journal club

Go to the Ant: Self Assembly

They modeled the ants - as a fluid. So they looked at their ant fluid, with individual ant molecules, and measured and modeled its density, viscosity, and surface tension as though they were exploring a new form of syrup.

Ants are not only adept at the Traveling Salesman problem and carrying oversized meals in groups. Put them in water, and an ant colony will self-assemble into a well-balanced, hydrophobic, pancake-shaped raft.

Let’s face it. At this point, I am clearly obsessed with these six-legged creatures. I happen to be taking a course right now in Bio-Inspired Multi-Agent Systems. It’s fascinating. And I’m spending plenty of time talking about how cool these ants are.

An example of a bio-inspired multi-agent system is using the dynamics of ant and bee colonies to inform swarm robotics.

Apparently, the problem of global behavior based off of local rules is problem for swarm roboticists. In other words, how do you set up an algorithm that applies simple rules to individual robots, but results in complex, self-assembling swarm behavior? We don’t know. Scientists are trying to find a way. And in the meantime, they are turning to our friends, the ants, to help them.

Global Behavior, Local Rules

In swarm robotics, we want to connect individual pieces to move as one. Each piece has a unique way it contributes to an overall group behavior. You can’t just tell the robots to each do the exact same thing; if the ants did that, they’d never be able to build bridges and rafts.

Instead, there needs to be a set of simple rules applied to each robot. Each robot must check on its neighbors, and respond based on that information. Or maybe it’s not a robot. Maybe it’s a cell within an animal embryo, which differentiates into an eye or heart cell based off of what the neighboring cells are doing.

Researchers Yamins & Nagpal (2008) built algorithms to replicate the complexity of zebrafish embryology by using a pattern of “global to local” rules. In the case of an embryo, the global behavior is a blob of undifferentiated cells morphing into the specialized cells that make up the fish. The local behavior is what each cell must do in order to get there.

Why care about swarm robotics? A swarm of small robots can go places dangerous to human beings. They could be used for search-and-rescue, toxic waste clean-up, land mine clearing, and exploration in the deep ocean or outer space.

Their algorithm applied to a string of components (in their case, each component had a different number). They set a “neighborhood” for that component based on some radius. If the radius is two, the component looks at four of its neighbors, two to the left, and two to the right. It considers the states they are in. The algorithm sets certain rules: if your neighbors have such-and-such a state, convert to x. This type of algorithm was all it took to convert a random three-dimensional pattern into an ordered, striped one (see Fig. 4), sort of like the ordering of the embryo.

Simple rules, complex behavior.

Bridging Gaps

In an ant colony, this might look something like what Reid et al. (2015) study when they take a look at Army Ants forming bridges. Their bridges are set with different angles: a small angle means a steep, narrow bridge with a narrow gap, and a large angle means a less steep, wide bridge with a wide gap. The ants don’t want to walk all the way up and down the bridge, so they self-assemble into a bridge of their own, across the gap it creates.

The ants didn’t just self-assemble into a bridge, however, locking feet together in a colony-feeding exercise. They were able to maximize what the researchers described as a cost-benefit analysis. The ants preferred situations that minimized the size of the bridge, and minimized the distance.

These two features were actually at odds with each other: in the case of the wide bridge, the shortest possible path requires a long path across the base of the gap. A lot of ants are needed to make a bridge that long. They’d rather have some of those ants foraging for food than just sitting there. So instead of taking the shortest possible route, they march halfway up trail, bridging across a shorter distance. They self-assemble into a state of equilibrium. They want the shortest possible distance, with the fewest necessary bridge ants.

What are the rules here, governing this behavior? There does seem to be some complicating factors here. Younger, less experienced ants tend to bridge up; presumably, they “know” they’ll be less efficient foragers anyway. The bridge ants seem to also be able to sense the level of traffic rushing across them. If too few ants are marching across this living bridge, it disassembles. A local rule of ant traffic appears to influence the global behavior of ant bridge formation.

Facing Floods

And with that, we can take a look at what I have deemed the most adorable scientific paper I have read in my life – a study of Fire Ants self-assembling into waterproof rafts (Mlot & Tovey 2011).

