The development of robot technology has received increased interest in three-wheeled mobile robots (TWMR) due to their flexibility and adaptability in various applications. However, due to the limitation of independent motion in all directions, highly nonlinear dynamics, and effects such as noise and wheel slippage, it is difficult to effectively control the motion of TWMR. In this paper, we studied the motion of TWMR through kinematic and dynamic models considering the phenomenon of wheel slippage. The lateral and longitudinal slippage components were added to the dynamic model, thereby designing the position control law using the backstepping method and the speed control law using the SMC method. We also adjusted the parameters of the controllers to help the robot perform trajectory tracking. In addition, controlling the input torque was performed to overcome the lateral and longitudinal slippage phenomena. The method was tested through simulations on MATLAB Simulink with different trajectory cases (circular trajectory, infinite trajectory, spiral trajectory). The results showed the suitability of the controller to the desired trajectory tracking problem of TWMR, and the trajectory tracking error converged to zero. This shows promise and is practical.