## 5 Introduction of Environment Selection Hormones with Sleep and Speed Regulating Hormone Systems
### Environmental Setup  
The new environment used for testing in this scenario was identical to that used in [7] and can be seen in Figure 11. It features two different terrains designed to challenge robots with two specific wheel types, using 7 robots of each type for a total of 14 as previously studied. \begin{table}
\begin{tabular}{c c c c c} \hline
**Item Target Number** & **Hormone Speed vs. Hormone Combination** & **Hormone Sleep vs. Hormone Combination** \\ \hline  & **(Environment 1)** & **(Environment 2)** & **(Environment 1)** & **(Environment 2)** \\ \hline
10 & 0.9680 & 0.0047 & 0.2315 & 0.019 \\
20 & 0.8830 & 0.0040 & 0.1653 & 0.0056 \\
30 & 0.5290 & \(p<0.0001\) & 0.5831 & \(p<0.0001\) \\
40 & 0.6017 & \(p<0.0001\) & 0.0810 & \(p<0.0001\) \\
50 & 0.5290 & \(p<0.0001\) & \(p<0.0001\) & \(p<0.0001\) \\
60 & 0.0809 & \(p<0.0001\) & \(p<0.0001\) & \(p<0.0001\) \\
70 & **0.0283** & \(p<0.0001\) & \(p<0.0001\) & \(p<0.0001\) \\
80 & **0.0047** & \(p<0.0001\) & \(p<0.0001\) & \(p<0.0001\) \\
90 & 0.0675 & \(p<0.0001\) & \(p<0.0001\) & \(p<0.0001\) \\
100 & **0.0024** & \(p<0.0001\) & \(p<0.0001\) & 0.430 \\
110 & 0.0910 & \(p<0.0001\) & 0.0024 & 0.0002 \\
120 & 0.0763 & \(p<0.0001\) & 0.9042 & \(p<0.0001\) \\
130 & 0.1081 & \(p<0.0001\) & 0.0211 & \(p<0.0001\) \\
140 & **0.0227** & \(p<0.0001\) & \(p<0.0001\) & \(p<0.0001\) \\
150 & 0.2648 & \(p<0.0001\) & \(p<0.0001\) & \(p<0.0001\) \\ \hline \end{tabular}
\end{table} 
Table 5: Wilcoxon rank sum tests comparing the combined hormone system with both the speed hormone system and the sleep hormone system, in both of the previously established environments. Tests were conducted for item collection targets between 10–150 in terms of energy efficiency. Significant differences (indicated by a \(p\) value of ¡0.05) are highlighted in **bold**. In order to incorporate heterogeneity into the swarm, while still using the energy characteristics presented in Section 3.1 to measure energy efficiency at different speeds, each wheel type was given a speed coefficient for respective terrains. These coefficients (displayed in Table 6) inhibited the speed properties of the wheels based on the ground a given robot was travelling on, these values are shown in Table 6. While not as realistic as the data used for wheel speeds in previous environment preference experiments, this allowed for the testing the combination of systems without extensive testing of robotic hardware. Effect of Demand on Environment Selection When the Speed Hormone Is Combined with Environmental Preference Hormone  
Before fully combining the systems, the speed hormone was added to the Environmental Preference System. The performance of the selection system was then measured by looking at the proportion of robots active in the environments they were best suited to as a percentage. In order to incorporate the speed hormone to the directional preference hormone system, demand functions identical to that previously produced in Section 3.2.1 were created for both the north and south environments, taking only items collected in the respective environment into account when producing demand. Depending on the environmental preference when returning to the nest site, robots within the swarm would then update their demand stimuli with the corresponding demand value. The full results of these tests are illustrated in Figure 12. Minimal differences were found in median categorisation across the range of item targets. Further, these were not found to differ from median categorisation found when the speed hormone was not included in the system. As the speed hormone did not appear to have a negative effect on the environmental preference hormones, it was deemed reasonable to further add the sleep hormone to the system. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Terrain Type** & **Wood Suited Wheels** & **Grass Suited Wheels** \\ \hline Grass & 0.6 & 0.7 \\ Wood & 1 & 0.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Speed Coefficients for Heterogeneous Robot Wheels on Different Terrains.