# Hierarchical Task Assignment and Path Finding with Limited Communication for Robot Swarms
## 5 Conclusions
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & & split16 & & & empty32 & \\ \hline \multirow{4}{*}{\begin{tabular}{c} Control \\ \end{tabular} } & & **greedy** & **CNP** & **HTAPF** & **greedy** & **CNP** & **HTAPF** \\ \cline{2-8}  & median & 141 & 154.5 & 193 & 240.5 & 279.5 & 280.5 \\  & Kruskal–Wallis & \(H=30.9\), \(p=1.9\ \times\ 10^{-7}\) & & \(H=5.4\), \(p=6.6\ \times\ 10^{-2}\) \\ \cline{2-8}  & greedy & – & 2.2\(\times\ 10^{-1}\) & \(6.4\times 10^{-9}\) & – & \(\times\) & \(\times\) \\  & CNP & – & – & \(4.5\times 10^{-6}\) & – & – & \(\times\) \\ \hline \multirow{4}{*}{\begin{tabular}{c} Control \\ \end{tabular} } & & **greedy** & **CNP** & **HTAPF** & **greedy** & **CNP** & **HTAPF** \\ \cline{2-8}  & median & 131 & 147 & 174.5 & 263 & 269 & 279.5 \\  & Kruskal–Wallis & \(H=22.5\), \(p=1.2\times 10^{-5}\) & & \(H=6.25\), \(p=4.4\times 10^{-2}\) \\ \cline{2-8}  & greedy & – & \(3.7\times 10^{-2}\) & \(3.1\times 10^{-9}\) & – & \(6.4\times 10^{-1}\) & \(5.3\times 10^{-3}\) \\  & CNP & – & – & \(1.2\times 10^{-4}\) & – & – & \(2.0\times 10^{-2}\) \\ \hline \multicolumn{8}{c}{facility} & & **lab** & \\ \hline \multirow{4}{*}{\
\begin{tabular}{c} Control \\ \end{tabular} } & & **greedy** & **CNP** & **HTAPF** & **greedy** & **CNP** & **HTAPF** \\ \cline{2-8}  & median & 173.5 & 187.5 & 191 & 226 & 260 & 276 \\  & Kruskal–Wallis & \(H=0.2\), \(p=9.1\times 10^{-1}\) & & \(H=11.3\), \(p=3.4\times 10^{-3}\) \\ \cline{2-8}  & greedy & – & \(\times\) & \(\times\) & – & \(5.0\times 10^{-6}\) & \(2.0\times 10^{-15}\) \\  & CNP & – & – & \(\times\) & – & – & \(7.7\times 10^{-4}\) \\ \hline \multirow{4}{*}{
\begin{tabular}{c} Control \\ \end{tabular} } & & **greedy** & **CNP** & **HTAPF** & **greedy** & **CNP** & **HTAPF** \\ \cline{2-8}  & median & 139.5 & 148.5 & 152.5 & 226 & 262 & 265.5 \\  & Kruskal–Wallis & \(H=2.2\), \(p=3.4\times 10^{-1}\) & & \(H=2.3\), \(p=3.2\times 10^{-1}\) \\ \cline{2-8}  & greedy & – & \(\times\) & \(\times\) & – & \(\times\) \\  & CNP & – & – & \(\times\) & – & – & \(\times\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results of the statistical tests on the simulations performed with different rates of robot failures. or scenarios where the system can be deployed without specific infrastructures, such as search and rescue scenarios and delivery systems for large industrial settings. Future work includes the study of the macroscopic dynamics of the system and the adaptive tuning of the tree exploration. A deep analysis of a macroscopic model representing the decision dynamics over the quad-tree can provide a better understanding of the dynamics characterizing the assignment process, leading to the identification of parameterizations that provide optimal performance and desired system properties, possibly including different parameters for different hierarchical levels in the quad-tree. Adaptive solutions to the tuning of some key parameters are important to dynamically respond to problem requirements. For instance, the possibility of online tuning the probability of descending the quad-tree can provide an important means to optimize the exploration-exploitation trade-off. Conceptualization D.A., W.H., V.T., N.A. and D.N. ; methodology D.A., W.H. and V.T. ; software D.A., W.H. and V.T. ; writing-review and editing, D.A., W.H., V.T., N.A. and D.N. ; funding acquisition V.T. and N.A. All authors have read and agreed to the published version of the manuscript. V.T. and D.A. acknowledge support from the Office of Naval Research Global (ONRG) for the project \"Collective Decisions in Dynamic Environments\" (Award N62909-18-1-2093). V.T. acknowledges support from the project \"TAILOR\" (H2020-ICT-48 GA: 952215). N.A. and W.H. acknowledge support from NSF under grant IIS-1724392. Not Applicable. The authors declare no conflict of interest.