J Electr Eng Technol.2016; 11(4): 1012-1019 http://dx.doi.org/10.5370/JEET.2016.11.4.1012 1012 Copyright ⓒ The Korean Institute of Electrical Engineers This is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/ licenses/by-nc/3.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. Robust Nonlinear Control of a Mobile Robot Ghania Zidani*, Said Drid † , Larbi Chrifi-Alaoui**, Djemaï Arar*** and Pascal Bussy** Abstract – A robust control intended for a nonholonomic mobile robot is considered to guarantee good tracking a desired trajectory. The main drawbacks of the mobile robot model are the existence of nonholonomic constraints, uncertain system parameters and un-modeled dynamics. in order to overcome these drawbacks, we propose a robust control based on Lyapunov theory associated with sliding-mode control, this solution shows good robustness with respect to parameter variations, measurement errors, noise and guarantees position and velocity tracking. The global asymptotic stability of the overall system is proven theoretically. The simulation results largely confirm the effectiveness of the proposed control. Keywords: Wheeled mobile robot (WMR), Kinematic control, Dynamic control, Nonlinear methods, Theorem Lyapunov, Nonholonomic mobile robot 1. Introduction One of the basic issues in the field of mobile robotics is the running path. The trajectory tracking is to guide the robot through intermediate points to arrive at the final destination. This guide is done under a time constraint, ie, the robot must reach the goal within a predefined time. In the literature, the problem is treated as the continuation of a robot reference (virtual processor) which moves to the desired trajectory with a certain pace. The real robot must follow this virtual robot accurately and try to minimize the error in distance, varying its linear and angular velocities [1-9]. There are lots of works on its tracking control. Their aims are mainly kinematic models; one method for dynamic models has been suggested [1]. In this case generally use linear and angular velocities of the robot (Fierro & Lewis, 1997; Fukao et al., 2000) or torques (Rajagopalan & Barakat , 1997; Topalov et al., 1998) as an input control vector [2]. The most authors determine the problem of mobile robot stability using nonlinear backstepping algorithm (Tanner & Kyriakopoulos, 2003) with steady parameters (Fierro & Lewis, 1997), or with the known functions (Oriollo et al., 2002) [1-6]. Other goals at the control architectures, the hybrid of the kinematic control, and the dynamic controller, the neural network controller, is proposed as some trajectory tracking methods [3]. In this paper, first, a kinematic controller is introduced to the WMR. Second, the dynamic controller, PI then Lyapunov theory associated to a sliding mode control, is proposed to make the actual velocity of the mobile robot to reach the wheel velocity control desired. 2. Kinematic Model Fig. 1 shows the typical model of a nonholonomic wheeled mobile robot. This last is operated by two independent wheels and with a passive wheel ensuring its stability. The posture of the WMR can be represented as [ ] q xy θ = (1) where the (, ) x y is the center of mass (COM) position of the WMR in the world X Y − coordinate, and θ is the included angle between the X-axis and ' X -axis † Corresponding Author: Laboratory LSPIE, Dept. of Electrical Engineering, Batna University, Algeria. (saiddrid@ieee.org) * Dept. of Electrical Engineering, Ouargla University, Algeria. (gh.zidani@gmail.com, zidani.gh@univ-ouargla.dz) ** Laboratoire des technologies innovantes (L.T.I), Université de Picardie Jules Verne, GEII, Cuffies, Soissons, France. ({larbi.alaoui, pascal.bussy}@u-picardie.fr) *** Advanced Electronics Laboratory (LEA), Dept. of Electronic, Batna University, Algeria. (d.arar@yahoo.fr) Received: September 28, 2014; Accepted: February 3, 2016 ISSN(Print) 1975-0102 ISSN(Online) 2093-7423 Fig. 1. Error posture of a nonholonomic WMR