Basic Income won't come naturally, look at how difficult a 40 hour week / 8hr day was to bring into existence. Basically, widespread strikes were required. The baseline productivity of the world is already sufficient for basic income, and/or increased leisure vs work weeks - the only thing that advanced automation might to in the future is make the disconnect between historical economic assumptions and modern productivity unavoidable from a political standpoint.
I feel this is a bit too early for basic income. That change will come to pass naturally when society will be able to continue to exist and function normally even if almost nobody will work. That would require some pretty hefty advancements in AI and robotics.
Basically, I don't see struggle-free basic income without the robots doing all the work for us.