Stabilization of motion of a wheeled robot with constrained control resource by means of a continuous feedback linearizing the closed-loop system in a neighborhood of the target path is considered. The problem of selection of the feedback coefficients is set and discussed. In the case of a straight target path, the desired feedback coefficients are defined to be those that result in the partition of the phase plane into two invariant sets of the nonlinear closed-loop system while ensuring the greatest asymptotic rate of the deviation decrease. A hybrid control law is proposed that ensures the desired properties of the phase portrait and minimal overshooting and is stable to noise. The proposed techniques are extended to the case of circular target paths.