This paper relates to the problem of a path following task for a wheeled mobile platform of (2,0) type. Two kinematic control algorithms, Micaelli-Samson algorithm and Soetanto-Lapierre-Pascoal algorithm, which are based on either the Serret-Frenet frame with an orthogonal projection or the Serret-Frenet frame with a nonorthogonal projection of a robot on the desired path, were presented. The additional condition that should be imposed on the function δ, which is a parameter depending on a linear velocity of the robot and on a distance error, was described. The influence of the function δ on the convergence of the non-singular algorithm has been shown using computer simulations.