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Then, from such approximation, the control actions to get a minimal tracking error are calculated. Both simulation and experimental results on a PIONEER 2DX mobile robot are presented, showing a good performance of the four proposed mobile robot controllers. Also, an application of the proposed controllers to a leader robot following problem is shown; in it, the relative position between robots is obtained through a laser.<\/jats:p>","DOI":"10.1017\/s0263574708004669","type":"journal-article","created":{"date-parts":[[2008,6,23]],"date-time":"2008-06-23T09:19:05Z","timestamp":1214212745000},"page":"269-279","source":"Crossref","is-referenced-by-count":41,"title":["Numerical methods based controller design for mobile robots"],"prefix":"10.1017","volume":"27","author":[{"given":"Gustavo","family":"Scaglia","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Luc\u00eda Quintero","family":"Montoya","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vicente","family":"Mut","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fernando","family":"di Sciascio","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2009,3,1]]},"reference":[{"key":"S0263574708004669_ref9","doi-asserted-by":"publisher","DOI":"10.1109\/70.880812"},{"key":"S0263574708004669_ref18","doi-asserted-by":"publisher","DOI":"10.1109\/70.481750"},{"key":"S0263574708004669_ref10","doi-asserted-by":"crossref","unstructured":"10. Kim S. , Shin J. and Lee J. , \u201cDesign of a Robust Adaptive Controller for a Mobile Robot,\u201d Proceedings of the 2000 IEEE\/RSJ International Conference on Intelligent Robots and Systems, Vol. 3, pp. 1816\u20131821.","DOI":"10.1109\/IROS.2000.895235"},{"key":"S0263574708004669_ref15","doi-asserted-by":"publisher","DOI":"10.1109\/MCS.2007.365004"},{"key":"S0263574708004669_ref3","doi-asserted-by":"publisher","DOI":"10.1016\/S0967-0661(99)00025-8"},{"key":"S0263574708004669_ref14","doi-asserted-by":"publisher","DOI":"10.1016\/j.rcim.2004.04.002"},{"key":"S0263574708004669_ref6","unstructured":"6. Tsuji T. , Morasso P. and Kaneko M. , \u201cFeedback Control of Nonholonomic Mobile Robots Using Time Base Generator,\u201d Proceedings of IEEE International Conference on Robotics and Automation, Nagoya Japan (1995), Vol. 2, pp. 1385\u20131390."},{"key":"S0263574708004669_ref7","doi-asserted-by":"crossref","unstructured":"7. Fierro R. and Lewis F. , \u201cControl of a Nonholonomic Mobile Robot: Backstepping Kinematics into Dynamics,\u201d Proceedings of the 34th Conference on Decision & Control, New Orleans, LA (Dec. 1995), Vol. 4, pp. 3805\u20133810.","DOI":"10.1109\/CDC.1995.479190"},{"key":"S0263574708004669_ref13","doi-asserted-by":"publisher","DOI":"10.1016\/S0736-5845(03)00052-8"},{"key":"S0263574708004669_ref11","doi-asserted-by":"publisher","DOI":"10.1109\/TCST.2004.824953"},{"key":"S0263574708004669_ref12","doi-asserted-by":"publisher","DOI":"10.1109\/TRA.2003.819730"},{"key":"S0263574708004669_ref2","unstructured":"2. Lee S. and Park J. H. , \u201cVirtual Trajectory in Tracking Control of Mobile Robots,\u201d Proceedings of the 2003 IEEE\/ASME International Conference on Advanced Intelligent Mechatronic (AIM 2003), Port Island, Kobe, Japan (2003) pp. 35\u201339."},{"key":"S0263574708004669_ref16","doi-asserted-by":"publisher","DOI":"10.1016\/S0967-0661(01)00066-1"},{"key":"S0263574708004669_ref17","doi-asserted-by":"publisher","DOI":"10.1109\/TCST.2003.819587"},{"key":"S0263574708004669_ref19","volume-title":"Linear Algebra and Its Applications","author":"Strang","year":"1980"},{"key":"S0263574708004669_ref5","doi-asserted-by":"publisher","DOI":"10.1016\/j.rcim.2005.03.002"},{"key":"S0263574708004669_ref20","unstructured":"20. Konolige K. , \u201cSaphira software manual version 6.1,\u201d Peterborough, NH-USA, ActivMedia Inc., October 1997."},{"key":"S0263574708004669_ref1","unstructured":"1. Del Rio F. , Jim\u00e9nez G. , Sevillano J. , Amaya C. and Balcells A. , \u201cError Adaptive Tracking for Mobile Robots,\u201d Proceedings of the 2002 28th Annual Conference of the IEEE Industrial Electronics Society, Saville, Spain (2002) pp. 2415\u20132420."},{"key":"S0263574708004669_ref8","doi-asserted-by":"crossref","unstructured":"8. Kanayama Y. , Kimura Y. , Miyazaki F. and Noguchi T. , \u201cA Stable Tracking Control Method for an Autonomous Mobile Robot,\u201d Proceedings of IEEE International Conference on Robotics and Automation, Cincinnati, Ohio (1990) pp. 384\u2013389.","DOI":"10.1109\/ROBOT.1990.126006"},{"key":"S0263574708004669_ref4","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1109\/87.911382","article-title":"Tracking control of unicicle-modeled mobile robots using a saturation feedback controller","volume":"9","author":"Lee","year":"2001","journal-title":"IEEE Trans. Control Syst. 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