Robot taxation is a bit like corporate income taxation. Like corporations, robots don't pay taxes, people pay taxes. In the words of Herb Stein:
I remember that in addressing the issue in the 1980s, the late Herb
Stein said that it's as if people think that if the government imposed
a tax on cows, the tax would be paid by the cows.
Are Taxes on Corporations Taxes on People? by David Henderson
There really are only three entities to tax. You can tax the people who own the robots, you can tax the people who buy what the robots make, or you can tax the income of people who work with robots. If you try to tax the robots directly, you'll end up with an effective combination of these other taxes.
In general, it is thought that the providers of capital are unlikely to bear very much of the incidence of taxation. Instead, it is thought that generally expected capital returns will adjust to keep the expected returns similar before and after the tax. This happens because capital is mobile. If the US tries to tax capital heavily investors can invest elsewhere, and will do so until after tax rates of return are equated. Robots are just another sort of capital, suggesting that it will be as difficult to tax them as any other sort of capital.
Taxing the buyers of robot produced goods is also problematic. As long as consumers can purchase imports without a special robot tariff then robotic produced imports will force domestic produced goods with a robotic tax to have a lower prices to leave consumers indifferent. Or they may not produce at all. Either way, consumers likely won't bear the burden.
Which leaves labor, the relatively immobile factor of production, to bear the burden.