## 6 Baseline Statement and AAMO Approach Results
### Aamo Assessment
#### 6.4.3 _Aamo_ vs. Baseline Comparison
\begin{table}
\begin{tabular}{l c c c c c c c c c} \hline \hline \multirow{2}{*}{**HO-Threshold**} & \multirow{2}{*}{\(|R|\)} & \multicolumn{4}{c}{\(|R^{u}|\)**that are simultaneously making a decision**} \\ \cline{3-10}  & & \multicolumn{2}{c}{**1**} & \multicolumn{2}{c}{**2**} & \multicolumn{2}{c}{**3**} & \multicolumn{2}{c}{**4**} \\ \cline{3-10}  & & **AVE** & **StD** & **AVE** & **StD** & **AVE** & **StD** & **AVE** & **StD** \\ \hline \multirow{3}{*}{AAMO:10} & 3 & 0.959 & 0.01 & 0.041 & 0.01 & \(\simeq 0\) & \(\simeq 0\) & n/a & n/a \\  & 5 & 0.895 & 0.02 & 0.097 & 0.02 & 0.011 & 0.01 & \(\simeq 0\) & \(\simeq 0\) \\  & 8 & 0.807 & 0.02 & 0.153 & 0.04 & 0.037 & 0.02 & \(\simeq 0\) & \(\simeq 0\) \\ \hline \multirow{3}{*}{AAMO:15} & 3 & 0.969 & 0.02 & 0.031 & 0.02 & \(\simeq 0\) & \(\simeq 0\) & n/a & n/a \\  & 5 & 0.929 & 0.02 & 0.068 & 0.03 & 0.003 & 0.01 & \(\simeq 0\) & \(\simeq 0\) \\  & 8 & 0.823 & 0.03 & 0.146 & 0.03 & 0.024 & 0.01 & \(\simeq 0\) & \(\simeq 0\) \\ \hline \multirow{3}{*}{AAMO:20} & 3 & 0.968 & 0.02 & 0.032 & 0.02 & \(\simeq 0\) & \(\simeq 0\) & n/a & n/a \\  & 5 & 0.917 & 0.02 & 0.080 & 0.02 & 0.003 & 0.01 & \(\simeq 0\) & \(\simeq 0\) \\ \cline{1-1}  & 8 & 0.838 & 0.02 & 0.148 & 0.03 & 0.018 & 0.01 & \(\simeq 0\) & \(\simeq 0\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: _AAMO_ Robot Coincidence on Decision Making moments. Figure 20: The maximum amount of unassigned robots \(|R^{u}|\) in any connected component over time under different sized multi-robot systems. All images concern instances of _AAMO_ set with HO-Threshold = 15. Blue dots represent the \(|R^{u}|\) (on average) that are simultaneously deciding along the exploration. the exploration. In such a stage, the new available tasks generally appear further to each other and its total amount \(|T^{u}|\) is decreasing. Therefore, since the tasks \(T^{\text{HO}}\) are the ones which are closer than a relative distance _HO-Threshold_, under the _AAMO_ approach, it is statistically less demanding for the robots to select a task during the last exploration stage than in the initial one. Additionally, either when the fleet size increase or the _HO-Threshold_ decrease, the transition from the first to the second exploration stage is achieved faster. This fact can be corroborated in both Figures 21 and 22. For instance, concerning Figure 21, the 3-Robot system spends about 410 s to reach the end of the dispersion stage whereas the 5-Robot system and 8-Robot system spend about 320 s and 260 s, respectively. Likewise, from Figure 22, the AAMO:20 instance spends about 310 s to reach the end of the dispersion stage whereas the AAMO:15 and AAMO:10 spend about 260 s and 150 s, respectively. Hence, despite the fact the impact of the fleet size on the exploration stage transition appears to be higher than the one caused by the _HO-Threshold_ value, both aspects contribute to reducing the task selection effort enabling robots to save time in the task allocation procedure anticipatedly. In conclusion, when the _AAMO_ is executed in bounded environments, the addition of robots and the decreasing of _HO-Threshold_ can almost entirely mitigate the worsening in the total exploration time performance. Please note that the performance degradation of AAMO:10 instances is almost null for eight-sized fleets. From these promising results, in the following, all _AAMO_ instances are compared with the other approaches concerning non-ideal communication conditions. Figure 21: Amount of unassigned tasks \(|T^{u}|\) over time for different sized multi-robot systems. All images concern instances of _AAMO_ set with HO-Threshold = 15. The maximum \(|T^{u}|\) and the end of the dispersion stage are reached at the same time. Red dots represent the \(|T^{u}|\) considered by robots (on average) along the exploration. Figure 22: Number of unassigned tasks \(|T^{u}|\) over time for different instances of the _AAMO_ approach on 8-Robot systems. The maximum \(|T^{u}|\) and the end of the dispersion stage are reached at the same time.