The animal-inspired robot menagerie holds enough species to populate a robot zoo: cheetah bots, seal bots, wasp bots and T-Rex bots. For practicality, elegance, and the potential ability to find alien life in extraterrestrial oceans, however, nothing beats a robot that swims like a fish.

But here’s the problem hampering ambitious would-be aquatic roboticists: Physicists can’t explain how fish swim.

Even though the first robot fish actually took to the water in the early 1990s, with MIT’s “robotuna. But despite that work and many advances since then, the math of fish propulsion remains murky.

Fortunately, that’s changing. Today a team of physical engineers share a new technique for measuring and modeling how fish swim in the journal Chaos. (Chaos‘ noble ambition is “increasing the understanding of nonlinear phenomena in all disciplines.) Swimming, it turns out, is way more complicated than you’d think. “It’s a funny way to move. Everybody knows how fish swim more or less, but the mechanism is actually quite subtle, says Mattia Gazzola, animal locomotion expert at Harvard University and a co-author on the new paper.

Fish move by creating “structures in waterthree-dimensional whorls of fluid. After capturing a whorl with a concave, flexed part of their body, they push against it and shed it with their tail, shooting forward.

Researchers’ inability to quantify the forces behind all that whorl-pushing have slowed the field. But studying it isn’t easy. “You can put a model airplane in a wind tunnel and attach pressure sensors to it, but with animals we typically don’t have that same ability, says John Dabiri, director of the Biological Propulsion Laboratory at CalTech, who was not involved in the current study.

Gazzola’s team got around this problem by modeling the fish-water interactions with a computer. The new work looks at the momentum exchange between a computerized fish and the vortices it createsnumerically fleshing out their previous theoretical work. Quantifying the behavior of these balls (known more fancily as Lagrangian coherent structures) could allow robot designers to work backwards. If they know how the whorls spin and how much water they contain, they might be able to program robot fish to use them for forward momentum.

Any improvement would be welcome. Currently fish are far better swimmersspeedier and more energy efficientthan machines. (No surprise there, though. Millions of years of evolutionary tinkering works wonders.) Lagrangian structures do seem like a good route, says Jifeng Peng, a mechanical engineer at the University of Alaska, Anchorage, who has also analyzed fish momentum this way. The next step is to confirm the model with a real, live, swimming fish. “They don’t move as ideally as models, says Peng.

Whoever takes on that challenge will have to do it without Gazzola. He’s moved on to studying the movement of slender-bodied animals, like snakes and slugs. That’s fine. The animal-robot menagerie can never have too many members.

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