Positioning, 2013, 4, 153-159 http://dx.doi.org/10.4236/pos.2013.42015 Published Online May 2013 (http://www.scirp.org/journal/pos) 153 Dynamic Based SMC of Nonholonomic Mobile Robots Jafar Keighobadi, Mohammad Sadeghi Shahidi, Abazar Nezafat Khajeh, Khadijeh Alioghli Fazeli Faculty of Mechanical Engineering, University of Tabriz, Tabriz, Iran. Email: keighobadi@tabrizu.ac.ir Received January 24 th , 2013; revised February 23 rd , 2013; accepted March 10 th , 2013 Copyright © 2013 Jafar Keighobadi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. ABSTRACT The aim of the paper is trajectory tracking control of a non-holonomic mobile robot whose centroid doesn’t coincide to its rotation center in the middle of connecting axle of driving wheels. The nonholonomic dynamic model of the Wheeled Mobile Robot (WMR) is developed in global Cartesian coordinates where the WMR’s forward and angular velocities are used as internal state variables. In order to include the effects of parameter uncertainties, measurement noises and other anomalies in the WMR system, a bounded perturbation vector is embedded to the developed dynamical model. Through defining the control inputs by computed torque method, a Dynamic Sliding Mode Controller (DSMC) is proposed to stabilize the sliding surfaces. Based on the proposed robust control system, the effect of uncertainties and noises in the robot performance is attenuated. By use of the WMR forward and angular velocities as internal state vari- ables in the dynamic modeling, the developed model is relatively simple and mainly independent of the robot states. This makes the dynamical model more robust against measurement errors. Design of the DSMC based on such a model leads to perfect trajectory tracking and compensation for initial off-tracks even in the presence of disturbances and modeling uncertainties. Keywords: Sliding Mode Control; Mobile Robot Dynamics; Robustness; Feedback Linearization 1. Introduction Nowadays, Wheeled Mobile Robots (WMRs) have found many applications in industry, transportation, and in- spection fields. Therefore, trajectory tracking control of nonholonomic WMRs has been an important problem in state of the art research works of recent literatures. The assumption of pure rolling and not slipping mo- tion leads to a non-integrable constraint in the kinematics of nonholonomic mobile robots. Since a non-holonomic system cannot be stabilized via smooth state feedback methods, the conventional linear control theories may not be applied to this class of systems [1]. Another important issue in real WMRs is arisen from parameter uncertain- ties, measurement noises and any other probable anoma- lies. In order to come over these problems and make the WMR converge to its reference trajectory, remarkable at- tempts have been done by researchers. For example, dif- ferent controllers of time-invariant, time-varying and hy- brid types based on Lyapunov control theories have been proposed by Kolmanovsky and McClamroch [2]. The global trajectory tracking problem has been discussed based on backstepping techniques [3]. In a research work done by Sun, the kinematic model of a mobile robot has been transformed into a linear time invariant system by state and input transformation, then, the pole-assignment method has been applied to design the controller [4]. Keighobadi, Menhaj and Kabganian have designed a mixed feedback-linearization and fuzzy controller for perfect trajectory tracking control of the WMR [5], see also [6-8] for more robust and intelligent applications. As a robust control approach, sliding mode controller (SMC) is recently receiving increasing attentions. The advantages of using SMCs are fast response, good tran- sient performance and significant robustness against pert- urbations and noises. This method is also respectively simple and doesn’t have complexities. The trajectory tracking of a nonholonomic WMR based on an improved sliding mode control method has been done in which the switch function of the variable structure control is de- signed based on the back stepping technique [9]. An artificial neural network based sliding mode control for nonholonomic WMRs has been applied to reduce the ef- fects of model uncertainty [10]. Shin, Kim and Koh have used a variable structure control law that makes the WMR converge to reference trajectories with bounded error of position and velocity components [11]. In tra- jectory tracking field, the controllers are designed com- Copyright © 2013 SciRes. POS