Decision-Making Swarms Sanza Kazadi, George Jeno, Xinyu Guan, Nick Nusgart, Andriy Sheptunov Hello, my name is Xinyu Guan and I’d like to talk to you today about swarms that can make decisions 1500 Sullivan Rd., Aurora, IL 60506 1

Decision-making swarms are prevalent in the world Bees, for example, are able to collectively decide on a new home. In one study, a hive chose the best nest out of 3 possible % of the time. 2

Decision-making swarms are prevalent in the world A decision-making swarm that you may or may not be aware of is Government. Gov’t’s entire job is to make policy decisions. So a good question to ask is how we can design swarms to make the proper decisions, and that is what this talk is about. 3

Outline Swarm Definitions Swarm Design Designing Ant Swarms Measuring Shortest Length with Ant Swarms Designing Locust Swarms Measuring Density with Locust Swarms This is the outline of the talk. First we’ll go over some definitions, then we’ll talk about how the Hamiltonian method can be used to design a swarm, and finally, we’ll show two examples of the Hamiltonian Method of Swarm Design in action. 4

An agent is a subset of a system which controls at least one degree of freedom Local measureables are anything the agent can directly interact with, observe. We use this notation to denote the set of local measureables for an agent. 5

{put a picture of a swarm here!} A swarm is a collection of agents that has more abilities than any individual agent. Local measureables are anything the agent can directly interact with, observe. We use this notation to denote the set of local measureables for an agent. {put a picture of a swarm here!} 6

How do we mathematically analyse a swarm? Local measureables are anything the agent can directly interact with, observe. We use this notation to denote the set of local measureables for an agent. {put a picture of a swarm here!} 7

{put a picture of a swarm here!} Local properties are anything the agent can directly observe or interact with. A Local Property is Relative Position Local measureables are anything the agent can directly interact with, observe. We use this notation to denote the set of local measureables for an agent. {put a picture of a swarm here!} 8

{put a picture of a swarm here!} Global properties are well-defined, differentiable functions of the local properties. A Global Property is Width of Swarm Local measureables are anything the agent can directly interact with, observe. We use this notation to denote the set of local measureables for an agent. {put a picture of a swarm here!} 9

{put a picture of a swarm here!} Global properties are well-defined, differentiable functions of the local properties. A Global Property is Length of Swarm Local measureables are anything the agent can directly interact with, observe. We use this notation to denote the set of local measureables for an agent. {put a picture of a swarm here!} 10

{put a picture of a swarm here!} Global properties are well-defined, differentiable functions of the local properties. A Global Property is Center of Mass Local measureables are anything the agent can directly interact with, observe. We use this notation to denote the set of local measureables for an agent. {put a picture of a swarm here!} 11

The Global Property space, or the Phase Space, can be drawn. Local measureables are anything the agent can directly interact with, observe. We use this notation to denote the set of local measureables for an agent. {put a picture of a swarm here!} Length of Swarm (L) 12

{put a picture of a swarm here!} The Phase Space shows clearly the ways in which the swarm must change in order to reach the desired end phase. goal Local measureables are anything the agent can directly interact with, observe. We use this notation to denote the set of local measureables for an agent. {put a picture of a swarm here!} initial Length of Swarm (L) 13

{put a picture of a swarm here!} The Hamiltonian Method of Swarm Design entails looking at the phase space and determining which direction the Global Properties must change. The direction that they must go determines the swarm conditions, which must be met in order for the desired outcome to be achieved. goal Local measureables are anything the agent can directly interact with, observe. We use this notation to denote the set of local measureables for an agent. {put a picture of a swarm here!} initial Length of Swarm (L) 14

A swarm decision is a change in attractor in Phase Space. goal Local measureables are anything the agent can directly interact with, observe. We use this notation to denote the set of local measureables for an agent. {put a picture of a swarm here!} initial Length of Swarm (L) 15

How do we make the swarm flexible so it can decide to converge to a closer food source if the closer one is made available to the swarm at a much later time than the further food source? The first swarm we designed to make a decision is the ant swarm. Ant swarms have the interesting ability to converge onto the shortest path to a food source, even though each ant is practically blind. They are able to do this by laying pheromone. However, we would like to generate an ant swarm that is flexible, so that if a closer food source is suddenly dropped onto the world, the swarm would be able to make the decision to switch from the first food source to the second. 16

How do we make the swarm flexible so it can decide to converge to a closer food source if the closer one is made available to the swarm at a much later time than the further food source? The first swarm we designed to make a decision is the ant swarm. Ant swarms have the interesting ability to converge onto the shortest path to a food source, even though each ant is practically blind. They are able to do this by laying pheromone. However, we would like to generate an ant swarm that is flexible, so that if a closer food source is suddenly dropped onto the world, the swarm would be able to make the decision to switch from the first food source to the second. 17

