Supply doesn't matter. The land owning class, me, gives no shit about supply. We'll all just raise rates to match what the government gives. Why wouldn't we? This is exactly what happens with any government entitlement. Medicare covers mobility scooters up to $5000. Guess what? My $2500 scooter now costs $5000. My competitors will do the same. Then in a day that becomes the new norm.
That's only one problem with UBI. The others are worse like in a generation you have people who have no useful skills, so once those robots running everything aren't competitive with robots from market economies that don't do UBI and expect people to work and be competitive and find innovations, then our goods are too expensive and our economy collapses because we all decided to model ourselves after a retirement arts community. Not to mention that history has shown that if you give people enough cash to just get by, they tend to lean towards a leisure lifestyle of drug abuse, gambling, non-education, non-productivity, etc. Why not? If no worries, then you might as well party. People in the ghetto aren't any different than you and me. They just realized that a lifetime of welfare means a lifetime of leisure, so they adapt to a leisure lifestyle and deal with all the problems that brings.
Lastly, robots aren't magically going to remain competitive by themselves. Industries won't magically take care of themselves. Even with heavy automation you still need people coming in day in and day out to make sure we don't fall behind the curve. If a Chinese robot can make 100 dresses in 5 minutes and ours can only make 50, then suddenly we're in a lot of trouble as our per item cost has literally doubled. If anything, the tech arms race is heavily accelerated because the stakes are so much higher. We'd probably have record levels of employment and education to just keep up.