An order picking system includes an automatic guided trolley for picking objects for an order in at least one shelving and having at least two running wheels and gear wheel supports cooperating with two pairs of uprights so as to allow the trolley to rise along the uprights. A stretched roller chain is fixed on each of the uprights, the chain extending substantially parallel to the longitudinal axis of the upright to which it is fixed to receive a tooth of the gear wheel cooperating with the upright to which it is fixed. Two adjacent rollers of the chain are spaced apart by the pitch value of the gear wheel. Each movable support has a securing element with one of the four uprights to maintain a predetermined distance between the axis of the gear wheel mounted on the movable support and the chain receiving the teeth of the gear wheel.