An order picking system comprising: - two uprights attached to two separate shelves ; - a self-guiding trolley having at least two running wheels for picking objects from an order in at least one of said racks , and motorised climbing means adapted to cooperate with said uprights so as to allow said trolley to rise along said uprights, said climbing means comprising two and only two toothed wheels and/or two and only two toothed belts with substantially parallel axes, each intended to cooperate with one of said two uprights , the axes of the toothed wheels and/or the axes of the pulleys driving said toothed belts being substantially orthogonal to the axes of the rolling wheels , each of said posts having a plurality of notches extending substantially perpendicular to the longitudinal axis of said post for receiving the teeth of said toothed wheel or toothed belt cooperating with that post and spaced apart by the amount of the pitch of said toothed wheel or toothed belt, each of the sprockets or toothed belts being mounted on a support movable relative to the frame of said carriage between two positions: - a retracted position, in which the sprocket or toothed belt mounted on said carrier faces said frame; and - a retracted position, in which the toothed wheel or toothed belt mounted on said support faces said frame; characterised in that said climbing means comprises means for preventing tilting of said carriage comprising at least one counterwheel for rolling on one of said posts , mounted on one of said supports, and in that said supports are mounted substantially at two opposite ends of the frame of said carriage , along a diagonal. - two uprights attached to two separate shelves ; - a self-guiding trolley having at least two running wheels for picking objects from an order in at least one of said racks , and motorised climbing means adapted to cooperate with said uprights so as to allow said trolley to rise along said uprights, said climbing means comprising two and only two toothed wheels and/or two and only two toothed belts with substantially parallel axes, each intended to cooperate with one of said two uprights , the axes of the toothed wheels and/or the axes of the pulleys driving said toothed belts being substantially orthogonal to the axes of the rolling wheels , each of said posts having a plurality of notches extending substantially perpendicular to the longitudinal axis of said post for receiving the teeth of said toothed wheel or toothed belt cooperating with that post and spaced apart by the amount of the pitch of said toothed wheel or toothed belt, each of the sprockets or toothed belts being mounted on a support movable relative to the frame of said carriage between two positions: - a retracted position, in which the sprocket or toothed belt mounted on said carrier faces said frame; and - a retracted position, in which the toothed wheel or toothed belt mounted on said support faces said frame; - a retracted position, in which the sprocket or toothed belt mounted on said carrier faces said frame; and - a retracted position, in which the toothed wheel or toothed belt mounted on said support faces said frame; characterised in that said climbing means comprises means for preventing tilting of said carriage comprising at least one counterwheel for rolling on one of said posts , mounted on one of said supports, and in that said supports are mounted substantially at two opposite ends of the frame of said carriage , along a diagonal. <EOS>