This paper deals with the trajectory tracking control problem in the kinematic bicycle model. To avoid possible singular states in the control system for the model under consideration we apply a sigmoid function (hyperbolic tangent) in the feedback loop. We present an error function between the real and virtual vehicles that follows the required trajectory, and introduce a control law that stabilizes asymptotically the zero error state in the error dynamics. In addition, the proposed algorithm allows us to handle the control problem in cases where actuator saturations and state constraints exist. The paper is concluded with an example that demonstrate the characteristics of the control law and its performance.