With the widespread application of mobile robots in industries, services, and exploration, their capabilities in motion planning and obstacle avoidance have become a focal point of research. Nonholonomic constraints, especially those of wheeled mobile robots, significantly impact the motion planning of robots. This paper focuses on the nonholonomic characteristics of Differential Wheeled Robots (DWRs), establishes their kinematic and dynamic models, and analyzes the influence of these constraints on robot motion planning. By introducing the Lagrange multiplier method, nonholonomic constraints are incorporated into the dynamic equations, and the unknown multipliers are eliminated through transformation, resulting in the dynamic equations for DWRs. Moreover, the paper analyzes the controllability of the system using the Chow-Rashevskii theorem, proving that the DWR system is locally controllable in the short term.