Can a Robot Save Power by Flapping to Nature's Rhythm?

A tuna, a sea turtle and a lamprey look nothing alike, but when they cruise, they swim to nearly the same rhythm. Researchers at Tallinn University of Technology in Estonia and at Vrije Universiteit Brussel (VUB) and IMEC in Belgium gave a four-fin underwater robot, U-CAT, a controller that aims every fin at that rhythm.

Before each flap, a planner for each fin chooses how far and how fast the fin swings, trading the push the robot asked for against staying near that rhythm. In pool tests against the usual controller, the robot's fins used up to nearly a third less power, estimated from how the fins moved, and the robot reached a speed the usual controller couldn't. In this independent explainer, I walk through how it works and what the paper shows.

In the video

• The rhythm: the Strouhal number is how often a fin beats, times how wide it sweeps, divided by the speed. A fin's tip draws a wave through the water, and the number is how tall that wave is compared with how long it is. Cruising tuna, turtles, lampreys and even insects land between about 0.2 and 0.4. The team aims every fin at 0.3, with a sweet spot of 0.25 to 0.35
• Why it matters: at the sweet spot, the swirls a fin leaves behind line up in two rows, and a jet of water shoots straight back between them. That jet is the push. Those swirls are too complex to simulate while the robot swims, so the team uses the sweet spot as a rule of thumb
• The usual way: many fin robots beat at a fixed rate and sweep wider to push harder, so the Strouhal number climbs out of the sweet spot
• The new controller: model predictive control, with its own planner for each fin. It predicts each option's push with a simple model of lift and drag, and scores it on the push, the sweet spot, stroke size and smoothness. It tries 500 random flaps, keeps the best one and fine-tunes it, and can do that more than 25 times a second per fin on the robot's own computer. In a second version, the back fins move as one
• In the team's model: with the full score, 88% of the cases landed in the sweet spot. Without the sweet-spot penalty, just over a third did, though the push was matched slightly better. Matching the push alone doesn't give efficient flapping
• In the pool, at 0.1 to 0.4 m/s: both new versions kept the fins closer to the sweet spot, though at the slower speeds they still strayed well outside it. Their fins used less power at every speed the usual controller could reach, with the biggest saving, 32%, at 0.2 m/s. The usual controller couldn't reach 0.4 m/s; both new versions did. The power was worked out from how the fins moved, not measured at the battery
• In a lake: five minutes circling in Rummu Lake in Estonia, set to stay 3 meters deep. The team used the version where the two back fins move as one. It worked its way down to that depth and held it, and kept going around, though its turning wobbled
• The limits: the pool tests compared whole controllers, so they don't show how much of the saving comes from the sweet-spot rule alone. The lake run tested steering, not savings, and the paper reports no power or Strouhal numbers for it. It's one robot with four fins, tested up to 0.4 m/s, with a simple model of the water, and the paper doesn't measure the swirls themselves. The split of work between the fins is still fixed

The paper

"Strouhal-Aware Model Predictive Control for Efficient Multi-Fin Flapping Locomotion"
Yuya Hamamatsu, Zixi Chen, Maarja Kruusmaa, Asko Ristolainen
Tallinn University of Technology, Vrije Universiteit Brussel and IMEC
IEEE Journal of Oceanic Engineering (2026), doi:10.1109/JOE.2026.3700919
Free version: arXiv:2607.03216, July 2026

Read the paper

The paper goes much deeper than this video: the fin model and its coefficients, the full score and its weights, a benchmark of the two-step search, and the pool and lake data. If you build or control fin-driven robots, it's worth reading in full.

This is an independent explainer. I'm not affiliated with or endorsed by the authors, Tallinn University of Technology, Vrije Universiteit Brussel or IMEC, and the research is all theirs. The animations are my own illustrations of what the paper describes, not footage from the study. Charts marked schematic or illustrative are sketches, and the rest follow the paper's equations, tables and figures, with values read off the figures. Any mistakes in the explanation are mine.

I'm Bora Celik from Piccard. I explain new research in ocean science and robotics.