The main core of this paper is to design a trajectory tracking control algorithm for mobile robot using a cognitive PID neural controller based slice genetic optimization in order to follow a pre-defined a continuous path. Slice Genetic Optimization Algorithm (SGOA) is used to tune the cognitive PID neural controller's parameters in order to find best velocities control actions of the right wheel and left wheel for the mobile robot. Pollywog wavelet activation function is used in the structure of the cognitive PID neural controller. Simulation results and experimental work show the effectiveness of the proposed cognitive PID neural tuning control algorithm; This is demonstrated by the minimized tracking error and the smoothness of the velocity control signal obtained, especially with regards to the external disturbance attenuation problem.