Overview

This page provides supplementary material for the paper.

Simulation Experiments

Below are some sample videos from experiments which were performed to help give intuition on what the different block distributions looked like and the experimental parameters. The number of robots used in each corresponding (SS,DS,RN,PL) experiment below is the same, but the density is different. In the first set, the shown density is the maximum tested, 0.1. In the second set, the density is a constant 0.01. Experiments are sped up by a factor of 10.

Small Swarm Size, Variable Swarm Density

• Single Source (left), Dual Source (right)

• Random (left), Power Law (right)

Small Swarm Size, Constant Swarm Density

• Single Source (left), Dual Source (right)

• Random (left), Power Law (right)

Real-Robot Experiments

We use “extended” TurtleBot3 burger robots some additional sensors added, shown in the below video:

• Ultrasonic sensor to detect blocks
• 4 Light sensors to provide localization with respect to a light source.

In addition, static “arms” are added to help robots acquire blocks. The arms, ultrasonic sensor (bottom center), and light sensors (front; back/left/right not visible).

For the real robot experiments we perform 4 experimental runs of 5 minutes each with 1-5 robots. We use the single source (SS) block distribution and a bright light source created with photography lights is used as the nest. Below are two sample videos: a close up view of a run with 2 robots showing the foraging process in detail, and a run with 5 robots showing the full arena.

The purpose of these experiments was to show the feasibility of the methodology across both the simulation and real robot domains. As such, because our methodology assumes steady-state, we require that the number of blocks available for robots to find is the same. Thus, we do not run experiments from their start with N blocks until their are 0 blocks remaining. Instead, we run each experiment for 5 minutes during which time the robots generally do not collect enough blocks to appreciably diminish the overall number available, thus modeling a “slice” of steady-state time where the number of blocks remains approximately constant.

Effect Of Assumptions On Robot Behavioral Distributions

In its simplest form, ODE modeling fundamentally assumes that the modeled behaviors are steady-state (additional modeling techniques can be applied to help model transient behaviors, as described in the paper). Further, when modeling foraging behaviors, spatially symmetric steady-state behavioral distributions are more amenable to ODE modeling, because such distributions result in robots experiencing events in a non-Poisson way much less frequently because the spatial density is roughly uniform. This is why the random (RN) block distribution is the easiest to model, and the power law (PL) distribution is the most challenging.

The use of the nest in the corner vs. the center is the critical difference between the assumptions used in the two models: one results in non-symmetric spatial distributions more difficult to model with ODEs, and one results in symmetric spatial distributions more amenable to ODE modeling. The use of finite vs. infinite blocks also affects spatial distributions, but to a lesser degree: robots still acquire blocks roughly the same fashion in both cases, as can be seen below. However, the rate of acquisition differs–an asymmetry in time.

The below videos show the spatial distributions of different robot behaviors under each set of assumptions. In each video, the X and Y axes shows the X and Y extents of the arena, with the color showing the density of robots at a given (x,y) location.

LEFT: Finite blocks, nest in corner (Lerman et al.)

RIGHT: Using infinite blocks, nest in center (our work)

Searching robots (Where are robots when they are in the searching state?)

The nest in the corner results in a non-symmetric spatial distribution in steady state.

Acquisition locations (Where do robots acquire blocks from?)

Notice that the distribution on the left is much sparser, due to finite blocks.

Robot interference (Where are robots when they are experiencing interference?)

The nest in the corner results in a non-symmetric spatial distribution in steady state.

Robot occupancy (Where are robots generally, regardless of what state they are in?)

The nest in the corner results in a non-symmetric spatial distribution in steady state.