## 1 Smoothing paths for 2D planning. By analyzing the results for 2D exploration and planning, you can see how using slightly longer computation time, reducing the number of path points entered in the paths, and thereby reducing by a small proportion the total distance traveled by the swarm. Figure 5 shows the qualitative result of this algorithm for a single path, so that it can be observed more clearly how the algorithm eliminates those unnecessary intermediate nodes, since it is possible to connect one node to another further away without going through that intermediate point. Figure 5a shows on a 2D plane what the original path is, while Figure 5b shows the process of removing intermediate nodes and thus a path that reduces the Zig-Zag effect discussed above. Analyzing the algorithm from a quantitative point of view, the number of path points generated in the whole of the paths, the computational time derived from the implementation of that method or the total distance traveled by the swarm depending on the type of path used are aspects to deal with. To this end, it has been decided to compare the solution generated by the 2D path planner for both situations, considering only the labeled case, that is, in which the objective assignment-UAV is correlative to the order of registration of the aircraft and the final locations. The experiments have been conducted considering a swarm of 5 UAVs and, since the exploration of the environment is random, 5 different attempts have been made on the same scenario to be able to analyze the data more accurately. The first aspect to consider is the number of path points generated in each of the paths and how with the use of the smoothing algorithm it is possible to reduce, in most cases, the number of path points involved in each of the paths of the UAVs, as shown in Table 1.  
Figure 5: Example of 2D path smoothing. Although individually the reduction of path points may seem small, if you analyze their impact on all the paths generated for swarm it is observed that the overall is greater, as shown in Figure 6. It is drawn from the data collected in that figure that, in some cases, the reduction of the path points is greater than 20% and that, the mean is very close to it, with a value of 19.41%, which for a small scenario such as Figure 5 is not a significant number of path points, but that for large environments, a 20% reduction in the intermediate nodes to be achieved can result in a significant improvement in both the dynamic behavior and the total time spent by the UAV in covering that trajectory. If, in addition, one of the path points is present in the path of each UAV, which will always be present, and the reduction of path points is analyzed considering only the intermediate nodes, the reduction percentage rises to 23.85% of all possible nodes to be deleted, since that path point corresponding to the destination is part of all paths. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Test 1**} & \multicolumn{2}{c}{**Test 2**} & \multicolumn{2}{c}{**Test 3**} & \multicolumn{2}{c}{**Test 4**} & \multicolumn{2}{c}{**Test 5**} \\ \hline
**Paths** & **O** & **S** & **O** & **S** & **O** & **S** & **O** & **S** & **O** & **S** \\ \hline \(UAV_{1}\) & 5 & 4 & 5 & 3 & 6 & 4 & 6 & 4 & 5 & 4 \\ \hline \(UAV_{2}\) & 6 & 4 & 6 & 5 & 6 & 5 & 5 & 4 & 6 & 5 \\ \hline \(UAV_{3}\) & 6 & 4 & 7 & 5 & 6 & 5 & 5 & 5 & 5 \\ \hline \(UAV_{4}\) & 5 & 4 & 6 & 5 & 6 & 5 & 5 & 4 & 6 & 5 \\ \hline \(UAV_{5}\) & 4 & 4 & 4 & 3 & 5 & 4 & 4 & 4 & 4 & 4 \\ \hline \hline \end{tabular}  
* O = Original Path, S = Smooth Path.  
\end{table} 
Table 1: Comparison of waypoints entered in the original and smoothed 2D paths for each UAV in the swarm. Figure 6: Comparison of total waypoints for original paths and 2D smoothed paths for a swarm of 5 UAVs.