{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,5]],"date-time":"2026-02-05T11:18:13Z","timestamp":1770290293226,"version":"3.49.0"},"reference-count":35,"publisher":"Cambridge University Press (CUP)","issue":"8","license":[{"start":{"date-parts":[[2016,6,30]],"date-time":"2016-06-30T00:00:00Z","timestamp":1467244800000},"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":[[2017,8]]},"abstract":"<jats:title>SUMMARY<\/jats:title><jats:p>Legged robots may become unstable when subjected to unexpected disturbances such as external pushes and environmental irregularities mostly while moving on natural terrains. To enhance the mobility performance, legged robots should be able to keep or restore their balanced configuration when a sudden disturbance is exerted. The aim of this article is to design a controller for a quadruped robot to restore its balanced configuration despite exerting external pushes. This is achieved based on developing a full-dynamics model of the robot moving over even and uneven terrains. The proposed controller is based on a PD module which calculates the required accelerations for restoring the robot equilibrium. However, these accelerations may make the robot unstable and also cause the slippage of stance feet. Therefore, an optimization algorithm is used to compute the maximum admissible accelerations. The constraints of the optimization problem are the conditions which guarantee the robot stability and the stance feet slippage avoidance. The optimization algorithm is transformed into a linear constrained least-squares problem to be solved in real-time. The main contributions of this article are the development of a push recovery algorithm for quadruped robots and also the introduction of an appropriate condition which guarantees the stability of the robot even on uneven terrains. This stability condition is developed based on a full-dynamics model of the robot. The proposed algorithm is applied on an 18-DOF quadruped robot when the robot is standing over both even and uneven terrains. The obtained results show that the robot can successfully restore its balanced configuration by precise adjustment of the position and orientation of its main body while a massive external disturbance is exerted.<\/jats:p>","DOI":"10.1017\/s0263574716000394","type":"journal-article","created":{"date-parts":[[2016,6,30]],"date-time":"2016-06-30T06:36:49Z","timestamp":1467268609000},"page":"1670-1689","source":"Crossref","is-referenced-by-count":17,"title":["Push recovery of a quadruped robot on challenging terrains"],"prefix":"10.1017","volume":"35","author":[{"given":"Mahdi","family":"Khorram","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"S. Ali A.","family":"Moosavian","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2016,6,30]]},"reference":[{"key":"S0263574716000394_ref16","doi-asserted-by":"publisher","DOI":"10.1109\/ROBOT.2005.1570405"},{"key":"S0263574716000394_ref27","doi-asserted-by":"publisher","DOI":"10.1017\/S0263574713000829"},{"key":"S0263574716000394_ref1","first-page":"1928","volume-title":"Proceedings of the International Conference on Mechatronics and Automation","author":"Yu","year":"2009"},{"key":"S0263574716000394_ref29","doi-asserted-by":"crossref","unstructured":"C. Maufroy , H. Kimura and K. Takase , \u201cStable Dynamic Walking of a Quadruped via Phase Modulations Against Small Disturbances,\u201d IEEE International Conference on Robotics and Automation, ICRA'09. 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Schaal , \u201cMomentum-based balance control for torque-controlled humanoids,\u201d technical report, Computing Research Repository, arXiv preprint abs\/1305.2042 (2013) pp. 1\u20137."},{"key":"S0263574716000394_ref34","doi-asserted-by":"publisher","DOI":"10.1109\/TRO.2005.851380"},{"key":"S0263574716000394_ref35","volume-title":"15th International Conference on Climbing and Walking Robot","author":"Hutter","year":"2012"},{"key":"S0263574716000394_ref21","first-page":"26","volume-title":"Proceedings of IEEE-RAS International Conference on Humanoid Robots","author":"Ott","year":"2011"},{"key":"S0263574716000394_ref5","first-page":"52","volume-title":"10th IEEE-RAS International Conference on Humanoid Robots (Humanoids)","author":"Stephens","year":"2010"},{"key":"S0263574716000394_ref17","doi-asserted-by":"crossref","first-page":"2297","DOI":"10.1109\/ICRA.2014.6907177","volume-title":"IEEE International Conference on Robotics and Automation (ICRA)","author":"Wang","year":"2014"},{"key":"S0263574716000394_ref10","first-page":"589","volume-title":"Proceedings of IEEE-RAS International Conference on Humanoid Robots","author":"Stephens","year":"2007"},{"key":"S0263574716000394_ref7","first-page":"2799","volume-title":"Proceedings