# Evaluating Swarm Robotics for Mining Environments: Insights into Model Performance and Application
## 5 Results and Discussions
### Statistical Analysis  
To evaluate significant performance differences between the models, analysis of the variance (ANOVA) test was performed. The results summarized in Table 1 indicate that there is at least one model for which statistically significant differences in harvesting speeds versus the different models have been identified. These differences have operational significance in real-world mining scenarios, as the analysis can evaluate the varying levels of efficiency and suitability for specific tasks. To further investigate which specific models differed from one another, the Tukey honestly significant difference (HSD) post hoc tests were performed. Table 2 summarizes the results from the Tukey HSD test, showing the mean differences between each pair of models, as well as their corresponding \(p\)-values and confidence intervals. Statistical analysis showed that there were significant differences in the harvesting speeds of all four swarm models. The efficiency of the honeybee model was superior to the other models thanks to the hybrid control system. The results show that the honeybee model has the shortest harvesting time, mainly because its hybrid control system reduces idle time and maximizes task allocation. This makes the honeybee model particularly effective for real-world scenarios that require high precision and speed, such as for selective mining of high-grade ores, as for hematite in the Pilbara iron ore mine. In these operations, faster harvesting can improve profitability and reduce operating costs through more efficient resource positioning. However, given its slower harvesting speed, the baseline model may be less effective for tasks that must be completed quickly. But in smaller or less dynamic mining operations, where job consistency is more important than the speed, its simplicity may be an advantage. The ant model shows a moderate level of efficiency due to task specialization. This may make it useful in mining environments where ore is concentrated in specific areas, such as vein mining or block caving. Due to its ability to specialize its \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Source of Variation** & **Sum of Squares (SS)** & **Degree of Freedom (df)** & **Mean Squares (MS)** & **F-Ratio** & \(p\)**-Value** \\ \hline Between groups & 1,740,254 & 3 & 580,085 & 2307 & \textless{}0.05 \\ \hline Within groups & 14,084 & 56 & & & \\ \hline Total & 1,754,337 & 59 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Statistical analysis via ANOVA test. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Comparison** & **Mean Difference** & \(p\)**-Value** & **95\% CI Lower** & **95\% CI Upper** \\ \hline Baseline vs. Ant & 135.87 & \textless{}0.01 & 119.37 & 152.37 \\ \hline Baseline vs. Firefly & 222.13 & \textless{}0.01 & 205.63 & 238.63 \\ \hline Baseline vs. Honeybee & 387.53 & \textless{}0.01 & 371.03 & 404.03 \\ \hline Ant vs. Firefly & 86.27 & \textless{}0.01 & 69.77 & 102.77 \\ \hline Ant vs. Honeybee & 251.67 & \textless{}0.01 & 135.17 & 168.17 \\ \hline Honeybee vs. Firefly & 165.40 & \textless{}0.01 & 148.90 & 181.90 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Statistical analysis via Tukey HSD test. roles, this model may be useful in mining operations, where different task allocations are advantageous, such as for a vast mining area for transportation. The firefly model's performance is between the ant and honeybee models. Its bioluminescent communication system provides real-time communication and coordination capabilities that may be well-suited for complex environments such as large open pit mines like the Pilbara iron ore mine, where rapid detection and mining of large areas of ore is critical. Considering the firefly model's ability to significantly reduce the exploration time, it may be a good choice for operations that require rapid adaptation to changing environments.