The dynamic modeling and trajectory tracking control of a mobile robot is handled by a hierarchical constraint approach in this study. When the wheeled mobile robot with complex generalized coordinates has structural constraints and motion constraints, the number of constraints is large and the properties of them are different. Therefore, it is difficult to get the dynamic model and trajectory tracking control force of the wheeled mobile robot at the same time. To solve the aforementioned problem, a creative hierarchical constraint approach based on the Udwadia–Kalaba theory is proposed. In this approach, constraints are classified into two levels, structural constraints are the first level and motion constraints are the second level. In the second level constraint, arbitrary initial conditions may cause the trajectory to diverge. Thus, we propose the asymptotic convergence criterion to deal with it. Then, the analytical dynamic equation and trajectory tracking control force of the wheeled mobile robot can be obtained simultaneously. To verify the effectiveness and accuracy of this methodology, a numerical simulation of a three-wheeled mobile robot is carried out.