In this paper we suggest a new navigation strategy for nonholonomic wheeled mobile robots. The method is based on linear navigation functions with exponential and deviation terms. These linear navigation functions are based on the kinematics equations and the geometry of the navigation problem, where the robot's orientation angle is a linear function of the visibility angle. Another control law is suggested for the robot's linear velocity. This approach allows driving the robot from an initial configuration to a desired final configuration. The robot's orientation angle depends on four different parameters that allow to change the robot path in real time. The navigation functions are combined with a collision avoidance algorithm to avoid obstacles. The approach is illustrated using various simulation examples.