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How Fish Swim in Schools and Bird Fly in Flocks

What kinds of natural control mechanisms enable fish to swim together in schools and birds to fly together in flocks? And what implications do those graceful natural phenomena have for the development of unmanned underwater and aerial vehicles capable of carefully coordinated motion?

Those were some of the questions that motivated an ambitious, multi-disciplinary research project involving investigators from Yale, Princeton, Harvard, and Columbia universities along with the University of Washington. The work was carried out with support from a grant under the KDI program of the National Science Foundation.

Part of the project, at the University of Washington, involved three-dimensional photographing of fish swimming in a large tank. The fish were marked so that their positions relative to others could be observed as they schooled, enabling the development of an experimental database. This work was overseen by biologists Julia K. Parrish and David Grunbaum.

Naomi E. Leonard, a professor of mechanical and aerospace engineering at Princeton, has used findings of the fish schooling study and other data to help develop mechanisms for coordinating motions of a group of autonomous underwater robots. The objective is to develop mobile sensor arrays capable of cooperating to perform tasks such as clearing underwater mines.

This work and other projects elsewhere have re-energized a field of study known as "cooperative control." Leonard comments, "I would say that it's had a rebirth, an explosive rebirth over the past three or four years. A lot of people have gotten excited about it. … There's lots of interesting mathematics, lots of very challenging problems to solve. It's exciting because there are important things to do with it."

A. Stephen Morse, professor of electrical engineering at Yale, served as lead principal investigator for the KDI grant project. He was charged with developing the complex mathematic models needed to understand the natural and man-made coordinated motions.

Morse concurs that "this is a very hot topic. So if you pick up Nature or Science, you'll find all kinds of people writing papers about issues having to do with flocking and schooling and so forth. There's only a small number—and you can count them almost on one hand—who are really worried about proving that the theories are correct. … There's a very big difference between running [computer] simulations and establishing, on the basis of assumptions, that something in fact works."

Working under Morse at Yale was Ali Jadbabaie, at that time a postdoctoral fellow. He has since become an assistant professor of electrical and systems engineering at the University of Pennsylvania.

"We were trying to find mathematical proofs of under what conditions these types of coordinations are possible," Jadbabaie says. "We started analyzing some mathematical models that have some biological motivations—a simple model of how birds would fly in a group, flock together. We were most interested in the connection between that and how we could control a fleet of unmanned aerial vehicles, have them go perform a mission. We were interested in seeing basically how it is that you can control this group with simple control laws based on interaction with their neighbors and how simple local behavior could result in global results."

Jadbabaie says his work at Yale on the KDI grant was crucial to the development of his professional career, because he was able to work on a major project and prepare several published papers. "It was actually very, very important, because there were some results that basically helped me land this job—that's what came out of the that KDI project."

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