underactuated in single support phase. A geometric evolution of the biped configuration is controlled, instead of a temporal evolution. The input-output linearization with a PD control law and a feed forward compensation is used for geometric tracking. The controller virtually constrains 4 degrees of freedom (DoF) of the biped, and 1 DoF (the absolute orientation of the biped) remained. The temporal evolution of the remained system with impact events is analyzed using Poincar\u00e9 map. The map is given by an analytic expression based on the angular momentum about the contact point. The effect of the radii of the circular arc feet on the stability is studied. As a result, the speed of convergence decreases when the radii increases, if the radius is larger than the leg length the cyclic motion is not more stable. Among the stable cyclic motion, larger radius broadens the basin of attraction. Our results agree with those obtained for passive dynamic walking on stability, even if the biped is controlled through the geometric tracking.<\/jats:p>","DOI":"10.1017\/s0263574708005006","type":"journal-article","created":{"date-parts":[[2008,8,20]],"date-time":"2008-08-20T04:16:15Z","timestamp":1219205775000},"page":"621-632","source":"Crossref","is-referenced-by-count":12,"title":["Effect of circular arc feet on a control law for a biped"],"prefix":"10.1017","volume":"27","author":[{"given":"T.","family":"Kinugasa","sequence":"first","affiliation":[]},{"given":"C.","family":"Chevallereau","sequence":"additional","affiliation":[]},{"given":"Y.","family":"Aoustin","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2009,7,1]]},"reference":[{"key":"S0263574708005006_ref20","doi-asserted-by":"crossref","unstructured":"20. Morris B. and Grizzle J. W. , \u201cA Restricted Poincare Map for Determining Exponentially Stable Periodic Orbits in Systems with Impulse Effects: Application to Bipedal Robots,\u201d Proceedings of IEEE Conference on Decision and Control, (2005) pp. 419 9\u20134206.","DOI":"10.1109\/CDC.2005.1582821"},{"key":"S0263574708005006_ref10","doi-asserted-by":"publisher","DOI":"10.7210\/jrsj.25.440"},{"key":"S0263574708005006_ref1","doi-asserted-by":"crossref","unstructured":"1. Aoustin Y. and Formal'sky A. M. , \u201cDesign of Reference Trajectory to Stabilize Desired Nominal Cyclic Gait of a Biped,\u201d Proceedings of the International Workshop on Robot Motion and Control, ROMOCO'99, (1999) pp. 159\u2013165.","DOI":"10.1109\/ROMOCO.1999.791069"},{"key":"S0263574708005006_ref2","doi-asserted-by":"publisher","DOI":"10.1109\/9.898695"},{"key":"S0263574708005006_ref8","doi-asserted-by":"publisher","DOI":"10.1177\/027836499000900206"},{"key":"S0263574708005006_ref9","doi-asserted-by":"crossref","unstructured":"9. Kinugasa T. , Hashimoto Y. and Fushimi H. , \u201cPassive Walking of Biped Emu with Attitude Control of Body,\u201d Proceedings of IEEE\/RSJ International Conference on Intelligent Robots and Systems (2003) pp. 346\u2013359.","DOI":"10.1109\/IROS.2003.1250652"},{"key":"S0263574708005006_ref7","doi-asserted-by":"publisher","DOI":"10.1177\/0278364904044410"},{"key":"S0263574708005006_ref17","doi-asserted-by":"crossref","unstructured":"17. Asano F. and Luo Z. W , \u201cOn Energy-Efficient and High-Speed Dynamic Biped Locomotion with Semicircular Feet,\u201d Proceedings of the 2006 IEEE\/RSJ International Conference on Intelligent Robots and Systems, (2006) pp. 5901\u20135906.","DOI":"10.1109\/IROS.2006.282470"},{"key":"S0263574708005006_ref12","unstructured":"12. Chevallereau C. and Djoudi D. , \u201cFeet can Improve the Stability Property of a Control Law for a Walking Robot,\u201d Proceedings of International Conference on Robotics and Automation, (2006) pp. 1206\u20131212."},{"key":"S0263574708005006_ref3","first-page":"159","article-title":"Control design for a biped reference trajectory based on driven angles as functions of the undriven Angle","volume":"42","author":"Aoustin","year":"2003","journal-title":"J. Comput. Syst. Sci. Int."},{"key":"S0263574708005006_ref22","doi-asserted-by":"publisher","DOI":"10.1017\/S0263574703005460"},{"key":"S0263574708005006_ref5","doi-asserted-by":"publisher","DOI":"10.9746\/sicetr1965.17.596"},{"key":"S0263574708005006_ref11","doi-asserted-by":"publisher","DOI":"10.20965\/jrm.2008.p0098"},{"key":"S0263574708005006_ref19","doi-asserted-by":"publisher","DOI":"10.1242\/jeb.02455"},{"key":"S0263574708005006_ref18","doi-asserted-by":"crossref","unstructured":"18. Asano F. and Luo Z. W. , \u201cThe Effect of Semicircular Feet on Energy Dissipation by Heel-strike in Dynamic Biped Locomotion,\u201d Proceedings of IEEE International Conference on Robotics and Automation, (2007) pp. 3976\u20133981.","DOI":"10.1109\/ROBOT.2007.364089"},{"key":"S0263574708005006_ref4","doi-asserted-by":"publisher","DOI":"10.1109\/MCS.2003.1234651"},{"key":"S0263574708005006_ref16","doi-asserted-by":"crossref","unstructured":"16. Wisse M. , Hobbelen D. G. E. , Rotteveel R. J. J. , Anderson S. O. and Zeglin G. J. , \u201cAnkle Springs Instead of Arc-shaped Feet for Passive Dynamic Walkers,\u201d Proceedings of Humanoids 2006, (2006) pp. 110\u2013116.","DOI":"10.1109\/ICHR.2006.321371"},{"key":"S0263574708005006_ref15","doi-asserted-by":"publisher","DOI":"10.1109\/TRO.2004.838030"},{"key":"S0263574708005006_ref13","doi-asserted-by":"publisher","DOI":"10.1109\/TRO.2007.913563"},{"key":"S0263574708005006_ref6","unstructured":"6. Kajita S. and Tani K. , \u201cStudy of Dynamic Biped Locomotion on Rugged Terrain \u2013 Derivation and Application of the Linear Inverted Pendulum Mode,\u201d Proceedings of IEEE International Conference on Robotics and Automation (1991) pp. 1405\u20131411."},{"key":"S0263574708005006_ref14","unstructured":"14. Wisse M. and Frankenhuyzen J. van , \u201cDesign and Construction of Mike; A 2D Autonomous Biped based on Passive Dynamic Walking,\u201d Proceedings of Conference on Adaptive Motion of Animals and Machines WeP-I-1, Springer, Tokyo (2003)."},{"key":"S0263574708005006_ref21","doi-asserted-by":"publisher","DOI":"10.1115\/1.1427703"}],"container-title":["Robotica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0263574708005006","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,5]],"date-time":"2019-04-05T19:34:29Z","timestamp":1554492869000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0263574708005006\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,7]]},"references-count":22,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2009,7]]}},"alternative-id":["S0263574708005006"],"URL":"https:\/\/doi.org\/10.1017\/s0263574708005006","relation":{},"ISSN":["0263-5747","1469-8668"],"issn-type":[{"value":"0263-5747","type":"print"},{"value":"1469-8668","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,7]]}}}