*4.1. Preliminary Tests for Sleep Hormone in A Demand Lead Foraging Task*

The initial tests conducted on the new sleep hormone system used the same environments as the previous section and operated until a time limit of 500 seconds or until the target number of items was reached. A cumulative mean test indicated that a minimum of 14 trials were required. To ensure certainty, 20 trials were run.

#### 4.1.1. Environment 1—Square Open Arena

Observing the results for the first environment (illustrated in Figure 8) the results appear very different to those of the previous three systems. The energy efficiency starts low, peaking momentarily and, after a dip to median performance, increases as the number of target items does. This pattern leads to an increased energy efficiency at all item targets compared to the

previously tested static speed system and considerably better efficiency performance at item targets greater than 120 for the other two adaptive systems.

The initial spike in performance from this pattern is explained by the removal of poorly positioned robots at deployment. Those robots starting off in large groups will enter the sleep state either immediately or very soon after exploration. This initial state selection is then diluted as robots make more passes between the nest and the food area, seen as the Food Collected Per Energy used (FPE) reduces to a similar level as the non-adaptive system seen in Section 3.5. The gradual increase to FPE thereafter is due to the sleeping of poorly performing robots across greater periods of time, while robots with better positioning within the arena are able to collect food items more effectively.

While this system sees several increases to performance in terms of energy efficiency, it sacrifices this for poor performance in terms of item collection, with collection starting to drop at item targets of 90, lower than even the static system in the previous section. This is expected as the system actively impedes collection speed, with the sleep state removing swarm members for brief periods of time.

Though the collection percentage is lower in the sleep system than in the systems previously examined, this does show that it may be beneficial from the perspective of energy efficiency to combine the speed and sleep systems. With the intention of reducing the decrease to FPE seen in the adaptive speed systems as item target increases and using the speed system to compensate for the poor collection performance seen at targets above 90.

**Figure 8.** Hormone inspired sleep system tested in environment 1. Target number for items collected ranged from 10 to 150 items of food. Percentage of the items requested versus those collected by the end of the simulation is indicated by colour (Green 100% and Red < 70%).

#### 4.1.2. Environment 2—Funnelled Corridor Arena

The benefit of this enhanced hormone system is further proven in the second environment. Following a similar pattern to the first environment, the energy efficiency increases with the target number (illustrated in Figure 9). In this environment, the sleep system is able to outperform the static and engineered system in terms of energy efficiency across all item target values. In addition to this, while not able to compete at lower item targets, after 80 items the sleep system largely outperforms the hormone speed system.

This increase to energy efficiency is due to the sleep system regulating the number of robots present in the corridors at any given moment, retaining poorly performing robots until demand is high and as a result increasing the productivity of the foraging swarm.

Again these results, while producing good values for energy efficiency, sacrifice collection rate. With collection similar to the static system, failing past 50 items.

**Figure 9.** Hormone inspired sleep system tested in environment 2. Target number for items collected ranged from 10 to 150 items of food. Percentage of the items requested versus those collected by the end of the simulation is indicated by colour (Green 100% and Red < 70%).

#### *4.2. Combining the Sleep Hormone with the Speed Deviating System*

In an attempt to combine the benefits of both hormone systems and to identify the viability of combining existing hormone systems, the speed hormone was added to the already established sleep system. The parameter values established in prior testing were again used for the combined system. The speed hormone acted explicitly on motor speeds during exploration and the sleep hormone system regulated higher level behaviours.

The performance of this new combined system is illustrated in Figure 10. The first obvious improvement to the system can be seen in the results from the first environment, this set of data achieves the highest average collection rate of any system at a required collection of 150, obtaining an average of 92.3% of the needed items.

In addition to this the combined system achieves a significantly greater energy efficiency versus the sleep system at all item targets between 50 and 110 in the first environment and all item targets before 100 in environment 2 (*p* values for these tests can be found in Table 5). At higher value item targets the energy efficiency still crosses over, though the exceptional item collection rate more than compensates for this.

Relative to the adaptive speed system the combined hormone system obtains very similar results in the first environment at target item values below 70. Though there are large improvements to the energy efficiency at item targets larger than this. This increase to performance is mirrored in environment 2, though with a consistent increase at all item target values.

The substantial improvement in performance is proposed to be the mutually beneficial actions of the separate systems. It allows the system to avoid the circumstance in which positioned poorly robots in a high demand context might travel at high speeds that a cause large drain to power for poor returns.

It is clear from these results that these systems work better in combination than separately. This shows a strong symbiosis of already established hormone control, verifying the viability of combining hormone systems.

**Figure 10.** Combined hormone sleep and speed system tested in both environments. Target number for items collected ranged from 10 to 150 items of food. Percentage of the items requested versus those collected by the end of the simulation is indicated by colour (Green 100% and Red < 70%).


**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**.
