An orbital drilling device includes, on the same frame: a motor rotating a cutting tool on itself; a first, interior, eccentric, receiving the motor, mounted so as to be able to rotate; a second, exterior, eccentric, receiving the first eccentric, mounted so as to be able to rotate; a reference body, secured to the frame, receiving the second eccentric, mounted so as to be able to rotate; a first unit for driving the first eccentric; a second unit for driving the second eccentric, simultaneously with the rotation of the first eccentric; and a controller configured to reproduce any path of the cutting tool in the zone by continuous control of the angular offset between the first eccentric and the second eccentric.