I'd recommend reading The Dictator's Handbook - it is a great pop science summary of a huge body of research into how different forms of government sustain themselves.
The TL;DR from this book would be that what the dictator needs is the freedom to do whatever they want; for that, they need power; for power, they need support; for support, they need money to buy it; for money, they need...
Well, there are essentially two endpoints on a scale for how to raise money: either natural resources or people. You tend to get democracies when there are no natural resources, because money needs to be raised through taxing people. For that, people need to be healthy, reasonably educated, and content. The end result is that politicians in such a country tend to redistribute the wealth they raise from the people to the subset of people necessary to keep them in power - and in democracies, due to the education, health, etc, that tends to be a large subset.
Conversely, dictatorships happen when there is no need to keep people fed and healthy. When natural resource need a small fraction of people, and are consequently redistributed to a tiny minority of very powerful supporters.
So, a post-scarcity society with a dictatorship is somewhat of an anomaly.
Because without scarcity, you will very likely have a large base of the population sufficiently educated that they will make demands, and drive the country towards a democracy of sorts.
On the other hand, in a post-scarcity society, there really is no need for people any more - so also no need to keep them supplied. They can be cut out of the equation in the fund-raising game, leading to the worst kind of dictatorship imaginable.
Your use of robots leaves an interesting opening: they are effectively the third option in the fund raising game, instead of natural resources and biologically bred labour. The dictator would have to keep tight control over the robot population, and provide them much like their human counterparts with just enough to keep them ticking effectively.
As a contrived example (feel free to use it if you like it), maybe general AI isn't all that it's cracked up to be. Give robots general AI, and they start acting like humans and demanding fair treatment - with all the advantages at the negotiating table that a near-indestructible body brings with it. Specialized AI - such as for image recognition, etc. - on the other hand is so far advanced that humans seem crippled in comparison.
The breakthrough was to tap into people's brains - just a small part, not enough for them to even be fully aware of it or control it - and use this biological general AI to control the robots remotely. On the face of it, people don't work any more. A part of their brain does, though. But you don't really need to ask people to do this. You just stick the interface into their newborn heads (it works better when people grow into the robot, as it were), and keep them happy enough not to question this arrangement...
I'm pretty sure you can poke plenty of holes into this setup. My point is to provide something that seems somewhat sound in how dictatorships work.