A plane tractor that grips a nose gear of a plane is disclosed, which includes: a chassis; wheel modules connected to the chassis, with each wheel module including at least one actuator for inducing a vertical movement of the wheel module in relation to the chassis; a gripping platform for gripping the nose gear of a plane, with the platform together with the chassis having freedom of movement substantially in circular translation; and a damping and actuating means connecting the platform and the chassis.