Tunable stiffness enables fast and efficient swimming in fish-like robots

Researchers have built dozens of robots in an attempt to mimic the flexibility and swimming patterns of tuna and other fish, but none have matched the performance of the real things. In my lab at the University of Virginia, my colleagues and I ran into the same questions as others: How flexible should our robot be? And if there’s no one best flexibility, how should our robot change its stiffness as it swims. We looked for the answer in an old NASA paper about vibrating airplane wings. The report explains how when a plane’s wings vibrate, the vibrations change the amount of lift the wings produce. Since fish fins and airplane wings have similar shapes, the same math works well to model how much thrust fish tails produce as they flap back and forth. Using the old wing theory, postdoctoral researcher Qiang Zhong and I created a mathematical model of a swimming fish and added a spring and pulley to the tail to represent the effects of a tensing muscle. We discovered a surprisingly simple hypothesis hiding in the equations. To maximize efficiency, muscle tension needs to increase as the square of swimming speed. So, if swimming speed doubles, stiffness needs to increase by a factor of four. To swim three times faster while maintaining high efficiency, a fish or fish-like robot needs to pull on its tendon about nine times harder. To confirm our theory, we simply added an artificial tendon to one of our tunalike robots and then programmed the robot to vary its tail stiffness based on speed. We then put our new robot into our test tank and ran it through various “missions” – like a 200-meter sprint where it had to dodge simulated obstacles. With the ability to vary its tail’s flexibility, the robot used about half as much energy on average across a wide range of speeds compared to robots with a single stiffness.