Wheel Made of ‘Odd Matter’ Spontaneously Rolls Uphill

There is a wheel that can roll uphill by wiggling.

The ring is about 6 inches in diameter and consists of just six small motors linked together by plastic arms and rubber bands. When the motors are on, it starts playing tricks, squashing and stretching, and occasionally flinging itself into the air, as it slowly makes its way up a foam ramp.

The biophysicist who was not involved in making the wheel said it was very playful. It was a lot of fun.

Physicists are trying to get useful collective behavior to spontaneously emerge in robots assembled from simple parts that obey simple rules. Goldman is a physicist at the Georgia Institute of Technology.

One of the most important behaviors of living things is locomotion. We instinctively take these challenges in stride, but how we do this is not easy. Engineers can't program a robot to anticipate all the challenges it might encounter because they can't build one that won't collapse or lurch forward.

The odd wheel was developed by physicists Corentin Coulais of the University of Amsterdam and Vincenzo Vitelli of the University of Chicago. The wheel's uphill movement can be seen from the components. These parts don't know much about the environment but the wheel adjusts its motion to compensate.

The physicists came up with an odd ball that bounces to one side and an odd wall that controls where it absorbs energy.

Auke Ijspeert is a biorobotist at the Swiss Federal Institute of Technology Lausanne. While their paper is being reviewed, Coulais and Vitelli didn't comment.

The new research could lead to insights into the physics of living systems and inspire the development of novel materials.

Odd Matter

An umbrella term for systems whose parts consume energy from the environment is what inspired the odd wheel. The energy supply leads to instabilities that make it difficult to control.

If there is a way for a system to gain energy by moving from A to B, any process that takes the system from B to A must cost equal amounts of energy. With a constant influx of energy, this constraint is no longer applicable.

In a paper published in Nature Physics in 2020, Vitelli and others began to investigate nonreciprocal mechanical properties. Nonreciprocity can be seen in the relationship between stretching and squashing motions. Fakhri is a biophysicist at the Massachusetts Institute of Technology.

If you squash one side of a solid, you will cause it to bulge out in a different direction. You can distort it into a diamond shape by stretching it and squashing it. In an ordinary, passive solid, these two modes are independent and don't change the shape of the solid.

Squashing the solid in one direction will squash it along the axis, but squashing it along the diagonal will stretch it. Positive going one way and negative going the other way is what is described in the number. The phenomenon is called "odd elasticity."

The cycle of stretching and squashing motions that produce the elastic solid can leave it with some excess energy. The consequences of this are striking.

Coulais was studying nonreciprocity in robotic active matter consisting of a chain of simple modules. Coulais could use feedback loops to program its modules to respond to its neighbors' movements.

The two physicists collaborated to create robotic active matter that embodied the mathematics of odd elasticity.

Uncommon Oscillations

The springiness of matter is a bulk property that comes from interactions between matter's tiny particles. Coulais and Vitelli wanted to change the way robotic modules interact.

In their new design, each module consisted of a motor controlling the rotation of two plastic arms with rubber bands. A pair of modules sharing an arm was the start of the research. A clockwise turn of the first motor would cause a counterclockwise Torque on the second motor, but a clockwise rotation of the second motor would cause a counterclockwise Torque on the first.

The arrangement is not stable. The modules are left undisturbed, but even the smallest nudging will cause a tug of war:Whichever way a motor turns, its interaction with the other motor pushes it back in the opposite direction. The arms will start moving if the modules are strong.

On a 2D plot with axes representing the two motor angles, the growing spirals will appear as an outward spiral, gaining energy on each cycle like a runner descending an M.C. Escher staircase. The motors are only able to put out so much Torque and energy is lost to Friction. The trajectory converges to a circle on the plot of motor angles. This constant-amplitude oscillation is called a limit cycle by physicists.

A victory of stable, regular motion over the chaos that plagues complex systems is represented by the module's limit-cycle oscillations. Small changes in its initial conditions soon lead to totally different trajectory through space. Limit cycles are the opposite of this phenomenon. The system eventually exhibits the same steady-state oscillations regardless of which arm was initially pushed or pushed back.

Limit-cycle oscillations are more special because of this key feature. If you start the pendulum swinging at a different speed, it will trace a larger or smaller circle. If the system is pushed away from the same path it will get pulled back in.

Researchers were able to tame the unruly dynamics of active matter with the help of these limit-cycle oscillations.

Behind the Wheel

It was time to put the building blocks together. The modules connected in the right way would look similar to the elastic solid Vitelli had originally imagined. If the modules were linked together, what would happen?

The loop began to move when the team provided power to the motor. The two modes of self-deformation were used in the theory. There was a limit cycle in the collective motion of the wheel. The Escher staircase broke the symmetry between clockwise and counterclockwise laps because of the oddness of the motor'scoupling. The wheel was able to push off against the ground because of the energy generated.

It is difficult to pin down why the wheel is so strong, because the limit cycle is not seen in individual modules. Nick is a roboticist at the University of California, San Diego. He said that the emergence ofcollective motion from low-level oscillations has parallels in biology.

Coulais and Vitelli looked at the effects of oddcouplings on collision. An odd ball, a projectile assembled from odd modules, would always bounce off in a specific direction, while an odd wall could control the direction in which it absorbed energy from a projectile. Denis Bartolo, a physicist at the cole Normale Supérieure in Lyon, France, said that the next big step would be to find a way to self- assemble these machines.

Robophysics

It wasn't clear before the recent experiments that odd interactions would lead to locomotion. The wheel moves forward despite the motor only responding to its neighbors. The absence of top-down control is intriguing to biologists who want to understand how swarms cooperate and how primitive animals look for food.

The building blocks of the odd wheel are very easy to build, which makes it appealing to researchers. Alert said that you can lose in the complexity of living systems. He pointed to a famous quote from Richard Feynman.

It is an open question if biology has made use of the same dynamics that Coulais and Vitelli did. M. Marchetti, a theoretical physicist at the University of California, Santa Barbara, said that the next step is to see how well the behavior continues in a noisy environment.

Evolution can miss opportunities if it doesn't find good solutions. The odd wheel may be a new thing. If you wanted to make a plane with beating wings, you would have to walk from Normandy to New York.

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