A reciprocating actuator includes at least one element moving reciprocally relative to a rack, a device for driving the moving element in a driving direction, an element for returning the moving element in an opposite direction, at least one sensor for detecting the position of the moving element, and a servocontrol adapted to deliver, for each displacement cycle of the moving element in the driving direction, at least one correction signal (S5) representative of the difference between the energy imparted on the moving element during at least one preceding cycle, and the nominal energy to be imparted on this moving element to displace it exactly to its extreme set-point position, and to adjust on each cycle the control signal of the driving device according to the correction signal (S5).