What would an AI need to bootstrap recursively self improving robots?

I suspect if an AI has some particular goal that requires destroying humanity and manufacturing things in the aftermath, and is intelligent and capable enough to actually do it, then it will consider these things in advance, and set up whatever initial automation it needs to achieve this before destroying humanity. AI with enough planning capabilities to e.g. design a bioweapon or incite a nuclear war would probably be able to think ahead about what to do afterwards, would have its own contingencies in place, and would not need to rely on whatever tools humanity happens to leave lying around when it is gone.

You've touched on a point that many posts don't address - the realities of the real world. So many AI is going to kill us posts start with AI is coming then ? and then we all die. 

Look at something like Taiwan chip manufacture - it's incredibly cutting edge and complicated and some of it isn't written down! There are all kinds of processes that we don't patent for various reasons. So much of our knowledge is in process rather than actually written anywhere. 

And all of these processes are themselves the pinnacle of hundreds of other interlinked processes. 

Not only does the malevolent AI need to take over chip manufacturing, but it needs to control the Australian lithium mine, plus the Saudi oilfields to run the ship to get the stuff to where it needs to go plus everything else. Hope it has rubber ring manufacture down for when an engine needs a part. 

So many actual real world processes are incredibly complex involving webs of production which simply cannot be taken over by AI in any meaningful sense. 

Not even with a hoard of dexterous robots. 

Even if an AI had the ability to make dexterous robots, millions of them, and then scatter them all over the world, it would be required to take on almost the entirety of human manufacturing -- and we're goddamn lazy and don't write so much of it down anywhere. Even with observation over time it wouldn't pick up so many things. 

There are machines that operate specific processes where the knowledge group is incredibly small. Whoops, you killed them AI, sorry, no more ultra-pure materials for those chips you need. 

As for nanobots, it always reads a bit like a joke that an AI will have these incredible knowledge leaps that produce magical robots to do all the things. 

I think most of the time it's a handwavey attempt at addressing the real world realities of manufacturing and production. 

We had one flood and it nearly wiped out the world supply of RAM years ago. The truth is that so many processes the AI would need are incredibly concentrated, run by a small number of people, not written down in clear enough detail for anyone to pick up easily, and contain all kinds of secret knowledge no AI can obtain.