I've played through 3 games as the YOR on the 3.02 build. Long story short:

Dependence on Promethion absolutely cripples robots. Please consider making "Build Population" require no special resources.

The recent v3.x move to make 1.0 pop units the minimum for colony ships only makes the problem worse.

Here's how it usually plays out:

I start with 5 pops on my homeworld. I build 2-4 colony ships and try to grab what i can while the gettin's good. Because of the 1-unit colony ship minimum, i'm out of administrators and also out of population, my homeworld now down to a skeleton crew. Now there is simply no way to expand any further, the production rate is crippled on every colony i have, and there is no good way to dig out of that hole.

And it stays this way for a very, very long time unless you happen upon a big clutch of Promethion. If you don't, there may not be a way to get any, especially if playing against high AI which will not trade any to you. In resource-poor galaxies, robots don't stand a chance.

It goes this way for the AI as well. Here are some stats for the AI populations at turn 36 on my most recent game (mixed AI difficulties, no invasions have occurred yet).

Organic AI populations: 119, 39, 34, 32, 20, 19, 19

Robots: 9, 7, 7 (myself)

It used to be that the YOR and other robotic civs started out slow but became a freight train if you let them alone too long. I thought this was an interesting way of developing them. Now however, they are extra gimpy and can't find a way to be much better. Removing the special resource requirement from their Build Population and increasing the build time would fix the issue.