How do we make the swarm flexible so it can decide to converge to a closer food source if the closer one is made available to the swarm at a much later time than the further food source? The first swarm we designed to make a decision is the ant swarm. Ant swarms have the interesting ability to converge onto the shortest path to a food source, even though each ant is practically blind. They are able to do this by laying pheromone. However, we would like to generate an ant swarm that is flexible, so that if a closer food source is suddenly dropped onto the world, the swarm would be able to make the decision to switch from the first food source to the second. 18

How do we make the swarm flexible so it can decide to converge to a closer food source if the closer one is made available to the swarm at a much later time than the further food source? The first swarm we designed to make a decision is the ant swarm. Ant swarms have the interesting ability to converge onto the shortest path to a food source, even though each ant is practically blind. They are able to do this by laying pheromone. However, we would like to generate an ant swarm that is flexible, so that if a closer food source is suddenly dropped onto the world, the swarm would be able to make the decision to switch from the first food source to the second. 19

How do we make the swarm flexible so it can decide to converge to a closer food source if the closer one is made available to the swarm at a much later time than the further food source? The first swarm we designed to make a decision is the ant swarm. Ant swarms have the interesting ability to converge onto the shortest path to a food source, even though each ant is practically blind. They are able to do this by laying pheromone. However, we would like to generate an ant swarm that is flexible, so that if a closer food source is suddenly dropped onto the world, the swarm would be able to make the decision to switch from the first food source to the second. 20

How do we make the swarm flexible so it can decide to converge to a closer food source if the closer one is made available to the swarm at a much later time than the further food source? The first swarm we designed to make a decision is the ant swarm. Ant swarms have the interesting ability to converge onto the shortest path to a food source, even though each ant is practically blind. They are able to do this by laying pheromone. However, we would like to generate an ant swarm that is flexible, so that if a closer food source is suddenly dropped onto the world, the swarm would be able to make the decision to switch from the first food source to the second. 21

{have a comic, of bird dropping food sourceS} How do we make the swarm flexible so it can decide to converge to a closer food source if the closer one is made available to the swarm at a much later time than the further food source? After some mathematical tricks, it can be seen that the dot product of the two global properties needs to be negative in order for the swarm to make the decision. {have a comic, of bird dropping food sourceS} 22

A global property is the length of the paths = 400 300 The length of the paths is our first global property. 23

A global property is the number of ants on each path. = 364 333 The second property is the number of ants on the paths. 24

After some mathematical tricks, it can be seen that the dot product of the two global properties needs to be negative in order for the swarm to make the decision. The state change can be seen below. Swarm Condition: After some mathematical tricks, it can be seen that the dot product of the two global properties needs to be negative in order for the swarm to make the decision. 25

How can we engineer a swarm that can determine the size of a room by merely bumping into each other? The first swarm we designed to make a decision is the ant swarm. Ant swarms have the interesting ability to converge onto the shortest path to a food source, even though each ant is practically blind. They are able to do this by laying pheromone. However, we would like to generate an ant swarm that is flexible, so that if a closer food source is suddenly dropped onto the world, the swarm would be able to make the decision to switch from the first food source to the second. A group of grasshoppers is in an enclosed space 26

How can we engineer a swarm that can determine the size of a room by merely bumping into each other? The first swarm we designed to make a decision is the ant swarm. Ant swarms have the interesting ability to converge onto the shortest path to a food source, even though each ant is practically blind. They are able to do this by laying pheromone. However, we would like to generate an ant swarm that is flexible, so that if a closer food source is suddenly dropped onto the world, the swarm would be able to make the decision to switch from the first food source to the second. As they move around, they contact each other 27

How can we engineer a swarm that can determine the size of a room by merely bumping into each other? The first swarm we designed to make a decision is the ant swarm. Ant swarms have the interesting ability to converge onto the shortest path to a food source, even though each ant is practically blind. They are able to do this by laying pheromone. However, we would like to generate an ant swarm that is flexible, so that if a closer food source is suddenly dropped onto the world, the swarm would be able to make the decision to switch from the first food source to the second. Upon contact, the grasshopper’s serotonin level increases 28

How can we engineer a swarm that can determine the size of a room by merely bumping into each other? The first swarm we designed to make a decision is the ant swarm. Ant swarms have the interesting ability to converge onto the shortest path to a food source, even though each ant is practically blind. They are able to do this by laying pheromone. However, we would like to generate an ant swarm that is flexible, so that if a closer food source is suddenly dropped onto the world, the swarm would be able to make the decision to switch from the first food source to the second. Continued collisions further increase the serotonin levels, until… 29

