The inventive rack control unit comprises at least one gripping arm (12) which is arranged on a rotating drive element (11) and with which a container (2) or a pallet is grasped for storing and displacing. The gripping arm (12) is inclined toward the direction of traction of the drive element (11) and describes, with cams (25), a path (26) that extends along at least one deviation area (10) of the transport element (11) essentially outside of the path (27) of said element (11). The course of movement is more simple and enables a higher level of efficiency while requiring less space. If two gripping arms (12, 12') are provided, one gripping arm (12) enters, with the cam (25) thereof, into a groove (4) of the container (2) from underneath during displacement, and the next gripping arm (12') enters, with the cam thereof (25), into another channel (4') from above. The containers (2) or the pallets are carefully transported, the chain load is reduced, and smaller vertical grids can be used without collisions.
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