A method by which a floating offshore drilling rig, or an LNG vessel, is maintained in position over an offshore well location automatically in severe weather conditions including waves of up to 16 meters and wind speed of up to 41 meters per second. Generally, several motors called thrusters are located on the hull(s) of the structure and are actuated by a sensing system. A computer to which the system feeds signals then directs the thrusters to maintain the rig on location.