Picture a futuristic swarm of robots deployed on a time-sensitive task, like cleaning up an oil spill or assembling a machine. At first, adding robots is advantageous, since many hands make light work. But a tipping point comes when too many crowd the space, getting in each other’s way and slowing the whole task down.
It’s a deceptively simple too-many-cooks problem: Given a fixed area, how many robots should you deploy to optimize a task? Harvard applied mathematicians think they have an elegant solution.
A study from the lab of L. Mahadevan, the Lola England de Valpine Professor of Applied Mathematics, Organismic and Evolutionary Biology, and Physics, combines mathematics, computer simulations, and experiments to show that in crowded environments, adding just the right amount of randomness, or “noise,” to how individuals move, can ease gridlock and dramatically improve efficiency. It’s an example of how simple, local rules can lead to the emergence of complex task completion, with implications for the design of coordinated robotic fleets, crowded public spaces, and more. Published in Proceedings of the National Academy of Sciences, the study was led by applied mathematics Ph.D. student Lucy Liu. She was co-advised by SEAS Senior Research Fellow Justin Werfel.
Mathematical analysis of crowd density is notoriously complex because there are so many possible paths and interactions to consider, Liu said. To get around this difficulty, the researchers embraced the idea of randomness — treating each individual as a simple agent with a tunable amount of “wiggle” in its path.
“This might be counterintuitive, because how could randomness make things easier to work with?” said Liu. “But in this case, when you have a lot of randomness, it becomes possible to take averages — average distances, average times, average behaviors. This makes it a lot easier to make predictions.”
To test their ideas, they made computer simulations of fleets of robots, or agents, with each starting at a random position and being given an equally random goal location. Once each agent reached its goal, it was immediately assigned a new destination; this setup was meant to mimic fleets of robots or workers deployed on tasks.
The study confirmed a core theoretical insight: A powerful central computer or ultra-intelligent robots aren’t necessary to achieve coordinated tasks. A simple local set of navigational rules, at least up to certain densities, may be all you need.
“Understanding how active matter, whether it is a swarm of ants, a herd of animals, or a group of robots, become functional and execute tasks in crowded environments using the principles of self-organization, is relevant to many questions in behavioral ecology,” Mahadevan said. “Our study suggests strategies that might well be much broader than the instantiation we have focused on.”
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