{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T18:30:32Z","timestamp":1777487432007,"version":"3.51.4"},"reference-count":52,"publisher":"Cambridge University Press (CUP)","issue":"10","license":[{"start":{"date-parts":[[2018,8,1]],"date-time":"2018-08-01T00:00:00Z","timestamp":1533081600000},"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":[[2018,10]]},"abstract":"<jats:title>SUMMARY<\/jats:title><jats:p>This study deals with the problem of trajectory tracking of wheeled mobile robots (WMR's) under non-holonomic constraints and in the presence of model uncertainties. To solve this problem, the kinematic and dynamic models of a WMR are first derived by applying the recursive Gibbs\u2013Appell method. Then, new kinematics- and dynamics-based multivariable controllers are analytically developed by using the predictive control approach. The control laws are optimally derived by minimizing a pointwise quadratic cost function for the predicted tracking errors of the WMR. The main feature of the obtained closed-form control laws is that online optimization is not needed for their implementation. The prediction time, as a free parameter in the control laws, makes it possible to achieve a compromise between tracking accuracy and implementable control inputs. Finally, the performance of the proposed controller is compared with that of a sliding mode controller, reported in the literature, through simulations of some trajectory tracking maneuvers.<\/jats:p>","DOI":"10.1017\/s0263574718000565","type":"journal-article","created":{"date-parts":[[2018,8,1]],"date-time":"2018-08-01T08:26:27Z","timestamp":1533111987000},"page":"1551-1570","source":"Crossref","is-referenced-by-count":39,"title":["Modeling and trajectory tracking control of a two-wheeled mobile robot: Gibbs\u2013Appell and prediction-based approaches"],"prefix":"10.1017","volume":"36","author":[{"given":"Hossein","family":"Mirzaeinejad","sequence":"first","affiliation":[]},{"given":"Ali Mohammad","family":"Shafei","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2018,8,1]]},"reference":[{"key":"S0263574718000565_ref37","doi-asserted-by":"publisher","DOI":"10.1109\/TCST.2009.2034639"},{"key":"S0263574718000565_ref43","doi-asserted-by":"publisher","DOI":"10.1080\/00207179508921561"},{"key":"S0263574718000565_ref9","doi-asserted-by":"publisher","DOI":"10.1109\/9.293207"},{"key":"S0263574718000565_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/S0967-0661(96)00205-5"},{"key":"S0263574718000565_ref5","doi-asserted-by":"publisher","DOI":"10.1115\/1.2897157"},{"key":"S0263574718000565_ref50","volume-title":"Nonlinear Systems","author":"Khalil","year":"1996"},{"key":"S0263574718000565_ref41","doi-asserted-by":"publisher","DOI":"10.1016\/S0921-8890(02)00172-0"},{"key":"S0263574718000565_ref45","first-page":"179","article-title":"A new approach for modelling and control of two-wheel anti-lock brake systems","volume":"225","author":"Mirzaeinejad","year":"2011","journal-title":"Proc. Institut. Mech. Eng., Part K: J. Multi-body Dyn."},{"key":"S0263574718000565_ref47","doi-asserted-by":"publisher","DOI":"10.1109\/TMECH.2017.2749002"},{"key":"S0263574718000565_ref18","doi-asserted-by":"publisher","DOI":"10.1109\/TCST.2002.804116"},{"key":"S0263574718000565_ref21","doi-asserted-by":"publisher","DOI":"10.1016\/S0947-3580(97)70059-1"},{"key":"S0263574718000565_ref16","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2013.12.036"},{"key":"S0263574718000565_ref3","doi-asserted-by":"crossref","unstructured":"O. Khatib , K. Yokoi , K. Chang , D. Ruspini , R. Holmberg , A. Casal and A. Baader , \u201cForce Strategies for Cooperative Tasks in Multiple Mobile Manipulation Systems,\u201d In: The 7th International Symposium on Robotics Research 7 ( G. Giralt and G. Hirzinger , eds.) (Springer, Berlin, 1996) pp. 333\u2013342.","DOI":"10.1007\/978-1-4471-1021-7_37"},{"key":"S0263574718000565_ref34","doi-asserted-by":"publisher","DOI":"10.1109\/TCST.2004.824953"},{"key":"S0263574718000565_ref26","first-page":"504","article-title":"Neural adaptive output feedback formation control of type (m, s) wheeled mobile robots","volume":"21","author":"Shojaei","year":"2016","journal-title":"IET Control Theory Appl."},{"key":"S0263574718000565_ref24","doi-asserted-by":"publisher","DOI":"10.1016\/S0005-1098(02)00229-7"},{"key":"S0263574718000565_ref42","doi-asserted-by":"publisher","DOI":"10.1016\/j.robot.2017.09.015"},{"key":"S0263574718000565_ref36","doi-asserted-by":"crossref","unstructured":"M. R. Azizi and J. Keighobadi , \u201cRobust sliding mode trajectory tracking controller for a nonholonomic spherical mobile robot,\u201d IFAC Proc. Vol. 47, 4541\u20134546 (2014).","DOI":"10.3182\/20140824-6-ZA-1003.01430"},{"key":"S0263574718000565_ref30","doi-asserted-by":"publisher","DOI":"10.3233\/ICA-2006-13307"},{"key":"S0263574718000565_ref14","doi-asserted-by":"publisher","DOI":"10.1016\/j.compag.2014.04.013"},{"key":"S0263574718000565_ref15","doi-asserted-by":"publisher","DOI":"10.1016\/j.scient.2012.05.001"},{"key":"S0263574718000565_ref10","doi-asserted-by":"crossref","unstructured":"K. Thanjavur and R. Rajagopalan , \u201cEase of Dynamic Modeling of Wheeled Mobile Robots (WMRs) Using Kane's Approach,\u201d Proceedings of the IEEE International Conference on Robotics and Automation, Albuquerque, New Mexico (1997) pp. 2926\u20132931.","DOI":"10.1109\/ROBOT.1997.606731"},{"key":"S0263574718000565_ref38","first-page":"130","article-title":"Fuzzy based navigation and control of a non-holonomic mobile robot","volume":"2","author":"Rashid","year":"2010","journal-title":"J. Comput"},{"key":"S0263574718000565_ref27","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2011.2176738"},{"key":"S0263574718000565_ref33","doi-asserted-by":"publisher","DOI":"10.1007\/s11044-015-9472-9"},{"key":"S0263574718000565_ref40","doi-asserted-by":"publisher","DOI":"10.1002\/asjc.480"},{"key":"S0263574718000565_ref23","doi-asserted-by":"publisher","DOI":"10.1109\/9.173153"},{"key":"S0263574718000565_ref6","unstructured":"N. Hootsmanns and S. Dubowsky , \u201cThe Motion Control of Manipulators on Mobile Vehicles,\u201d Proceedings of the IEEE Conference on Robotics and Automation (1991) pp. 2336\u20132341."},{"key":"S0263574718000565_ref28","doi-asserted-by":"publisher","DOI":"10.1016\/j.rcim.2010.07.007"},{"key":"S0263574718000565_ref12","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-014-1845-8"},{"key":"S0263574718000565_ref51","doi-asserted-by":"crossref","unstructured":"Y. Li , L. Zhu , Z. Wang and T. Liu , \u201cTrajectory Tracking for Nonholonomic Wheeled Mobile Robots based on an Improved Sliding Mode Control Method,\u201d Proceedings of the ISECS International Colloquium on Computing, Communication, Control, and Management (2009) pp. 55\u201358.","DOI":"10.1109\/CCCM.2009.5267989"},{"key":"S0263574718000565_ref2","doi-asserted-by":"publisher","DOI":"10.1016\/j.robot.2011.06.005"},{"key":"S0263574718000565_ref39","doi-asserted-by":"publisher","DOI":"10.1016\/j.robot.2010.03.014"},{"key":"S0263574718000565_ref7","doi-asserted-by":"crossref","unstructured":"K. Liu and F. L. Lewis , \u201cDecentralized Continuous Robust