The mass center of non-holonomically constrained wheeled mobile robot (WMR) does not coincide with the geometric center. In order to solve this problem, the kinematics and dynamics modeling of mobile robot were carried out. The modeling process of WMR was analyzed in detail, and the model was simulated to verify the correctness of the established model. For this model, two controllers satisfying the Lyapunov stability condition were designed, namely PID kinematics controller and nonlinear feedback dynamics controller, and the comparative experiments were carried out. The experimental results show that the nonlinear feedback dynamic controller can control the trajectory tracking better than the PID kinematics controller and the error is smaller.