In this paper a special adaptive control of a caster-supported Wheeled Mobile Robot (WMR) having two active wheels driven by electric DC motors is considered. In such electrical subsystems the first time-derivative of the motor current has a direct voltage control that is related to the 3rd time-derivative of the angle of the motor's axle, therefore the precise problem would be a 3rd order control task. Furthermore, when the tracked point of the WMR is different to the mass center point of the cart (in a rigid body approximation) the equations of motion become more complicated than those constructed for tracking the mass center point. Since the great majority of the control literature concentrates on the model based tracking of the mass center point we decided to build up the dynamic model of the WMR based on the fundamentals of Classical Mechanics. Following that a low (2nd order) adaptive controller was designed based on the use of Robust Fixed Point Transformations (RFPT) and the operation of this control method was investigated via simulation. The simulation results reveal that in spite of the kinematic constraints constraining the possible motion of this non-holonomic device the adaptive approach can improve the precision of the trajectory tracking of this 3rd order system.