Adaptive control method and system in a terrestrial vehicle for tracking a route, particularly in an autonomous driving scenario

A method is described for the control of the lateral movement of a terrestrial vehicle arranged to track a predetermined trajectory, particularly in an assisted driving or autonomous driving scenario, comprising: determining a lateral offset of the vehicle center of mass from the predetermined trajectory; determining a look-ahead error defined as a distance of a virtual look-ahead position of the vehicle center of mass from the predetermined trajectory; and controlling the steering angle of the vehicle so as to also minimize the lateral offset and the first derivative of said look-ahead error over time.