of IEEE International Conference on Robotics and Automation","author":"Yun","year":"2014"},{"key":"S0263574716000394_ref3","doi-asserted-by":"publisher","DOI":"10.1017\/S0263574708004268"},{"key":"S0263574716000394_ref14","first-page":"159","volume-title":"Proceedings of IEEE-RAS International Conference on Humanoid Robots","author":"Aftab","year":"2012"},{"key":"S0263574716000394_ref9","first-page":"10822","volume-title":"Proceedings of the 17th IFAC World Congress","author":"Raibert","year":"2008"},{"key":"S0263574716000394_ref11","doi-asserted-by":"crossref","unstructured":"J. Urata , K. Nshiwaki , Y. Nakanishi , K. Okada , S. Kagami and M. Inaba , \u201cOnline Walking Pattern Generation for Push Recovery and Minimum Delay to Commanded Change of Direction and Speed,\u201d IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), (2012), pp. 3411\u20133416.","DOI":"10.1109\/IROS.2012.6385840"},{"key":"S0263574716000394_ref8","doi-asserted-by":"publisher","DOI":"10.1007\/s10846-012-9812-4"},{"key":"S0263574716000394_ref30","first-page":"610","volume-title":"Proceedings of IEEE International Conference on Mechatronics","author":"Havoutis","year":"2013"},{"key":"S0263574716000394_ref12","doi-asserted-by":"publisher","DOI":"10.1017\/S0263574707003542"},{"key":"S0263574716000394_ref24","doi-asserted-by":"publisher","DOI":"10.1145\/1531326.1531386"},{"key":"S0263574716000394_ref2","first-page":"692","article-title":"Postural balance strategies in response to disturbances in the frontal plane and their implementation with a humanoid robot systems","volume":"44","author":"Yoshida","year":"2014","journal-title":"IEEE Trans. Man Cybern.: Syst."},{"key":"S0263574716000394_ref20","first-page":"1","article-title":"A force-resisting balance control strategy for a walking biped robot under an unknown, continuous force","author":"Kim","year":"2014","journal-title":"Robotica"},{"key":"S0263574716000394_ref15","first-page":"57","volume-title":"Proceedings of 7th IEEE-RAS International Conference on Humanoid Robots","author":"Atkeson","year":"2007"},{"key":"S0263574716000394_ref18","doi-asserted-by":"publisher","DOI":"10.1109\/TRO.2007.904896"},{"key":"S0263574716000394_ref22","first-page":"3253","volume-title":"Proceedings of IEEE\/RSJ International Conference on Intelligent Robots and Systems","author":"Henze","year":"2014"},{"key":"S0263574716000394_ref4","first-page":"200","volume-title":"Proceedings of IEEE-RAS International Conference on Humanoid Robots","author":"Pratt","year":"2006"},{"key":"S0263574716000394_ref28","first-page":"2554","volume-title":"IEEE International Conference on Robotics and Automation (ICRA)","author":"Barasuol","year":"2013"},{"key":"S0263574716000394_ref19","first-page":"1248","volume-title":"Proceedings of IEEE\/RSJ International Conference on Intelligent Robots and Systems","author":"Stephens","year":"2010"},{"key":"S0263574716000394_ref23","doi-asserted-by":"crossref","unstructured":"S. Kajita , F. Kanehiro , K. Kaneko , K. Fujiwara , K. Harada , K. Yokoi and H. Hirukawa , \u201cResolved Momentum Control: Humanoid Motion Planning Based on the Linear and Angular Momentum,\u201d Proceedings of IEEE\/RSJ International Conference on Intelligent Robots and Systems, vol. 1642 (2003) pp. 1644\u20131650.","DOI":"10.1109\/IROS.2003.1248880"},{"key":"S0263574716000394_ref32","doi-asserted-by":"publisher","DOI":"10.1163\/156855304322758033"},{"key":"S0263574716000394_ref33","unstructured":"M. Mistry , J. Buchli and S. Schaal , \u201cInverse Dynamics Control of Floating Base Systems Using Orthogonal Decomposition,\u201d Proceedings of IEEE International Conference on Robotics and Automation, (2010) pp. 3406\u20133412."},{"key":"S0263574716000394_ref6","doi-asserted-by":"publisher","DOI":"10.1007\/s10514-013-9343-2"},{"key":"S0263574716000394_ref25","doi-asserted-by":"publisher","DOI":"10.1007\/s10514-012-9294-z"},{"key":"S0263574716000394_ref13","first-page":"137","volume-title":"IEEE-RAS International Conference on Humanoid Robots","author":"Wieber","year":"2006"}],"container-title":["Robotica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0263574716000394","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,17]],"date-time":"2019-04-17T14:54:47Z","timestamp":1555512887000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0263574716000394\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,6,30]]},"references-count":35,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2017,8]]}},"alternative-id":["S0263574716000394"],"URL":"https:\/\/doi.org\/10.1017\/s0263574716000394","relation":{},"ISSN":["0263-5747","1469-8668"],"issn-type":[{"value":"0263-5747","type":"print"},{"value":"1469-8668","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,6,30]]}}}