I write warehouse control systems for some of the world's biggest automated warehouses. There's very little in use that meets the colloquial usage of 'robot'. The shuttle ASRS systems mentioned are machines that technically fulfil the robot criteria, but you wouldn't look at one and call it a robot. The stuff that does look like a robot, the ROI just doesn't seem to be there just yet.
This is one area where Europe leads America still. In Europe, higher costs for land and unskilled labour mean logistics companies have been forced to automate more. ASRS solutions give much better storage density, and goods to person pick stations make much more efficient use of human labour (a person stands at a fixed station, and moves units from one box to another, the machines move all the boxes around).
I can't quite see where mobile robots are really going to make a leap forwards in the next few years in these sorts of warehouse. A little Kiva-style robot moving a pallet round is more flexible than fixed conveyors, but doesn't add any fundamental new capabilities: AGVs have been around for at least 18 years and they haven't really caught on in a big way. And unit picking robots like that Magazino right now are too finicky, and can't keep up with a goods to person station - it's just not an efficient use of machinery.
That will probably have changed in 10 or 20 years, but not by 2021.