## 6 Baseline Statement and AAMO Approach Results
### Aamo Assessment
#### 6.4.3 _Aamo_ vs. Baseline Comparison  
Concerning _TT_, as was expected in multi-robot systems, all _AAMO_ instances benefit from adding robots to the fleet. This result can be seen in Figure 18a. Nevertheless, compared to the baseline results all _AAMO_ instances show performance degradation (see Figure 18b). The evidence indicates that the more efforts made in favour of connectivity (bigger HO-Threshold) the worst _TT_. In other words, not all _HO-Threshold_ setup values produce the same level of performance  
Figure 17: _AAMO_ Coverage ratio. Regardless of how different the _HO-Threshold_ values are, in all cases, the _AAMO_ approach can cover more than 99% of the terrain. Figure 18: _AAMO_ Total Exploration Time (TT) under non-ideal communication conditions and Degradation with respect to baseline results. (**a**) All _AAMO_ instances show a decreasing trend of TT as the fleet size increase. The _Yamauchi_ and _MinPos_ approach results (coloured in purple and green, respectively) obtained under ideal communication conditions are placed together to make the comparison easier; (**b**) The degradation is expressed in terms of the difference between the TT achieved by each of the _AAMO_ instances and the one achieved by the _MinPos_ approach, for each fleet size. degradation. Since the degradation of TT performance could be very problematic in many application fields, this subject is carefully analysed. At first, the PL indicator can help to initially explain why the fleet spends more time under _AAMO_ approach than under the _MinPos_ approach, to explore the same environment. In Figure 19a it is possible to observe the same behaviour as in the baseline (see Section 6.3): larger fleets imply bigger PL; while Figure 19b shows the difference between the corresponding total length of the paths traversed by fleets. The similarity between Figures 18b and 19b is remarkable and could explain, to a large extent, the origin of TT degradation. Simply, under the _AAMO_ approach, the robots are asked to invest some effort (translated as a distance using the HO-Threshold) in order to keep the fleet connected and hence it is logic to get a bigger PL as a result. Moreover, the tradeoff between path and connectivity utility discussed in Section 3.1 shows up through these results, reflecting that the price of connectivity maintenance is the inability to apply an optimal policy concerning path costs. Nevertheless, there exists a small portion of the TT degradation that cannot be explained by the PL increasing. Therefore, the hypothesis assumed in the tractability analysis made at the end of Section 5.2 are compared here with the simulation results in order to add a complementary explanation on the TT degradation. Furthermore, this TT degradation shows a parabolic trend as the fleet size increase, reaching a maximum about three-sized fleets, independently of the _HO-Threshold_ values. Thus, the analysis will be conducted observing what happens when the fleet size does change but the _HO-Threshold_ does not (in order to explain the shape of the curve or the relative values), and the opposite conditions are imposed in order to explain the absolute values. In any case, it is worth knowing that the _Task selection_ algorithm is the most demanding software component in the software architecture of the robots. Hence, the overall performance of the multi-robot system is highly determined by the performance of this component. In turn--as was pointed out in Section 5.2--its performance is strongly influenced by the number of unassigned thresholded tasks \(n=|T^{\text{HO}}|\) and the number of unassigned robots in a connected component \(m=|R^{u}|\) that are making a decision at the same time, in the following way: \(|Ar_{m}^{n}|=\frac{n!}{(n-m)! }=\Pi_{m=0}^{n-1}(n-m)\to O(n^{m})\). Therefore,  
Figure 19: _AAMO_ Path length (PL) under non-ideal communication conditions and Degradation with respect to baseline results. (**a**) An increasing trend of PL is shown by all _AAMO_ instances as the fleet size increase.