Precision Instrument and Mechanology PIM PIM Volume1, Issue 1 April 2012 PP. 7-11 www. pim-journal.org ○ C World Academic Publishing 7 Tracking Control of a Nonholonomic Wheeled Mobile Robot Ibrahim M.H. Sanhoury 1 , Shamsudin H.M. Amin 2 , Abdul Rashid Husain 3 Centre for Artificial Intelligence and Robotics, Cybernetics Research Alliance, Universiti Teknologi Malaysia, 81310, Johor Bahru, Malaysia 1 sanhoury124@yahoo.com; 2 sham@fke.utm.my; 3 rashid@fke.utm.my Abstract-This paper proposed a tracking control law for the kinematic model of the nonholonomic wheeled mobile robot (WMR). A Lyapunov candidate function is used to prove the stability of the controller. Simulation results verify the effectiveness of the proposed control law, where, a better path tracking of the mobile robot is achieved. Keywords-Wheeled Mobile Robot; Trajectry Tracking; Steering System; Nonholonomic; Kinematic Model I. INTRODUCTION Nowadays, wheeled mobile robot (WMR) attracts researchers’ and industrial people’s attention due to its use in numerous applications, and its capability to carry out tasks that have been considered as hazardous, costly or impossible to humans. WMR experience nonholonomic constraints, which is the movement of the robot in the direction of axis of the driving wheels. The path tracking of WMR is a nonlinear problem [1], in addition, since the desired tracking path for the robots is correlated directly with time, the problem becomes very difficult for conducting research. However, many engineers and researchers have been attracted to apply their efforts to solving this issue [2-4]. The control problem for the path tracking is to design a control rule for the linear and angler velocity/acceleration of the nonholonomic WMR in order to track its desired path. The control scheme aims to minimize the error between the real and the desired path. The tracking error is occurred due to slippage, disturbances, noise, and the measured sensor errors form both internal and external sources [5]. The WMR can’t move laterally due to the nonholonomic constraint, and it is rolling but not sliding. The kinematic model of the WMR with two parallel wheels fails to meet the necessary condition for feedback stabilization. This indicates that no smooth or even continuous time invariant feedback law exists that makes the closed-loop system asymptotically stable. This attracts researchers’ interest to the complicated and attractive problem of mobile robot control. Dong synchronized the motion of the two driving wheels of the WMR by applying adaptive coupling control law [6]. Yang proposed a tracking control method for real navigation of nonholonomic WMR that based on a backstepping model and a biological inspired neural dynamics model which can resolve the speed jump problem [7]. Many researchers focused their work on motion planning of the WMR under nonholonomic constrains. Kanayama et al. and Samson et al. proposed a nonlinear feedback control law [4, 8]. Others proposed a robust control method to force the mobile robot to follow a reference path [9–11]. Many tracking controllers have been suggested, where in general, it can be categorized into four groups: linear [12], nonlinear [6-11], geometrical [13] and intelligent methods [14, 15]. Li considered the kinematics and dynamics models of the nonholonomic WMR, where an adaptive tracking algorithm was proposed based on the kinematic model of the WMR to solve the nonholonomic constraints for the mobile robot trajectory tracking [16]. Chwa suggested a sliding-mode control rule for the WMR in polar coordinates, where two controllers were developed to asymptotically stabilize the tracking errors of the position and orientation direction [17]. In this work, a new tracking controller is designed based on the Lyapunov direct method. The proposed controller is different from Kanayama work [4] in the linear velocity, where in Kanayama work, the linear velocity depends on the error in the forward directions and the heading error, where he ignores the lateral error. On the other hand, the angular velocity depends on the errors in the longitudinal direction and the orientation, respectively. Therefore, if the error in the x-direction is zero, and the error in the y-direction is large, in this case, Kanayama’s controller fails to stabilize the error. To solve this problem, a new term added to the linear velocity that depends on the error in the longitudinal coordinate, and the asymptotic stability of the tracking errors is proven based on Lyapunov approach. II. PROBLEM STATEMENT Fig. 1 shows the non-holonomic WMR, whose two rear wheels are differential driving wheels and the front wheel is additional shoring. The WMR are located in a two dimensional (2D) plane in the global Cartesian coordinate system, on the other hand, the robot possesses three dimensional (3D) for its positioning as represented by the posture. [ ] T x y θ = q (1) where the heading direction θ is taken counter clockwise from the x-axis and the forwarding direction of the WMR, and (x,y) is the coordinate of the WMR. The movement of the robot is controlled by its linear velocity v and the angler velocity w, where they represent the input to the system. [ ] T v w = u (2)