Those robots consume quite a bit of energy, I think racks hanging on linkages constraining their orientation (so they don't tilt) and constrain their translational motion to cycloids, so that a hanging rack can be let loose, swing across the lowest point and be caught at approximately the starting height but on the other side.
From wikipedia,
"The cycloid, with the cusps pointing upward, is the curve of fastest descent under uniform gravity (the brachistochrone curve). It is also the form of a curve for which the period of an object in simple harmonic motion (rolling up and down repetitively) along the curve does not depend on the object's starting position (the tautochrone curve)."
So swinging a rack along the cycloid is the fastest motion without having to contribute energy (apart from that to overcome friction etc.).
So you can have a large number of racks in the "left" position, choose to open a passage between racks 34 and 35 by having all racks >=35 swing to the right position. In this way all N racks can be accessed with only the loss of space of a single planar passage.
If everything which enters is weighed before insertion, the loading and unloading could happen near reversibly by arming or releasing appropriate counterweights.
Kinetic energy can also be stored gravitationally: accelerate (by dropping the weight) and decelerate (by lifting it again) for quick motions.
Better design for the ultimate cost center, energy consumption.