In recent years, autonomous mobile platforms are finding an increasing range of applications in inspection or surveillance tasks, or to the transport of objects, in places such as smart warehouses, factories or hospitals. In these environments it is useful for the robot to have omnidirectional capability in the plane, so it can navigate through narrow or cluttered areas, or make position and orientation changes without having to maneuver. While this capability is usually achieved with directional sliding wheels, this work studies a particular robot that achieves omnidirectionality using conventional wheels, which are easier to manufacture and maintain, and support larger loads in general. This robot, which we call ``Otbot'' (for omnidirectional tire-wheeled robot), was already conceived in the late 1990s, but all the controllers that have been proposed for it are based on purely kinematic models so far. These controllers may be sufficient if the robot is light, or if its motors are powerful, but on platforms that have to carry large loads, or that have more limited motors, it is necessary to resort to control laws based on dynamic models if the full acceleration capacities are to be exploited. This work develops a dynamic model of Otbot, proposes a plausible methodology to identify its parameters, and designs a control law that, using this model, is able to track prescribed trajectories in an accurate and robust manner.