# Scale-Free Features in Collective Robot Foraging
## 2 Methods
### Simulation Setup  
We designed and implemented a set of physics-based simulations using the state-of-the-art simulator for large-scale swarms, ARGoS [15]. An overview of all parameter values used in our simulations is given in Table 4. The simulations are conducted in a square-shaped arena, which is confined within four walls, each being of the length of 50 m. The arena is divided into two regions: (i) the nest \(A_{n}\): it is the gray \(10\times 50\) m\({}^{2}\) area in Figure 1a, and (ii) the foraging area \(A_{f}\): it is the white \(40\times 50\) m\({}^{2}\) area in Figure 1a. The items are scattered uniformly over the foraging area, and keep reappearing after robots retrieve them to the nest--as in [14]--with constant probability. This prevents the system from drifting into an absorbing state in which there are no items left to recover. A phototaxis behavior is used to assist the robots in leaving and re-visiting the nest. For that purpose, light beacons are positioned equidistantly at the nest wall (yellow dots at the bottom of Figure 1a). Their light is perceived by the robots' light sensors. Each robot is programmed to move _away_ from the beacons when it needs to _leave_ the nest and _towards_ the beacons when it needs to _return_. We use a homogeneous swarm of Footbots (see [[http://www.swarmanoid.org/swarmanoid_hardware.php](http://www.swarmanoid.org/swarmanoid_hardware.php)]([http://www.swarmanoid.org/swarmanoid_hardware.php](http://www.swarmanoid.org/swarmanoid_hardware.php))) in our simulations, \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline _Robot parameters_ & \\ \hline Type & Footbot \\ Proximity sensor range \(r_{prox}\) & 0.1 m \\ Range-and-bearing sensor range \(r_{rab}\) & 1.25 m \\ Maximum moving speed & \(1\frac{m}{5}\) \\ No-turn threshold \(\alpha_{nt}\) & \(10^{\circ}\) \\ Soft-turn threshold \(\alpha_{st}\) & \(30^{\circ}\) \\ Hard-turn threshold \(\alpha_{ht}\) & \(90^{\circ}\) \\ \(s_{e},i_{e},i_{r},s_{r}\in\{0,0,0.01,0.5,0.9\}\) & \\ \hline _Arena parameters_ & \\ \hline Total area \(A\) & \(50\times 50\) m\({}^{2}\) \\ Nest area \(A_{n}\) & \(10\times 50\) m\({}^{2}\) \\ Foraging area \(A_{f}\) & \(40\times 50\) m\({}^{2}\) \\ Number of robots \(N_{robots}\) & 950 \\ Number of items \(N_{items}\) & 300 \\ Radius of an item \(r_{item}\) & 0.2 m \\ Total experiment duration \(T\) & \(10^{4}\) ts \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Robot and arena parameters used for the simulation setup. Figure 1: Illustrations of the arena. (**a**) A snapshot from a simulation in ARGoS. Gray area: nest; white area: foraging field; black dots: items; blue objects: Footbots; light-blue lines: communication (range-and-bearing) links. (**b**) 3D view on the same arena. In both figures, the communication links are formed _only_ for _resting_ robots _inside_ the nest, as in our experiments moving robots neither broadcast nor listen to any messages. and the communication radius of the robots is set such that the fraction of the circular communication area around the robot is 0.982 % of the nest area, which is close to the fraction used in [14]. For better readability, we will limit our discussion of the robot states to only _resting_ and _exploring_. While the former is distinct, the latter is composed of further states of which only _f foraging_ and _homing_ are relevant because they are the most time consuming (for a detailed list of the robot states please see Supplementary Material Section 2). At the beginning of the simulation, each robot switches from resting to exploring with a probability of 0.01. Consequently, within the first 500 time steps (ts) most robots leave the nest. After another \(\approx 500\) ts most of the swarm returns, with or without an item. Although this behavior is subsequently repeated several times, the number of simultaneously switching robots gradually decreases, and the switching rate from resting to exploring (or vice versa) approaches a constant limit.