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In this paper, in order to cope with both parametric and nonparametric uncertainties in the robot model, an optimal Mamdani-type fuzzy logic controller is introduced for trajectory tracking of wheeled mobile robots (WMRs). The dynamic model of a nonholonomic mobile robot was implemented in the Matlab/Simulink environment. The parameters of input and output membership functions, and PID controller coefficients are optimized simultaneously by random inertia weight Particle Swarm Optimization (RNW-PSO). Simulation results show the system performance is desirable.