Emerging industrial applications involving mobile manipulation in the presence of humans is driving attention to- wards steerable wheeled mobile robots (SWMR), since these can perform arbitrary 2D planar trajectories, providing a reasonable compromise between maneuverability (necessary for human avoiding algorithms) and effectiveness. In- stantaneous center of rotation (ICR) based kinematic models and controllers are the most suited for such robots, as they assure the existence of a unique ICR point at all times. However, unsatisfactory behavior do exist in numerous applications requiring frequent changes in the sign of the angular velocity command. This is typically the case for robot heading control: moving the ICR point from one border of the 2D ICR space to the other makes it pass by the robot geometric center, where only pure rotations are feasible. This behavior is not desirable and should be avoided. In this paper, we propose a novel complementary route ICR controller, where the ICR can go from one extreme to the other by means of border switching in one sample period. Thanks to this approach, fast response to the velocity commands is achieved with little steering motion. The new algorithm has been tested successfully in simulations and experiments, and is more time efficient with far more satisfactory behavior than the state-of-art direct route based controllers. These results have been also confirmed quantitatively, using a newly developed metric, the command fulfillment index (CFI).