【文章內(nèi)容簡介】 ntripetal and Coriolis matrix,G(q)?Rn is the gravitational vector. Equation () represents the kinematics or steering system of a mobile robot. Notice that the noslip condition imposed a nonholonomic constraint described by (2), that it means that the mobile robot can only move in the direction normal to the axis of the driving wheels. ycos? xsin? =0 (2) B. Tracking Controller of Mobile Robot Our control objective is established as follows: Given a desired trajectory qd(t) and orientation of mobile robot we must design a controller that apply adequate torque τ such that the measured positions q(t) achieve the desired reference qd(t) represented as (3): 0)(lim ???? tqq dt （ 3） To reach the control objective, we are based in the procedure of [5], we deriving a τ(t) of a specific vc(t) that controls the steering system () using a Fuzzy Logic Controller (FLC). A general structure of tracking control system is presented in the Fig. 2. III. CONTROL OF THE KINEMATIC MODEL We are based on the procedure proposed by Kanayama et al. [10] and Nelson et al. [15] to solve the tracking problem for the kinematic model, this is denoted as vc(t). Suppose the desired trajectory qd satisfies (4): qd =0sincosdd??100ddwv (4) Using the robot local frame (the moving coordinate system xy in figure 1), the error coordinates can be defined as (5): e=Te (qd q),?eeeyx =1000cossin0sincos????? =?????dddyyxx (5) And the auxiliary velocity control input that achieves tracking for () is given by (6): vc =fc (e,vd ),ccwv =?? ekvekww ekevdyddxd s inc os321?? ?? (6) Where k1, k2 and k3 are positive constants. IV. FUZZY LOGIC CONTROLLER The purpose of the Fuzzy Logic Controller (FLC) is to find a control input τ such that the current velocity vector v to reach the velocity vector vc this is denoted as (7): 0vlim ???? vdt （ 7） As is shown in Fig. 2, basically the FLC have 2 inputs variables corresponding the velocity errors obtained of (7) (denoted as ev and ew: linear and angular velocity errors respectively), and 2 outputs variables, the driving and rotational input torques τ (denoted by F and N respectively). The membership functions (MF)[9] are defined by 1 triangular and 2 trapezoidal functions for each variable involved due to the fact are easy to implement putationally. Fig. 3 and Fig. 4 depicts the MFs in which N, C, P represent the fuzzy sets [9] (Negative, Zero and Positive respectively) associated to each input and output variable, where the universe of discourse is normalized into [1,1] range. Fig. 2. Tracking control structure Fig. 3. Membership function of the input variables ev and ew Fig. 4. Membership functions of the output variables F and N. The rule set of FLC contain 9 rules which governing the inputoutput relationship of the FLC and this adopts the Mamdanistyle inference engine [16], and we use the center of gravity method to realize defuzzification procedure. In Table I, we present the rule set whose format is established as follows: Rule i: If ev is G1 and ew is G2 then F is G3 and N is G4 Where G1..G4 are the fuzzy set associated to each variable and i= 1 ... 9. TABLE 1 FUZZY RULE SET In Table I, N means NEGATIVE, P means POSITIVE and C means ZERO. V. SIMULATION RESULTS Simulations have been done in Matlab174。 to test the tracking controller of the mobile robot defined in (1). We consider the initial position q(0) = (0, 0, 0) and initial velocity v(0) = (0,0). From Fig. 5 to Fig. 8 we show the results of the simulation for the case 1. Position and orientation errors are depicted in the Fig. 5 and Fig. 6 respectively, as can be observed the errors are sufficient close to zero, the trajectory tracked (see Fig. 7) is very close to the desired, and the velocity errors shown in Fig. 8 decrease to zero, achieving the control objective in less than 1 second of the whole simulation. We show in Fig. 9 the Simulink block diagram to test the controller. We also show in Fig. 10 the