Some of them do, yes. For reference, the Jet Propulsion Laboratory is a NASA Lab, administered by Caltech. DARPA is a a funding agency and doesn't actually do any research itself. It generally employs only late-career scientists and engineers as program managers that hand out the money to researchers at actual labs at universities and companies.

iRobot was started by Rodney Brooks, at the time the most famous roboticist in North America and Director of CS and AI at MIT, and his students. This team has attracted a lot of good talent over the years. Now the team has broken up and there has been little interesting robot development for a while. But the intelligent robot industry is still very small, and the good grads have to go somewhere. Outside university labs, the hot job recently has been at Willow Garage.

(robot research prof here)