Wheeled mobile robot dynamics and suitable controller design are challenging but rewarding fields of study. By understanding the dynamics of wheeled mobile robots, it could be possible to design suitable hybrid control schemes for wheeled mobile robots. Since hybrid control schemes involve combining individual control methods to create a more effective overall control strategy. This can be done in a variety of ways, such as using fuzzy linear quadratic Gaussian control. We were therefore inspired to create dynamic models and their controller designs for the wheeled mobile robot by examining the dynamics of the wheeled mobile robot. The novelty of the current paper is to hybridize the different control schemes for wheeled mobile robots in order to get better performance. Entire systems models were simulated in a MATLAB/SIMULINK environment. The results obtained for the settling time response by FLQG were 87.1% over LQG; this study compared the effectiveness of current and previous FLQG controllers in external disturbances and found peak amplitude improvements of 71.25%. Therefore, the proposed controller is suitable for use with the wheeled mobile robot.