Expect a big drop in fulfillment center workers when Amazon gets bin picking that works.
Thinking from first principles helps. First, simplify the problem domain. The challenges are generally oddball shapes (think: heavy golf club), heavy items, speed, spatial efficiency, specialist handling requirements, environment, reliability, mobility and cost. If you have unlimited patience (retries allowed, no hard speed requirement) and less limited space (more power, better viewing angles, opportunity for stereoscopic vision), roughly similar form factor SKUs (=CPG), a purpose-built environment and no special handling requirements (nuclear waste/fresh food/fast-melting ice cream), no mobility requirement or cost sensitivity, then it's much easier.
Second, simplify handling by batching items in standard containers. What these system vendors never show you is how much they overcharge you for plastic boxes and how much energy is wasted loading, unloading and cleaning them.
Third, a grid-based system is clearly the most spatially efficient, so design around that.
In these systems the true spatial efficiency for most items is probably poor as Dematic Autostore for instance only offer 3 bin sizes. The true spatio-temporal efficiency is probably middling except when considered in parallel for huge order throughput requirements and a large number of SKUs because an untrained primate can pick faster than a bot for arbitrary items in most cases. Capex is very high, so these systems only make sense if you have a guaranteed large-SKU picking problem that won't go away, and you don't care about owning the knowledge to implement it cost-efficiently (eg. you are a manager looking out for #1 instead of the company's long term bottom line).
These things are terrible for the world, however, as they basically enable the accelerated consumption of single use plastics which is the CPG industry as a whole. I predict that in progressive countries such systems will be taxed or outlawed within our lifetimes, probably first in Europe, probably first in Holland as they are so good with agriculture and logistics.