How can we engineer a swarm that can determine the size of a room by merely bumping into each other? The first swarm we designed to make a decision is the ant swarm. Ant swarms have the interesting ability to converge onto the shortest path to a food source, even though each ant is practically blind. They are able to do this by laying pheromone. However, we would like to generate an ant swarm that is flexible, so that if a closer food source is suddenly dropped onto the world, the swarm would be able to make the decision to switch from the first food source to the second. Continued collisions further increase the serotonin levels, until… 30

How can we engineer a swarm that can determine the size of a room by merely bumping into each other? The first swarm we designed to make a decision is the ant swarm. Ant swarms have the interesting ability to converge onto the shortest path to a food source, even though each ant is practically blind. They are able to do this by laying pheromone. However, we would like to generate an ant swarm that is flexible, so that if a closer food source is suddenly dropped onto the world, the swarm would be able to make the decision to switch from the first food source to the second. Continued collisions further increase the serotonin levels, until… 31

How can we engineer a swarm that can determine the size of a room by merely bumping into each other? The first swarm we designed to make a decision is the ant swarm. Ant swarms have the interesting ability to converge onto the shortest path to a food source, even though each ant is practically blind. They are able to do this by laying pheromone. However, we would like to generate an ant swarm that is flexible, so that if a closer food source is suddenly dropped onto the world, the swarm would be able to make the decision to switch from the first food source to the second. The grasshopper begins its transition into a locust 32

How can we engineer a swarm that can determine the size of a room by merely bumping into each other? The first swarm we designed to make a decision is the ant swarm. Ant swarms have the interesting ability to converge onto the shortest path to a food source, even though each ant is practically blind. They are able to do this by laying pheromone. However, we would like to generate an ant swarm that is flexible, so that if a closer food source is suddenly dropped onto the world, the swarm would be able to make the decision to switch from the first food source to the second. The erratic behavior of locusts lead to many more collisions, increasing the rate of serotonin increase for surrounding grasshoppers 33

How can we engineer a swarm that can determine the size of a room by merely bumping into each other? The first swarm we designed to make a decision is the ant swarm. Ant swarms have the interesting ability to converge onto the shortest path to a food source, even though each ant is practically blind. They are able to do this by laying pheromone. However, we would like to generate an ant swarm that is flexible, so that if a closer food source is suddenly dropped onto the world, the swarm would be able to make the decision to switch from the first food source to the second. As a result, more grasshoppers turn into locusts 34

How can we engineer a swarm that can determine the size of a room by merely bumping into each other? The first swarm we designed to make a decision is the ant swarm. Ant swarms have the interesting ability to converge onto the shortest path to a food source, even though each ant is practically blind. They are able to do this by laying pheromone. However, we would like to generate an ant swarm that is flexible, so that if a closer food source is suddenly dropped onto the world, the swarm would be able to make the decision to switch from the first food source to the second. As a result, more grasshoppers turn into locusts 35

How can we engineer a swarm that can determine the size of a room by merely bumping into each other? The first swarm we designed to make a decision is the ant swarm. Ant swarms have the interesting ability to converge onto the shortest path to a food source, even though each ant is practically blind. They are able to do this by laying pheromone. However, we would like to generate an ant swarm that is flexible, so that if a closer food source is suddenly dropped onto the world, the swarm would be able to make the decision to switch from the first food source to the second. Eventually, all of the grasshoppers have transitioned into locusts 36

How can we engineer a swarm that can determine the size of a room by merely bumping into each other? The next swarm we designed were locust swarms that can determine the size of a room. Each agent has an internal state, with a threshold. The agents randomly move around, and bounce off the walls and each other. Each time they bounce off each other, the internal state is increased. Once threshold has been reached, the agent changes state, and increases other agent’s internal states by a greater amount upon contact. 37

The internal state of the agent increases by a constant amount for collisions with other agents. This state also decays exponentially over time. After the threshold, the agent is triggered. 38

Global Property Desired Behavior The global property is the sum of each agent’s internal property, and so the swarm condition is that the global property must increase over time. Global Property Desired Behavior 39

The swarm condition can be expressed in terms of parameters that determine the dynamics of the internal state. Swarm condition Ntrigger = 2 Ntrigger = 20 40

The state change can be seen below The state change can be seen below. The swarm condition is verified through experimental data. 41

How do we engineer swarms to make decisions provably? ??? Swarm works a priori 42

Hamiltonian Method of Swarm Design Swarm Conditions ??? The Hamiltonian Method of Swarm Design can be used to generate the swarm conditions, but there is no general methodology to go from those conditions to the swarm working a priori. Hamiltonian Method of Swarm Design Swarm Conditions ??? Swarm works a priori What’s a general methodology for the third step? 43

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Thank you! The last slide always thanks the audience 45