Omnidirectional mobile robots are widely used in studies and services as they are effective and efficient in moving in any direction regardless of their current orientation. These significant properties are very useful in energy-efficient navigation and obstacle avoidance in dynamic environments. The literature on modeling and control of omni-wheel robots usually relies on the kinematic model or simplified kinematic model. Then developing control laws based on these reduced-effect models. In this article, we developed an efficient full dynamic model of a nonholonomic omni-wheel robot, including roller dynamics. That allows for a proportional–integral–derivative control law to accurately follow arbitrary paths. Kane’s approach was used for the dynamic model derivation. Kinematic modeling is less complex than multibody dynamic modeling. But to have an accurate simulation of the realistic motions of a mechanical system, the multibody dynamic model is required.