# Long-Range Navigation in Complex and Dynamic Environments with Full-Stack S-DOVS +
## 4 Experiments and Discussion
### Quantitative Experiments  
Our quantitative experiments aimed to evaluate the effectiveness of the global planner in helping S-DOVS to avoid collisions by utilizing the previous static map information and adding new static obstacles to the cost map that are avoided with the global plan. The first experiments compared the use of the waypoint generator in a simple \(4\times 4\) m\({}^{2}\) room as the scenario and in a map with multiple rooms, as shown in Figure 5. Static and dynamic obstacles were randomly placed, and the robot had to navigate to a goal. Quantitative experiments were performed to measure the differences between navigating with the S-DOVS by itself and the S-DOVS with the waypoint generator in sets of 200 scenarios for any number of obstacles in the range of 1 to 15. The results of the experiments are presented in Table 1. The robot can reach the goal in more episodes when using the complete navigation stack, even in the map with only one room. This is because obstacles on the way to the goal can remain static; the global planner adds them to the cost map, assisting the S-DOVS. In the nine-room map the benefits are clear, as the S-DOVS has to reactively navigate through the rooms and is unable to, falling into trap situations from which it is not able to escape. The intersections of the walls are convex obstacles that a reactive planner may not be able to avoid by itself. Nevertheless, the intermediate goals sent by the waypoint generator help S-DOVS to avoid the walls properly. The approaches perform similarly in terms of time on both the single-room map and multi-room map, although the full system is evidently safer and more successful. The time comparison is somewhat unfair, as only the successful scenarios are accounted for in the metrics, and longer scenarios were almost always solved by only the system with the waypoint generator, meaning that its mean time to reach the goal is much higher. Our approach proposed for the waypoint generator was compared with other state-of-the-art approaches. We randomly generated 200 scenarios with 5, 10, and 15 obstacles in the multi-room environment, and gathered success and time metrics using different planners, plotting the results in Figure 6. The approaches compared here used several alternatives: using only the final goal and no intermediate waypoints; a simple subsampling of the original path, as in [26]; using only space-horizon goals, as in [27]; our previous approach in [2], which did not use importance-varying spacial horizon goals, but included selection of the points of \(path_{aux}\) of Algorithm 1; and our improved approach presented in this work. We included replanning with the same criteria in every method; thus, the only difference was in the selection of the waypoints and the look-ahead distance. The scenarios in which every approach led to a collision were discarded, as the randomness involved in scenario generation may have made them unsolvable. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Map**} & **Metric** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** & **11** & **12** & **13** & **14** & **15** \\ \hline \multirow{2}{*}{Single} & Success & 1.02 & 1.12 & 0.99 & 1.05 & 1.02 & 1.19 & 1.19 & 1.02 & 1.16 & 1.06 & 1.23 & 1.06 & 1.29 & 1.39 \\  & Time & 1.02 & 1.01 & 0.97 & 0.99 & 0.98 & 1.09 & 1.05 & 1.00 & 1.06 & 1.08 & 0.93 & 1.03 & 0.89 & 1.06 & 1.11 \\ \hline \multirow{2}{*}{Multi} & Success & 3.09 & 2.89 & 3.41 & 2.84 & 3.09 & 4.16 & 4.11 & 3.08 & 3.67 & 3.21 & 3.73 & 2.86 & 3.93 & 3.52 & 3.53 \\  & Time & 1.09 & 1.32 & 1.11 & 1.07 & 1.21 & 1.08 & 1.13 & 1.07 & 0.95 & 1.11 & 1.25 & 1.24 & 1.10 & 1.10 & 1.11 \\ \hline \hline \end{tabular}
\end{table}