Ultimately what will be (I believe) the best solution is some form of tax on commercial automation, that will be used to fund a Basic Income. As automation increases and replaces more jobs, the fund will increase and can support more people. The stock answer to automation is "but that creates jobs for robot engineers/repairmen", but eventually, machines will be able to repair one another, and engineer new designs. Unfortunately, the transition to a fully-automated economy will be slow enough that we can't suddenly drop into a "everything free for everyone!" economy, so a transitory solution is required.
The detail devil is that the tax will need to be well-calibrated, so that utilizing automation is still cost-effective, and that robotics startups will be able to get off the ground. Another issue is what exactly counts as 'automation': do more-efficient tools like carbon-fiber handsaws count as 'automation', since they're modern tools which increase efficiency, or must it have moving mechanical parts like a chainsaw? What about a spinning saw rotated by someone pedaling on a stationary bicycle?
Perhaps that issue could by avoided by setting a standard of productivity per man-hour used, with any excess (through overwork, or better tools, or more usage of machines) being taxed. The rate of 'base productivity' would have to be set by the government, although I'm unsure how that would be calibrated, particularly for a new fully-automated factory that never had human workers. It should also be predictable such that a startup would know how much they would be taxed, when determining if the venture would be profitable. The downside of THIS method is that it's difficult to assess productivity in some fields (computer programmers and similar), and many jobs which utilize automation are service jobs; the field of medicine changes so frequently that assessing 'productivity' there would be difficult. A strict definition of 'productivity' as 'billable value' might help take care of service jobs, but assessing productivity of the more abstract cognitive jobs remains elusive. Call-centers that use automation to provide free tech support for a purchased product, for example, would have their automation taxed how? A combination of the two methods may be required.
Many Americans who are unemployed, or criminals, or on welfare, already live off of $5k or less per year, so a $5k basic income would be 'liveable' to them; if you live in a house/apartment with a few other people like you, you can cover the bills. As the basic income rises to $10k, the unemployed would feel less desperate, and crime would no longer seem like a necessary evil to stay alive. For reference, paying $10k to the lower 50% of adults in the USA would cost $1.2trillion per year, around what we were spending in Iraq each year we were there; and it could replace welfare programs, so the net amount wouldn't be as much.