In this paper, the problem associated with accurate control of a four-wheel steering mobile robot following a path, while keeping different desired absolute orientations and ensuring different desired lateral deviations, is addressed thanks to a backstepping control strategy. In particular, the control of each steering angle is investigated through a new parallel steering approach based on an extended kinematic model of a bicycle-model robot assuming that the two front steering angles are equal and likewise for the two rear ones. Two control laws are then proposed to ensure a suitable path following according to orientation and position conditions. In order to balance the lateral effects, notably the sideslip angles, an observer has been used to estimate the sliding. This estimation permits to feed the proposed control laws appropriately, enabling an accurate path tracking and orientation keeping along the trajectory. This new point of view permits to achieve difficult manoeuvres in narrow environments such as a parallel parking or sharp turns. Previous approaches have focused on the control of four-wheel steering mobile robots with respect to the trajectory but do not combine path following with independent heading angle control and slippery conditions.