This paper addresses the control of wheeled mobile robots based on visual information of perspective lines. These lines can be generated by the projection of environment lines like those formed by the intersection of walls and floor, the structural features delimiting paths, or by painted lines on the floor. The control objective is to navigate at a desired speed along the lines, keeping a specified separating distance from them. No assumption is made on the absolute location of either the robot or the lines. A smooth time-invariant controller is proposed in order to command the angular velocity of the robot, while the linear velocity is generated to achieve a cautious and smooth motion. By invoking the LaSalle's invariance principle convergence is shown to a proper invariant set which guarantees accomplishment of the control objective. Finally, experimental results illustrating the performance of the control system are presented.