# Robot Swarms Decide under Perception Errors in Best-of-N Problems
## 5 Results  
### Classification Accuracy  
In this section, we investigate the classification accuracy of the three algorithms by applying the extended model presented in Section 3. Each of these algorithms enables robots to classify themselves as accurate, overestimation, or underestimating after exploring site A. For Site B (as mentioned in experiments set (i)), all robots measure the site's quality accurately. That is \(\gamma_{i}(l)\sim Gaussian(\mu_{l},\sigma_{l})\), where \(\mu_{l}=\psi_{l}+\delta_{l}\) and \(\delta_{l}=0\). We investigate four swarm sizes for each algorithm: 210, 150, 90, and 30 robots. For a swarm size of 210, we examine different population configurations, shifting from one dominant population to equal populations (see Table 2). For the distance-based algorithm, our findings show that the system is highly sensitive to variations in swarm size with \(R^{2}=0.78\) as the goodness of linear fit. This decrease can be explained by a decrease in neighborhood size, which impacts the size of the measurements sample used by the robot to decide which population it belongs to. For large swarm sizes (210 in our simulations), the algorithm's accuracy declines only when a single population of robots participates in the site selection task, unless it is the population of accurate robots. Surprisingly, when two populations are recognized, the distance-based approach remains accurate in the majority of cases. We believe that maintaining such an accurate classification is due to the use of global knowledge of parameter \(\delta_{l}\) by individual robots. For the k-means algorithm, we set k = 3 for all experiments, and the maximum number of iterations is set to 100. In general, k-mean performs less accurately than the distance-based algorithm. Its accuracy drops specifically when the swarm has two or less robot populations. The reason for this low performance is that the acquired data are forced to be dispersed in three clusters (k = 3), regardless of the actual number of populations. \begin{table}
\begin{tabular}{l l r} \hline \hline \(\mu_{A}\) & mean of quality value of site A & \(20\times 10^{2}\) \\ \(\mu_{B}\) & mean of quality value of site B & \(25\times 10^{2}\) \\ \(\sigma_{l\in\{A,B\}}\) & standard deviation of quality value of sites A and B & \(2\times 10^{2}\) \\ \(\delta_{l\in\{A,B\}}\) & robot’s erroneous parameter for sites A and B & \(5\times 10^{2}\) \\ \(\xi\) & minimum number of robot’s on-site measurements & 50 \\ \(\epsilon\) & parameter used to differentiate between a symmetric and a non-symmetric decision & 50 \\ \(N_{min}\) & minimum number of neighbors required by the robot to update its opinion & 5 \\ \(\theta_{mix}\) & period used to mix up robots in nest after exploration and before dissemination & 1250 ts \\ \(\theta_{classify}\) & period used to collect data by the robots as input for their classification algorithm & 1250 ts \\ \(\zeta\) & a robot’s interaction threshold after which robots from any population shift their classification to accurate & 50 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The selected parameter values for both the basic and extended behavioral models. \begin{table}
\begin{tabular}{|c|c|c|c|c|} \hline
**Swarm Size** & **Population Composition** & **Distance-Based** & **k-Means** & **DBSCAN** \\ \hline \multirow{8}{*}{210 robots} & 70 A, 70 U, 70 O & 99\% & 71.5\% & 98\% \\  & 90 A, 90 U, 30 O & 90.5\% & 71\% & 89.5\% \\  & 90 A, 30 U, 90 O & 99.5\% & 70.5\% & 90.5\% \\  & 30 A, 90 U, 90 O & 99\% & 70\% & 82.5\% \\  & 1  
Classification accuracy shows linear decline with a swarm size with \(R^{2}=0.74\) as the goodness of linear fit. For the DBSCAN, we set \(Amin=3\) and \(\rho=50\) (the threshold used to build the adjacent list) for all experiments. If _rho_ is set too small, it becomes difficult in small swarms to encounter measurements that are within _rho_ distance from each other; similarly, if _rho_ is set too large, it becomes difficult to map the collected data to the correct number of populations.