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Mini Robots Reveal Links Between Bird Flocks and General Relativity

Mini Robots Reveal Links Between Bird Flocks and General Relativity

When self-propelling objects or living things interact with each other, interesting phenomena can occur. Birds align with each other when they flock together. People at a concert spontaneously create vortices when they nudge and bump into each other. Fire ants work together to create rafts that float on the water's surface.

Two small robots move on a stretchy, trampoline-like surface.

While many of these interactions happen through direct contact, like the concert-goers' nudging, some interactions can transmit through the material the objects are on or in—these are known as indirect interactions. For example, a bridge with pedestrians on it can transmit vibrations, like in the famous Millennium Bridge "wobbly bridge" instance.

Physicists from Georgia Tech, The University of Texas at Austin and elsewhere are using small, wheeled robots to better understand these indirect mechanical interactions, how they shape the behavior and structure of the larger group of objects or living things and how we can control them. Their findings were published earlier this year in the Proceedings of the National Academy of Sciences.

A large collection of agents that each move or exert forces—such as fish in a school, cells in an organism or a swarm of robots—are collectively known as active matter. In the paper, the researchers illustrated that active matter on deformable surfaces can interact with others through non-contact force—then created a model to allow control of the collective behavior of moving objects on deformable surfaces through simple changes in the engineering of the robots. The work might help roboticists develop teams of robots that are better at avoiding collisions or working together.

The research was led by Shengkai Li, former Ph.D. student at Georgia Tech, now a Center for the Physics of Biological Function (CPBF) fellow at Princeton University. UT Austin co-authors are Pablo Laguna, professor and chair of the Department of Physics, and graduate student Gabriella Small.

The significance of this research spans from biology to general relativity.

"The mapping to general relativistic systems is a breakthrough in bridging together the field of general relativistic dynamics and that of active matter," Li explained. "It opens a new window to better understand the dynamical properties in both fields."

"Our work is the first to introduce the view that an active-matter system can be recast as a dynamical space-time geometry—and thus gain an understanding of the system by borrowing the tools of Einstein's theory of general relativity," added Laguna.

Other co-authors include Georgia Tech co-authors Daniel Goldman, Dunn Family Professor; Gongjie Li, assistant professor; and graduate student Hussain Gynai — along with Yasemin Ozkan-Aydin (University of Notre Dame), Jennifer Rieser (Emory University) and Charles Xiao (University of California, Santa Barbara).

The research was funded by the Department of Defense, the Army Research Office, the National Science Foundation and NASA.


Setting the stage

The researchers built robots that drove at a constant speed over flat, level ground. When encountering a surface with dips and curves, these robots maintained that constant speed by reorienting themselves and turning. The amount that the robot turned was a result of how steep the slope or curve was.

When these robots were placed on a circular, trampoline-like surface, the researchers were able to monitor how the robots turned in response to the changing surface, because the robots created new dips in the surface as they moved, depressing it with their weight. An overhead system tracked the robots' progress across the trampoline, recording their courses.

The researchers began by testing how just one robot might move across the trampoline with a central depression, and they found that they could construct a mathematical model to predict how the vehicle would move. By using tools from general relativity to map the orbits to the motion in a curved spacetime, they showed that one could qualitatively change the precession—a shift in the path of an object around another object with each successive orbit—by making the vehicle lighter. This model explains the orbital property: how the movement of the "loops" shown here in the team's video (the precession of the farthest point in the robot's orbit) depend on the initial condition and the trampoline's central depression.

"We were excited and amused that the paths the robot took—precessing ellipses— looked a lot like those traced by celestial bodies like Mars and explained by Einstein's theory of General Relativity," Goldman said.

When more robots were added to the trampoline, the researchers found that the deformations caused by each robot's weight changed their paths across the trampoline.

The overall model works to guide designs of engineering schemes — like speed and tilt of the researchers' robots — to control the collective behavior of active matter on deformable surfaces (for example, whether the robots collide on the trampoline or not). The work could also help advance the understanding of general relativity.

"Our conventional visualization of general relativity is of marbles rolling on an elastic sheet," explained Li, the paper's lead author. "That visual demonstrates the idea that matter tells spacetime how to curve, and spacetime tells matter how to move. Since our model can create steady-state orbits, it can also overcome common issues in previous studies: with this new model, researchers have the ability to map to exact general relativity systems, including phenomena like a static black hole."

This article is adapted from a press release by Georgia Tech

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Tuesday, 29 November 2022

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