In this paper, a method of dynamic modeling and a dynamic control of a mobile robot are presented to show the superiority of the dynamic control comparing to the PD control. This dynamic model is derived from the cartesian coordinates using lagrange equations. Based upon the derived dynamic model, we implemented the dynamic control of the mobile robot using the computed torque method. Time varying non-linear friction terms are not incroporated in this dynamic model. Instead, those are considered as disturbances. This uncertainty in dynamic model of mobile robot is compensated by the outer loop controller using PD algorithm. The validity of this model and the control algorithm are confirmed through the experiments, where the dynamic control algorithm demonstrated robust velocity tracking performance against the unmodeled non-linear frictions. The superiority of this algorithm is demonstrated by comparing to classical PD control algorithm.