Might be wrong, but my understanding is that China currently leads the world in robotic labor; meaning all robotic labor preformed by robots own by Chinese companies regardless of where the robots are.
True or Not, it makes no difference, given the choice between a robotic product made in china delivered in two weeks and a robotic product made in the USA delivered in 24 hours, consumers will always pick the later. And given this example why would the cost be any different to the consumer? If anything you would expect the Chinese example to have higher shipping costs. When talking about a truly competitive global economy which we do not really have no because of wildly different costs of labor. A robot in the US costs just as much to run as in China.
Where your customers are, insofar as there is capital and labor (even robotic factories break down) there to support it. That might mean onshoring for Americans, but I don't think that's true everywhere.
Look at how China is investing in Africa. In this hypothetical future, I can still see a country with large amounts of robotic equipment, lots of people educated to operate and program them, and good shipping infrastructure dominating global trade.
It will just be a highly developed China shipping to developing nations, instead of a developing China shipping to developed nations.
You can plug in your choice of robotic manufacturing country for China if you'd like, the point stands, but I see China as well positioned to maintain their lead in manufacturing if they are very smart.