# Hierarchical Task Assignment and Path Finding with Limited Communication for Robot Swarms
## 4 Experimental Evaluation
### Results
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & \multicolumn{3}{c}{split 16} & \multicolumn{3}{c}{empty32} \\ \hline  & & **greedy** & **CNP** & **HTAPF** & **greedy** & **CNP** & **HTAPF** \\ \cline{2-8} \multirow{4}{*}{\(\big{\|}\)} & median & 145.5 & 174 & 183 & 240 & 287 & 281.5 \\  & Kruskal–Wallis & \(H=58.5\), \(p=5.9\times 10^{-12}\) & & \(H=34.4\), \(p=6.0\times 10^{-7}\) \\ \cline{2-8}  & \multirow{2}{*}{\(\big{\|}\)} & greedy & – & \(1.7\times 10^{-4}\) & \(1.9\times 10^{-7}\) & – & \(8.8\times 10^{-7}\) & \(4.6\times 10^{-5}\) \\  & & CNP & – & – & \(1.5\times 10^{-1}\) & – & – & \(4.0\times 10^{-1}\) \\ \hline  & & **greedy** & **CNP** & **HTAPF** & **greedy** & **CNP** & **HTAPF** \\ \cline{2-8}  & median & 139 & 165.5 & 191 & 241.5 & 277 & 280.5 \\  & Kruskal–Wallis & \(H=72.86\), \(p=5.6\times 10^{-15}\) & & \(H=21.67\), \(p=2.3\times 10^{-4}\) \\ \cline{2-8}  & \multirow{2}{*}{\(\big{\|}\)} & greedy & – & \(1.2\times 10^{-2}\) & \(3.7\times 10^{-9}\) & – & \(6.6\times 10^{-3}\) & \(2.1\times 10^{-5}\) \\  & CNP & – & – & \(7.3\times 10^{-4}\) & – & – & \(1.2\times 10^{-1}\) \\ \hline  & & **greedy** & **CNP** & **HTAPF** & **greedy** & **CNP** & **HTAPF** \\ \cline{2-8}  & median & 145.5 & 150 & 177 & 244 & 285.5 & 268.5 \\  & Kruskal–Wallis & \(H=35.5\), \(p=3.7\times 10^{-7}\) & & \(H=13.7\), \(p=8.3\times 10^{-3}\) \\ \cline{2-8}  & \multirow{2}{*}{\(\big{\|}\)} & greedy & – & \(2.6\times 10^{-1}\) & \(3.8\times 10^{-5}\) & – & \(1.1\times 10^{-3}\) & \(2.5\times 10^{-1}\) \\  & CNP & – & – & \(2.7\times 10^{-3}\) & – & – & \(3.3\times 10^{-2}\) \\ \hline  & & \multicolumn{3}{c}{facility} & \multicolumn{3}{c}{lab} \\ \hline  & & **greedy** & **CNP** & **HTAPF** & **greedy** & **CNP** & **HTAPF** \\ \cline{2-8}  & median & 203 & 208.5 & 191 & 224 & 273.5 & 252.5 \\  & Kruskal–Wallis & \(H=8.2\), \(p=8.3\times 10^{-2}\) & & \(H=60.5\), \(p=2.3\times 10^{-12}\) \\ \cline{2-8}  & \multirow{2}{*}{\(\big{\|}\)} & greedy & – & \(\times\) & \(\times\) & – & \(3.2\times 10^{-12}\) & \(3.7\times 10^{-8}\) \\  & CNP & – & – & \(\times\) & – & – & \(1.4\times 10^{-1}\) \\ \hline  & & **greedy** & **CNP** & **HTAPF** & **greedy** & **CNP** & **HTAPF** \\ \cline{2-8}  & median & 196.5 & 195 & 175 & 227 & 271.5 & 271 \\  & Kruskal–Wallis & \(H=17.2\), \(p=1.8\times 10^{-3}\) & & \(H=43.1\), \(p=1.0\times 10^{-8}\) \\ \cline{2-8}  & \multirow{2}{*}{\(\big{\|}\)} & greedy & – & \(1.2\times 10^{-1}\) & \(8.5\times 10^{-4}\) & – & \(7.4\times 10^{-8}\) & \(1.5\times 10^{-7}\) \\  & CNP & – & – & \(7.4\times 10^{-2}\) & – & – & \(8.9\times 10^{-1}\) \\ \hline  & & **greedy** & **CNP** & **HTAPF** & **greedy** & **CNP** & **HTAPF** \\ \cline{2-8}  & median & 194 & 171.5 & 158.5 & 227 & 256.5 & 273.5 \\  & Kruskal–Wallis & \(H=38.4\), \(p=9.1\times 10^{-8}\) & & \(H=35.8\), \(p=3.2\times 10^{-7}\) \\ \cline{2-8}  & \multirow{2}{*}{\(\big{\|}\)} & greedy & – & \(3.8\times 10^{-3}\) & \(2.0\times 10^{-6}\) & – & \(2.0\times 10^{-2}\) & \(6.0\times 10^{-5}\) \\  & CNP & – & – & \(6.4\times 10^{-2}\) & – & – & \(2.8\times 10^{-2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results of the statistical tests on the simulations performed with different limited communication range. than the greedy approach, although a higher variability for CNP is observed when the communication sensitivity is worse (\(S=-100\) and \(S=-80\)). In the latter case, CNP performs slightly better, thanks to the ease of motion granted to the robots (see Figure 6, top-right, and Table 2). When robot failures are introduced, instead, HTAPF performs better than the other approaches for the highest failure rate, as it proves to be more robust in re-allocating the residual robots when needed. Indeed, there is no significant drop in performance with increasing failure rates (see Figure 7, top-right, and Table 3). The facility environment is the one that presents the harshest communication limitations, with thick walls preventing a proper exchange of information.