A kinematic modeling method is proposed which uses augmenting variables to match the dimensions of the input vector and output vector of each serial subchain of the mobile robots. Firstly, kinematic models of various type of wheels are derived including skidding and sliding velocities. Then the method of augmented generalized coordinates is applied to obtain inverse and forward kinematic models. The kinematic models derived by the direct inverse of the augmented matrices provide an accurate solution, which was not achievable by the modeling method based on the pseudo-inverse method which provides an approximate solution. Lastly, two kinematic models for typical, differential-driven mobile robots are presented to show the effectiveness of the proposed modeling method.