{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T17:16:55Z","timestamp":1772299015618,"version":"3.50.1"},"reference-count":27,"publisher":"Cambridge University Press (CUP)","issue":"12","license":[{"start":{"date-parts":[[2017,1,31]],"date-time":"2017-01-31T00:00:00Z","timestamp":1485820800000},"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":[[2017,12]]},"abstract":"<jats:title>SUMMARY<\/jats:title><jats:p>Trajectory tracking is one of the main control problems in the context of Wheeled Mobile Robots (WMRs). Control of underactuated systems has been focused by many researchers during past few years. In this paper, tracking control of a Tractor\u2013Trailer Wheeled Mobile Robot (TTWMR) has been discussed. TTWMR includes a differential drive WMR towing a passive spherical wheeled trailer. Spherical wheels in contrast with standard wheels make the robot highly underactuated with severe non-linearities. Underactuation is due to the use of spherical wheeled trailer to increase robots' maneuverability and degrees of freedom. In fact, standard wheels are subjected to non-holonomic constraints due to pure rolling and non-slip conditions, which reduce robot maneuverability. In this paper, after introducing the robot, kinematics and kinetics models are obtained. Then, based on a physical intuition, a novel control algorithm is developed for the robot, i.e. Lyapunov-PID control algorithm. Subsequently, singularity avoidance of the proposed algorithm is discussed and the stability of the algorithm is analyzed. Finally, simulation and experimental results are presented which reveal the effectiveness of the proposed algorithm.<\/jats:p>","DOI":"10.1017\/s0263574716000886","type":"journal-article","created":{"date-parts":[[2017,1,31]],"date-time":"2017-01-31T08:15:21Z","timestamp":1485850521000},"page":"2297-2318","source":"Crossref","is-referenced-by-count":39,"title":["Modeling and control of an underactuated tractor\u2013trailer wheeled mobile robot"],"prefix":"10.1017","volume":"35","author":[{"given":"Asghar","family":"Khanpoor","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ali Keymasi","family":"Khalaji","sequence":"additional","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":[[2017,1,31]]},"reference":[{"key":"S0263574716000886_ref11","doi-asserted-by":"publisher","DOI":"10.1016\/j.mechatronics.2008.09.004"},{"key":"S0263574716000886_ref21","doi-asserted-by":"publisher","DOI":"10.1049\/iet-cta.2009.0617"},{"key":"S0263574716000886_ref15","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2013.12.036"},{"key":"S0263574716000886_ref23","doi-asserted-by":"crossref","unstructured":"A. Khanpoor , A. K. Khalaji and S. A. A. Moosavian , \u201cDynamics Modeling and Control of a Wheeled Mobile Robot with Omni-Directional Trailer,\u201d 22nd Iranian Conference on, Electrical Engineering (ICEE), Tehran, Iran (2014) pp. 1254\u20131259.","DOI":"10.1109\/IranianCEE.2014.6999727"},{"key":"S0263574716000886_ref26","first-page":"97","article-title":"Non-Model Based Control for a Wheeled Mobile Robot Towing Two Trailers","volume":"229","author":"Khalaji","year":"2014","journal-title":"Proceeding of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics"},{"key":"S0263574716000886_ref17","doi-asserted-by":"publisher","DOI":"10.1177\/027836499000900206"},{"key":"S0263574716000886_ref10","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2007.07.013"},{"key":"S0263574716000886_ref2","doi-asserted-by":"crossref","first-page":"817","DOI":"10.1163\/156855312X633020","article-title":"Effect of terrain traction, suspension stiffness and grasp posture on the tip-over stability of wheeled robots with multiple arms","volume":"26","author":"Alipour","year":"2012","journal-title":"J. Adv. Robot."},{"key":"S0263574716000886_ref24","doi-asserted-by":"publisher","DOI":"10.1109\/TMECH.2013.2261534"},{"key":"S0263574716000886_ref6","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1109\/37.476384","article-title":"Developments in nonholonomic control problems","volume":"15","author":"Mc","year":"1995","journal-title":"IEEE Control Syst."},{"key":"S0263574716000886_ref20","doi-asserted-by":"crossref","unstructured":"M. W. Spong , \u201cUnderactuated Mechanical Systems,\u201d Proceedings of the Control Problems in Robotics and Automation (Springer, Berlin Heidelberg, 1998) pp. 135\u2013150.","DOI":"10.1007\/BFb0015081"},{"key":"S0263574716000886_ref25","first-page":"169","article-title":"Adaptive sliding mode control of a wheeled mobile robot towing a trailer","volume":"229","author":"Khalaji","year":"2015","journal-title":"Proc. Inst. Mech. Eng. Part I: J. Syst. Control Eng."},{"key":"S0263574716000886_ref9","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2003.817909"},{"key":"S0263574716000886_ref13","unstructured":"E. Yang , D. Gu , T. Mita and H. Hu , \u201cNonlinear Tracking Control of a Car-Like Mobile Robot Via Dynamic Feedback Linearization,\u201d Proceeding of Control Conference, Bath, United Kingdom (2004)."},{"key":"S0263574716000886_ref16","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2011.2176738"},{"key":"S0263574716000886_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/S0736-5845(03)00052-8"},{"key":"S0263574716000886_ref4","first-page":"242","article-title":"Dynamics of wheeled mobile robots with flexible suspension: Analytical model and verification","volume":"23","author":"Alipour","year":"2008","journal-title":"Int. J. Robot. Autom."},{"key":"S0263574716000886_ref12","doi-asserted-by":"publisher","DOI":"10.1016\/j.conengprac.2008.03.004"},{"key":"S0263574716000886_ref7","doi-asserted-by":"publisher","DOI":"10.1177\/0278364907076790"},{"key":"S0263574716000886_ref27","volume-title":"Analysis and Control of Nonlinear Process Systems","author":"Hangos","year":"2004"},{"key":"S0263574716000886_ref14","doi-asserted-by":"publisher","DOI":"10.1016\/j.mechatronics.2008.09.004"},{"key":"S0263574716000886_ref18","unstructured":"K. Y. Wichlund , O. J. S\u00f8rdalen and O. Egeland , \u201cControl of Vehicles with Second-Order Nonholonomic Constraints: Underactuated Vehicles,\u201d Proceedings of the European Control Conference, Rome, Italy (1995) pp. 3086\u20133091."},{"key":"S0263574716000886_ref1","volume-title":"Introduction to Autonomous Mobile Robots","author":"Siegwart","year":"2011"},{"key":"S0263574716000886_ref3","doi-asserted-by":"publisher","DOI":"10.1108\/01439911111106354"},{"key":"S0263574716000886_ref5","doi-asserted-by":"publisher","DOI":"10.1109\/70.481750"},{"key":"S0263574716000886_ref22","doi-asserted-by":"publisher","DOI":"10.1109\/TMECH.2008.2007482"},{"key":"S0263574716000886_ref19","doi-asserted-by":"publisher","DOI":"10.1115\/1.3143860"}],"container-title":["Robotica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0263574716000886","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,10,1]],"date-time":"2020-10-01T06:10:38Z","timestamp":1601532638000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0263574716000886\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,1,31]]},"references-count":27,"journal-issue":{"issue":"12","published-print":{"date-parts":[[2017,12]]}},"alternative-id":["S0263574716000886"],"URL":"https:\/\/doi.org\/10.1017\/s0263574716000886","relation":{},"ISSN":["0263-5747","1469-8668"],"issn-type":[{"value":"0263-5747","type":"print"},{"value":"1469-8668","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,1,31]]}}}