Controller for Mobile Robots,\u201d Proceedings of the IEEE Conference on Robotics and Automation, Cincinnati, OH (1990) pp. 1822\u20131827.","DOI":"10.1109\/ROBOT.1990.126273"},{"key":"S0263574718000565_ref29","doi-asserted-by":"publisher","DOI":"10.1049\/iet-cta.2011.0169"},{"key":"S0263574718000565_ref22","doi-asserted-by":"publisher","DOI":"10.1007\/s12555-009-0114-y"},{"key":"S0263574718000565_ref20","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2007.05.014"},{"key":"S0263574718000565_ref35","first-page":"169","article-title":"Adaptive sliding mode control of a wheeled mobile robot towing a trailer","volume":"229","author":"Keymasi Khalaji","year":"2015","journal-title":"Proc. Institut. Mech. Eng., I: J. Syst. Control Eng."},{"key":"S0263574718000565_ref48","volume-title":"Applied Nonlinear Control","author":"Slotine","year":"1991"},{"key":"S0263574718000565_ref11","doi-asserted-by":"publisher","DOI":"10.1017\/S0263574701003381"},{"key":"S0263574718000565_ref1","doi-asserted-by":"publisher","DOI":"10.1080\/00207179.2013.862597"},{"key":"S0263574718000565_ref4","unstructured":"G. J. Wiens , \u201cEffects of Dynamic Coupling in Mobile Robotic Systems,\u201d Proceedings of SME Robotics Research World Conference, Gaithersburg, Maryland (1989) pp. 43\u201357."},{"key":"S0263574718000565_ref46","first-page":"401","article-title":"Enhancement of vehicle braking performance on split-k roads using optimal integrated control of steering and braking systems","volume":"230","author":"Mirzaeinejad","year":"2016","journal-title":"Proc. Institution Mech. Eng., Part K: J Multi-body Dynamics"},{"key":"S0263574718000565_ref13","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2014.09.030"},{"key":"S0263574718000565_ref19","doi-asserted-by":"publisher","DOI":"10.1108\/03684921011021291"},{"key":"S0263574718000565_ref32","doi-asserted-by":"publisher","DOI":"10.1016\/j.robot.2016.01.002"},{"key":"S0263574718000565_ref44","doi-asserted-by":"publisher","DOI":"10.1016\/j.conengprac.2010.03.015"},{"key":"S0263574718000565_ref17","first-page":"121","volume-title":"Recent Trends in Mobile Robots","author":"de Wit","year":"1993"},{"key":"S0263574718000565_ref52","doi-asserted-by":"crossref","unstructured":"S. S. Vishnu Prasad , V. Pottakulath and M. S. Ajmal , \u201cDevelopment of Backstepping Sliding Mode Tracking Control for Wheeled Mobile Robot,\u201d Proceedings of the IEEE International Conference on Advanced Communication Control and Computing Technologies (ICACCCT) (2014) pp. 1013\u20131018.","DOI":"10.1109\/ICACCCT.2014.7019249"},{"key":"S0263574718000565_ref31","doi-asserted-by":"publisher","DOI":"10.5772\/56757"},{"key":"S0263574718000565_ref25","doi-asserted-by":"publisher","DOI":"10.1016\/j.conengprac.2009.11.011"},{"key":"S0263574718000565_ref49","doi-asserted-by":"publisher","DOI":"10.1016\/S0005-1098(02)00272-8"}],"container-title":["Robotica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0263574718000565","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,13]],"date-time":"2019-04-13T20:09:43Z","timestamp":1555186183000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0263574718000565\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,8,1]]},"references-count":52,"journal-issue":{"issue":"10","published-print":{"date-parts":[[2018,10]]}},"alternative-id":["S0263574718000565"],"URL":"https:\/\/doi.org\/10.1017\/s0263574718000565","relation":{},"ISSN":["0263-5747","1469-8668"],"issn-type":[{"value":"0263-5747","type":"print"},{"value":"1469-8668","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,8,1]]}}}