I am not sure if inflation will work exactly the same in a world where AI/robots do all the work.

Inflation is driven by scarcity. More demand for a fixed/limited resource drives up the price. Historically, every good and service humans bought followed this pattern, so we didn’t even have to consider an alternative.

Already in our current economy, however, we have seen a good portion of our economy shift to things that do not have this characteristic. For example, take something like a video streaming service. The marginal cost for additional demand is small enough to be almost negligible; if everyone in the world decided they wanted a Netflix subscription, there wouldn’t suddenly be a shortage of streams or a run on episodes of The Great British Bake Off. They would have to build more datacenters, but the cost per additional user is tiny compared to almost every other traditional good that came before.

If AI and Robots start doing all work, then this would spread to more of the economy. The increase in productive capacity would severely reduce the limitations that have historically driven inflation. We obviously have to invest in building robots and AI, but once we have enough robots they would be making more of themselves and we would be limited by natural resources, but we could use robots to get more of those, too… and we could focus on clean energy, since we would have plenty of robots to do that work, too.