Why would it need to be robotic? If the friction on those tracks is low enough, then it should be possible to move the whole setup by hand.
Even with low friction, you probably need to apply brakes at rest to avoid having it to move uncontrollably at the wrong time. But certainly it could be manual. By using a motorized motion, you have more freedom in the design, and you can likely move heavier load. Not everyone is necessarily fit enough to push, squat, or reach some part. But this is a good point and I hope you can use the system without power, becaus…
My point is mostly that the robotic part seems to be slapped on to make the whole thing seem more futuristic, when in reality it is just a clever design for a folding bed.