# Robot Swarms Decide under Perception Errors in Best-of-N Problems
## 6 Conclusions  
In this study, we have investigated the emergence of collective decisions in best-of-N problems, when robots are subject to perception errors. Most works which investigated \begin{table}
\begin{tabular}{|c|c|c|c|c|} \hline \multirow{2}{*}{**Population Composition**} & \multicolumn{2}{c|}{**Basic Model**} & \multicolumn{2}{c|}{**Distance-Based Algorithm**} \\  & **\% Site A** & **\% Site B** & **\% Site A** & **\% Site B** \\ \hline
105 A, 105 U, 0 O & 7\% & 93\% & 16\% & 84\% \\ \hline
0 A, 210 U, 0 O & 0\% & 100\% & 0\% & 100\% \\ \hline
30 A, 120 U, 60 O & 33\% & 67\% & 63\% & 37\% \\ \hline
70 A, 70 U, 70 O & 36\% & 64\% & 40\% & 60\% \\ \hline
60 A, 120 U, 30 O & 23\% & 77\% & 53\% & 47\% \\ \hline
105 A, 0 U, 105 O & 7\% & 93\% & 33\% & 67\% \\ \hline
90 A, 90 U, 30 O & 57\% & 43\% & 46\% & 54\% \\ \hline
60 A, 30 U, 120 O & 20\% & 80\% & 30\% & 70\% \\ \hline
0 A, 105 U, 105 O & 47\% & 53\% & 60\% & 40\% \\ \hline \end{tabular}
\end{table} 
Table 4: Comparing the accuracy of consensus accuracy when using the basic behavioral model vs. the distance-based algorithm for different swarm compositions. Errors in measurements can occur at both sites A and B.  
Figure 5: The emergence of collective decision: (**a**) when robots follow the basic behavioral model, and (**b**) when robots classify themselves using the distance-based algorithm. We simulate a swarm of the following: 70 objective, 70 underestimating, and 70 overestimating robots, where Errors in measurements can occur at both sites A and B.  
best-of-N decisions in robot swarms assumed robots to perform accurate quality measurements of the available options. Nevertheless, reality diverges from this assumption as real robots are mostly associated with perception errors. Taking that into consideration, we have proposed three algorithms to help robots classify themselves into one of the three populations: overestimating, underestimating, and accurate. These populations can be mapped to robots in real scenarios with high-quality sensors vs. low-quality sensors. The algorithms we have exploited are as follows: (i) the distance-based algorithm, (ii) the k-means algorithm, and density-based algorithm for discovering clusters (DBSCAN). We have compared the performance of the three algorithms in terms of their classification accuracy using different swarm sizes and various population compositions. Our results showed that classification accuracy drops with decreasing swarm size; also, for a specific size, the different population compositions play a key role in the resultant classification accuracy. In general, the distance-based algorithm performed best in regards to classification accuracy across the different swarm sizes and compositions. After testing the classification accuracy of the three algorithms, we selected the best-performing algorithm and tested the accuracy of the collective decision when using classification (the distance-based algorithm) vs. no classification (the basic behavioral model). We have examined the decision accuracy for two cases: (a) measurement errors can occur at one site (here site B), and (b) measurement errors can occur at both sites A and B. When measurement errors are allowed at site B only (the site with the highest quality value), overestimating robots or accurate robots need to represent the majority of the swarm to converge with a high likelihood at the best option (i.e., site B). Moreover, using the distance-based algorithms by the robots to classify themselves results in a higher decision accuracy than when no classification is used. For the case where measurement errors were allowed at both sites, using the distance-based classification algorithm drops the decision accuracy below the one resulting from the basic behavioral model. These counterintuitive results can be explained as the population evaluating site A splits into overestimating, underestimating, and accurate instead of only accurate.