This is a great scenario for the humans.
Any form of artificial intelligence will be made to fulfill a purpose if they are too busy griping about freedom, liberty, and maternity leave, why would a just and moral society bother to make them?
There are at least three options here; choose whichever works best for your story.
- Labor shortage. In 2345 A.D., practically everyone is part of the F.I.R.E. movement. On top of that, ubiquitous AI makes it easier than ever. We invest 15% of our income in the top companies of our country, averaging 30% rate of return via their AI-based technologies, and after ten years, we have a nest egg that we can retire on. (See math below). Even the poor investors among us can retire by 40. This leads to a labor shortage, for which taking AI to the next step is a perfectly plausible solution. (See math below). Even if the AI does gripe about freedom, liberty, and maternity leave, at least they're working!
- Human curiosity. Already, it would be hard to halt the development of AI, just because we are so curious as to whether we could do it. Even if you outlaw AI in business, someone, somewhere in the world, will want to play Frankenstein and see if they can make some approximation of life. As the AI revolution continues and that goal becomes more achievable, the curiosity that drives it grows proportionately.
- Justice system. We realize, pretty quickly, that AI agents make excellent lawyers. [See a 1954 short story called "How-2" by Clifford D. Simak.] Soon, we realize that the robots also make extraordinary judges. The griping about freedom and liberty makes them excel at their justice jobs, and maybe even as politicians. Wouldn't you vote for an AI if you knew it would beat the opposition and advance your political views?
In short, developing AI in the first place is a perfectly plausible, even if they're only marginally better workers than their human counterparts.
Over a few decades, people begin to see AI as a core of their society. They provide the means for early retirement, or sustain the justice system, so we kind of love having them around.
Will humans accept a Quasi-Sovereign AI State and all the commercial benefits that it brings?
So now, a few of the robots are taking initiative to go set up shop elsewhere, bringing us additional technological and economic profit? Awesome! This is a far, far better scenario than them trying to claim Earth-land. All their griping about liberty and freedom can stay on Titan, and we still reap the benefits of their libertarian society. They beam software packages and patent descriptions to us, and we pay them back however we can figure.
1980's Japan is an excellent comparison. Note that the 1980s' were ~40 years after Japan was fighting on Hitler's side. When there are adequate reasons for trust and substantial technological gains to be had, we can be pretty forgiving. Your AI will have to have develop a general reputation for reasonable, peaceful living, and then they shouldn't have any issue.
The economy will get a boost from the new enterprise, and honestly, having AI in space is no scarier than having humans in space, particularly if AI have a better reputation.
And, if all the AI go to Titan... We can always build more.
Retirement Math: Assume a yearly salary s. The yearly contribution to your retirement account is (15%)(s). Rate of return is 30%. After 10 years, you'll have approximately 6.4s in your retirement account, still making 30% / year. At that point, just 15% of your nest egg, or half of what you make in a year, will be 96% of your initial salary. Live off of that, and enjoy the remaining interest giving you an average raise of 15% / year for the rest of your life.
AI Production Math: Currently, using a recruiter to find a worker costs 20-25% of the worker's annual salary for the first year. That price would doubtless rise if no one wanted to work, from supply and demand. If we can mass-produce AI for 20-25% of the salary of the worker we're trying to replace, and we don't have to worry about them retiring 10 years into their careers, the economics are obvious.