*3.5. Results*

The results are illustrated in Figure 6 for environment 1 and Figure 7 for environment 2.

**Figure 6.** 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%).

**Figure 7.** Three systems tested in 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%).

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

Visual inspection of the first environment (Figure 6) shows that the static speed system has a fairly consistent level of food collected per energy unit used as the demand increases. This is expected due to the lack of change in speed, though the lowest target number for item collection does see a drop in energy efficiency when compared with the rest of the collection rates. This is because not all of the robots in the swarm will have returned to the nest by the time the experiment terminates having reached the target number of items. This will result in unnecessary energy consumption from the robots unable to return food items within the short period of the experiment.

The downside of this consistent energy consumption is the inability to reach greater item target numbers. This drawback can be seen in the discolouration of the box plots starting at 100 food items required and saturating to red, indicating a collection of less than 70% of the required items, by 130 required items.

Disregarding the lack of success in large item demand experiments, the results from the static speed system provide a strong baseline for energy efficiency. Giving a clear target for the other two more intelligent systems to aim for.

When inspecting the results of the two adaptive system it is immediately obvious that target collections are met more consistently with the demand function introduced to the system, with discolouration starting at 120 in the engineered system and 130 in the hormone system. In the engineered system the collection rate drops to approximately 80% by the 150 item goal while the hormone system still manages to collect upwards of 90%.

In terms of energy efficiency the engineered adaptive system follows a similar initial trend to the none adaptive system. The similarity is maintained until an item target of 50, at which point the engineered system becomes increasingly less efficient. Table 2 supports this, showing that there is no significant difference in the data sets of the Engineered and static systems until 70 target items. At this point the systems diverge as the engineered system consumes more energy.


**Table 2.** Environment 1: Wilcoxon rank sum tests comparing the three systems for the tested 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**.

These results also show that the hormone system managed to outperform both systems in regard to energy efficiency. With a significant difference versus the engineered adaptation and increased median result at every collection target excluding 10, the hormone system results can be seen arcing over those of the engineered system after starting at a similar point. Similarly, when compared to the static system, the hormone system shows significant increases to the food collected per energy used in all cases but targets of 10, 120 and 130 items. The similarity in energy efficiency of the hormone and speed systems at item targets of 120 and 130 can be explained by the speed increase of the hormone system in cases of very high item demand, actually reaching collection targets while the static system misses them by a large margin.

The efficiency of the hormone system over the static and engineered systems was explained by three factors:


3.5.2. Environment 2—Funnelled Corridor Arena

The results for the second environment, the increased length of environment and introduction of corridors, predictably show a notable decrease in percentage of target collection completed. The static system started to fail collection targets at 50 items and the engineered adaptive system starting to fail at 70. Compared with these, the change to collection rate in the hormone system is substantially less reduced. The results show the hormone system falling to a 70% collection rate at the 130 item target mark, showing a considerable increase in collection performance versus the two comparison systems.

In terms of energy efficiency there is again an expected drop in performance, when compared to the first environment, across all experiments due to the larger, more cluttered arena.

Analysing the systems tested in this environment, there is very little statistical similarity. Table 3 shows that almost all of the data sets at each item target number, with the exception of the first 5 item targets of the engineered versus static system, are all significantly different. The data produced from this environment does however follow very similar patterns those of the first environment. The static system maintains a consistent energy efficiency, though dipping slightly in the case of the smallest collection target. The Engineered system, while improving collection, does little to benefit energy consumption and lessens as target numbers increase. The hormone system, while exceeding the two comparison systems in both collection and energy efficiency, as it did in the first environment, does so in a much more exaggerated manner in the second environment.



#### **4. Introduction of the Sleep Hormone to a Foraging Swarm**

The foundations of the introduced sleep hormone system are very similar to those presented in [5], following the same behaviour states as formerly designed. The system transitions through search, sleep, food collection and obstacle avoidance behaviours, directed by hunger, sleep and avoidance hormones. The hunger hormone was given an identical structure. However, due to the slight change in context to the foraging system, the stimulus to the sleep hormone in the system was edited from the original equation (first seen in [5]):

$$\text{Slleep Homogeneous (original): } H\_{\mathcal{T}}(t) = \lambda\_{\mathcal{T}} H\_{\mathcal{T}}(t-1) + \gamma\_{\mathcal{T}} H\_{A}(t-1) \tag{7}$$

In these equations a sub index of '*σ*' indicates relation to the sleep hormone and '*A*' the relation to the avoidance hormone. Numbers ensuring these symbols indicate an additional coefficient relating to the parameter type i.e., decay or stimuli.

The additions to the original equation include both an *α* value and an inhibitor in the form of *γσ*2*d* (where *d*(*t*) is the function of demand presented earlier in this paper) resulting in the new equation:

$$\text{New Sleep Formula: } H\_{\mathcal{V}}(t) = a\_{\mathcal{V}} + \lambda\_{\mathcal{V}} H\_{\mathcal{V}}(t-1) + \gamma\_{\sigma 1} H\_A(t-1) - \gamma\_{\sigma 2} d(t) \tag{8}$$

The introduction of an *α* value offsets the settling point of the hormone. This allowed for the implementation of the demand based inhibitor (*γAl*2*d*(*t*)) and ensured that the hormone could fluctuate below the settling point without producing a negative value. The demand inhibitor itself created a larger decrease to the sleep hormone under high demand circumstances, assisting the decay already present in the hormone and reducing sleep times when the swarm's rate of collection was inadequate.

Meanwhile *Hh* (the sub index of *h* indicating a parameters relation to the hunger hormone) was kept in the same format, using the equation:

$$\text{Hunger Hormone: } H\_h(t) = a\_h + \lambda\_h H\_h(t-1) + \gamma\_h S \tag{9}$$

where *S* is a Boolean value representing whether the robot successfully returned a food item to the nest site or not.

The parameters used for the hunger and sleep hormones were calculated in a similar manner as Section 3.2.4, using the approximate time scale across which the hormones were expected to operate and thereafter tuning stimuli for the fitting reaction. The parameter values selected for the coming experiments are displayed in Table 4.


**Table 4.** Parameter values for the Return and Speed Hormones.
