An anticipating module for a device for controlling, in real time, the path of a motor vehicle includes a sub-module for computing a turning command for compensating for the curvature of a bend in the lane of the vehicle and a variable-gain device that is connected to an output of the computing sub-module. The gain of the variable-gain device is connected to a controller to adjust the gain so as to decrease the lateral offset between the centre of gravity of the vehicle and the centre of the lane of the vehicle depending on the result of the comparison of components of a vector of current measurements of state variables of the device to one another and to a detection threshold, the output of the variable-gain device being the steering command for compensating for the curvature of the bend.