The insects build impressive, metres-high structures even though they can follow only simple rules and have no knowledge of an overall plan.
The Harvard researchers' robot brick-layers do something similar, sensing just the immediate area and taking limited cues from each other.
Nonetheless, as a report in Science magazine shows, the machines can also build large, coherent structures.
The researchers say this decentralised approach to robot programming can have some major advantages over very sophisticated systems.
The team gives the example of swarms of construction bots being sent into hazardous environments, such as in disaster zones or out into space.
In these types of settings, if one or more machines is destroyed, the others can continue to work together to complete the task.
Contrast this with a complex robot following high-levels commands. If it fails for some reason, the whole endeavour might be doomed.
"We're not going to Mars anytime soon, but a more medium-term application might be to use similar robots in flood zones to build levees out of sandbags," said lead author Dr Justin Werfel from the Wyss Institute for Biologically Inspired Engineering at Harvard University.
"That's a kind of classic of robotics: you want to use them in situations that are dirty, dangerous and dull."