A method for automatically controlling a vehicle includes giving a reference local path and a potential speed of the vehicle. The method also includes calculating a stirring angle automatic setpoint that makes it possible to calculate a lateral acceleration proportional to the square of the potential speed of the vehicle, making the vehicle describe an arc of a circle including a point of intersection with the reference local path at a distance from the vehicle. A speed setpoint is generated and set to a value equal to that of the potential speed when the lateral acceleration has a value lower than a maximum permissible lateral acceleration value and the value of the potential speed is decreased when the lateral acceleration has a value higher than or equal to the maximum permissible lateral acceleration value so as to calculate a reduced lateral acceleration by repeating the calculating.