To understand the appeal of this paper, please realize that the majority of the data reported here comes not in graphs, but in images of the ants themselves. In an attempt to analyze group dynamics of Fire Ant raft formation, researchers set up the following experiment. They scooped ants up in a spoon and dropped them into a flask. They swirled them with the spoon until the ants had been swept up into a sphere of insects. They removed the sphere from the flask and observed it under the following conditions: (1) the sphere was placed on a dry surface and (2) the sphere was placed on the surface of a body of water.

When set on dry land, you better believe that that sphere of ants turned into a chaotic mess of each individual running for her life. They scattered every which-away, quite unsure what to make of the spoonfuls of spherical confusion they had been subjected to. On the surface of water, however, the ants quickly engaged in a dynamic dance to achieve mutual balance and hydrophobicity.

Each ant is coated in a hydrophobic cuticle. That means that a little bit of water won’t hurt them – it bubbles up on their exoskeleton like the droplets on your freshly waxed car. Figure 2A showcases an ant wearing a water bubble like a top hat that clearly and concisely proves this point. If there is enough water around for the ant to be submerged, however, their hydrophobicity means that some air is trapped around their bodies, called a plastron. In Figure 2D, you see a submerged ant clutching its plastron, its tiny air bubble, like a teddy bear. By clinging to these bubbles, it improves its own buoyancy and can float. Still, this is a rough system for a single ant to deal with.

And that is why, given the choice, they will team up with a buddy in the water.

Ants plural are more hydrophobic than ants singular. (You can see this by comparing water bubble sizes between Fig. 2A and 2B. The group can repel more water than the one.) Not only that, but they can trap bigger plastrons as a submerged group (Fig. 2E shows a giant pocket of air a group of ants have generated while underwater; it can again be compared to the tiny plastron the single ant in Fig. 2D is shown with). For these reasons, the ants have good reason to stick together.

But they also don’t want to stay in the sphere they are in when plopped into the water. Imagine a spherical boat. Not very effective.

Instead, the ants must find some sort of equilibrium to maximize buoyancy and hydrophobicity. How do they do that? Global-to-local rules, of course.

On the water’s surface, they observed that each ant follows three (somewhat randomly followed) rules of behavior (See Fig. 3D). (1) Walk in a straight line. (2) Ricochet off the border of the ant raft. (3) [Eventually] pick an edge. With these simple local rules, the ants eventually equilibrated into a pancake-shaped raft that kept them floating happily.

Now, the researchers didn’t only want to watch the ants work their self-assembly magic. To learn from them, we want to be able to model their behavior into a system we might be able to use for our own technology. So they modeled the ants – as a fluid. They noticed that the movement of ants from sphere to pancake resembled the fluidic motion. So they looked at their ant fluid, with individual ant molecules, and measured and modeled its density, viscosity, and surface tension as though they were exploring a new form of syrup.

Now, the movement of ant molecules across the pancake, from edge to edge, is not very fluid-like. So the model had its difficulties. But they still conducted fascinating experiments, like poking a floating ant pancake with a twig to test their surface tension. They found the raft (ahem, ant fluid droplet) to be very buoyant and elastic (see Fig. 2C).

In the end, this study – and other like it – help swarm roboticists design robotic ant swarms of their own. Maybe we want to use swarms of little robots that self-assemble into dynamic hydrophobic rafts. Maybe we want robots to use similar rules to solve different problems. There’s much to learn from ants and their fellow social insects.

References

Mlot, N. J., Tovey, C. A., & Hu, D. L. (2011). Fire ants self-assemble into waterproof rafts to survive floods. Proceedings of the National Academy of Sciences of the United States of America, 108(19), 7669–7673. https://doi.org/10.1073/pnas.1016658108

Reid, C. R., Lutz, M. J., Powell, S., Kao, A. B., Couzin, I. D., & Garnier, S. (2015). Army ants dynamically adjust living bridges in response to a costbenefit trade-off. Proceedings of the National Academy of Sciences of the United States of America, 112(49), 15113–15118. https://doi.org/10.1073/pnas.1512241112

Yamins, D., & Nagpal, R. (2008). Automated Global-to-Local Programming in 1-D Spatial Multi-Agent Systems. AAMAS.

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