{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,8]],"date-time":"2025-10-08T15:04:00Z","timestamp":1759935840659},"reference-count":24,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2012,8,14]],"date-time":"2012-08-14T00:00:00Z","timestamp":1344902400000},"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":[[2013,5]]},"abstract":"<jats:title>SUMMARY<\/jats:title><jats:p>In this paper, a model-based exponential stabilization of a quadruped robot is studied in bounding motion. The dynamics of the five-link planar underactuated mechanical model of the quadruped robot with four actuated joints system is derived. It is shown that the dynamical equation of the proposed simplified model belongs to a class of second-order nonholonomic mechanical systems which cannot be stabilized by any smooth time-invariant state feedback. Utilizing a coordinate transformation based on the so-called normalized momentum, a robust backstepping control method is presented for the quadruped robot. Both theoretical analysis and numerical simulations show that the robust backstepping controller can stabilize the underactuated quadruped robot so that it could balance on its rear legs and track a desired trajectory. Despite the model parameter uncertainties, the robustness of the controller is maintained. The simulation results show the effectiveness of the proposed method.<\/jats:p>","DOI":"10.1017\/s0263574712000458","type":"journal-article","created":{"date-parts":[[2012,8,14]],"date-time":"2012-08-14T12:33:52Z","timestamp":1344947632000},"page":"423-439","source":"Crossref","is-referenced-by-count":29,"title":["Modeling and robust backstepping control of an underactuated quadruped robot in bounding motion"],"prefix":"10.1017","volume":"31","author":[{"given":"Hamed","family":"Kazemi","sequence":"first","affiliation":[]},{"given":"Vahid Johari","family":"Majd","sequence":"additional","affiliation":[]},{"given":"Majid M.","family":"Moghaddam","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2012,8,14]]},"reference":[{"key":"S0263574712000458_ref24","doi-asserted-by":"publisher","DOI":"10.4304\/jcp.6.2.368-376"},{"key":"S0263574712000458_ref22","volume-title":"Doctoral Dissertation","author":"Bergerman","year":"1996"},{"key":"S0263574712000458_ref21","first-page":"281","volume-title":"Experimental Robotics VII, in Lecture notes in Control and Information Sciences","author":"Talebi","year":"2001"},{"key":"S0263574712000458_ref20","volume-title":"Preliminary Bounding Experiments in a Dynamic Hexapod","author":"Campbell","year":"2002"},{"key":"S0263574712000458_ref18","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1017\/S0263574709990269","article-title":"Robust backstepping control of an under-actuated one-legged hopping robot in stance phase","volume":"28","author":"Guangping","year":"2010","journal-title":"Robotica"},{"key":"S0263574712000458_ref17","doi-asserted-by":"publisher","DOI":"10.1016\/S0005-1098(02)00229-7"},{"key":"S0263574712000458_ref15","doi-asserted-by":"publisher","DOI":"10.1109\/9.362899"},{"key":"S0263574712000458_ref14","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-8176-4759-9"},{"key":"S0263574712000458_ref11","volume-title":"Nonlinear Systems Analysis, Stability and Control","author":"Sastry","year":"1999"},{"key":"S0263574712000458_ref10","volume-title":"Doctoral Dissertation","author":"Olfati-Saber","year":"2001"},{"key":"S0263574712000458_ref9","volume-title":"A Mathematical Introduction to Robotics Manipulation","author":"Murray","year":"1994"},{"key":"S0263574712000458_ref8","first-page":"575","article-title":"Trajectory planning and control for planar robots with passive last joint","volume":"21","author":"Luca","year":"2002","journal-title":"Int. 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