Unlike human manufacturing, the grand designs of bees, ants, and termites emerge simply from their collective action with no central planning required. Now, researchers at Penn’s School of Engineering and Applied Science have developed mathematical rules that allow virtual swarms of tiny robots to do the same. In computer simulations, the robots built honeycomb-like structures without ever following — or even being able to comprehend — a plan.
“Though what we have done is just a first step, it is a strategy that could ultimately lead to a new paradigm in manufacturing,” said Jordan Raney, associate professor in mechanical engineering and applied mechanics (MEAM), and the co-senior author of a new paper in Science Advances. “Even 3D printers work step by step, resulting in what we call a brittle process. One simple mistake, like a clogged nozzle, ruins the entire process.”
Manufacturing using the team’s new strategy could prove more robust — no hive stops construction because a single bee makes a mistake — and adaptable, allowing for the construction of complex structures onsite rather than in a factory. “We’ve just scratched the surface,” said Raney. “We’re used to tools that execute a plan. Here, we’re asking: How does order emerge without one?”
While inspired by nature, the researchers didn’t try to precisely mimic how bees, ants or other natural builders behave. They focused on the deeper principle that nature uses: simple behaviors, repeated many times in parallel, can add up to create something complex and useful. “What we wanted was a system where structure emerges from behavior,” said Raney. “Not because the robots know what they’re building, but because they’re following the right set of local rules.”
In the end, the team focused on a handful of basic questions: What should a robot do when it bumps into something another robot built? Should it turn left or right, and by how much? How far should each robot go before stopping? This resulted in a dozen variables — like the robots’ speed and the angle at which they turn left or right — that the researchers played with over the course of many simulations. “By simulating the robots’ activity,” said Raney, “we could focus on fine-tuning which rules mattered the most.”
Ultimately, the amount of disorder in the system played a crucial role in the final structure. “The more we varied parameters like the turning angle, the more variation we got in the final structure,” said Yim. As prior work by Penn Engineers has found, adding the right amount of disorder to lattices like honeycombs can actually enhance their toughness. “We essentially found a lever that lets you vary the geometry of the final outcome, which can affect its resistance to cracking,” added Raney.
While the team created prototypes, actually building a swarm of robots is still a step away. First, they plan to update their simulation to better reflect how tiny robots might work in the real world.
“In our early models, we imagined the robots laying down material in straight lines, like a mini 3D printer,” said Mark Yim, Asa Whitney Professor in MEAM, Ruzena Bajcsy director of the General Robotics, Automation, Sensing and Perception (GRASP) Lab, and the paper’s other co-senior author. “But that may not be the most practical method. A better approach might be to use electrochemistry, where the robots grow metal structures around themselves.”
Making that happen will require progress in building tiny robots that can move, sense and interact with materials, but the team believes the concept itself represents perhaps their most important advance.

