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In this paper, fuzzy control laws for steering control of an autonomous nonholonomic mobile robot are designed and analyzed. The approach uses Lyapunov's direct method to formulate a class of control laws that guarantee the convergence of the steering error. Certain requirements for the control laws are presented for the designers to choose a suitable rule base for the fuzzy controller in order to make the system asymptotically stable. The stability of the proposed fuzzy controller is theoretically proved and also demonstrated by simulation studies. Simulations using the model of a four degree of freedom nonholonomic mobile robot are conducted to investigate the performance of the fuzzy controller. The proposed fuzzy controller is also implemented on a nonholonomic mobile robot described by the model and the results show that the proposed fuzzy controller can achieve the desired turning angle and the autonomous mobile robot follows the target satisfactorily.