I think this is the model that Karl Smith has in mind.
Assume robots are the same as humans. Robots can do all the work that humans can do. Robots need the same amount of energy/food to stay functioning as humans do, but robots themselves can produce that energy/food just like humans can. Robots will need maintenance and training as humans do, but robots themselves can produce that maintenance and training just like humans can. Robots can produce other robots, just as humans can produce other humans.
The only difference between robots and humans is that robots are owned by humans. Robots are just like human slaves.
Robots will earn the same wages as humans, but those wages, minus the costs of the robots' subsistence, will go to the robots' owners. Just like slaves.
Robots' owners will program their robots to build more robots, as long as the surplus of wages over subsistence is positive. Just like slave-owners will want their slaves to reproduce. And just like human workers reproduce in a Malthusian model. Given diminishing marginal product of human plus robot labour, the total population of humans plus robots will expand until the Malthusian limit is reached. At that Malthusian limit, wages are driven down to subsistence.
But unlike Malthus, who allowed that subsistence wages might be determined in part by custom and culture, the level of subsistence wages for robots would be a strict biological constant. It's the bare minimum that robots need to survive and reproduce.
At that strict Malthusian steady state, robots, like slaves, are no longer scarce. There's no point in owning either if the marginal product of their labour equals the cost of their subsistence.
In the Malthus/Ricardo model, land was the only scarce factor of production in the steady state. Land rents increased as population expanded and wages were driven down to subsistence. Land rents were the only surplus.
Time preference - a scarcity of capital in the strict (Austrian) sense - would slow down the transition to the Malthusian steady state. Robots breed robots, but doing so means future benefits are compared to present costs. The high rate of growth of the consumption of robot owners will mean those future benefits are discounted at a high rate of interest. So robot owners will limit the time that robots spend investing in new robots. But as growth in robots, and hence growth in the owners' consumption, slows as the steady state is approached, that rate of interest will decline too. Malthus/Ricardo, plus a consumption-Euler equation for the rate of interest.
Horses were once like robots. Horses could do a lot of the same work that humans could do. Humans and horses can pull things, if you feed them. But then mechanical horses, called tractors, were invented, that could pull heavier things with cheaper food. Tractors pushed horses' wages below subsistence, so the horse population declined.
The robot horse displaced horses, just as horses displaced humans from all the jobs where humans pulled things. But humans, unlike horses, can do lots of other jobs beside pulling things. Humans are very versatile. Horses can't really do anything except pull things. So humans switched to doing other jobs, while horses couldn't. And the marginal product of labour, and hence wages in those other jobs, increased. Horses and tractors were complementary factors to human labour in those other jobs.
But that won't happen if robots are invented that really are just like humans, and can do all the jobs that humans can do. Robots that are just like humans would be just like slaves, rather than like tractors and horses.
I own land.