# An Approach to Multi-Objective Path Planning Optimization for Underwater Gliders
## 3 Experimental Setup
### Simulation Scenarios  
The Canary Islands sea area was selected for the simulation, due to the special characteristics found in this zone, with the presence of a great variety of oceanographic structures of interest (eddies, upwelling cells, fronts, etc.). The area covered from \(-12\) to \(-19^{\circ}\) East and \(26\) to \(30^{\circ}\) North, between 16 and 18 May 2013, a period showing highly dynamic ocean currents, as can be observed in Figure 2.  
Ocean circulation forecasting maps (U and V variables) for the glider path simulator are read from MERCATOR-IBI [56], with a spatial resolution of \(1/12^{\circ}\) and daily outputs, with 3D data from surface down to 5000 m depth. Other ocean forecasts can also be used, but the decision of using this particular product is because its spatial resolution (approximately 2 km). To test this system and its robustness, a set of eight scenarios was defined around the islands. Each scenario, as shown in Figure 3, consist in a start location (green), two obstacles with a safety ratio (red), and a target location (purple). The factors considered were the ocean currents average direction (favourable/against) and variability (stable/unstable), obstacle configuration (overlapping/separated), and bathymFour scenarios with different trajectory directions (North-South, South-North, East-West, and West-East), are configured according to Table 1 for overlapping obstacles and Table 2 for same trajectories' direction but with separated obstacles. In all cases, the obstacle safety radius has been fixed to 12 km. The distance between the starting point and the target has been selected so it's not reachable in the 3 days planning horizon. Images in Figure 4 show the location of the different elements integrating the corresponding overlapping and separated scenarios in the map. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Seen.Id.** & **Direction** & **Start (\({}^{\circ}\) N; \({}^{\circ}\) E)** & **Target (\({}^{\circ}\) N; \({}^{\circ}\) E)** & **Obstacle 1 (\({}^{\circ}\) N; \({}^{\circ}\) E)** & **Obstacle 2 (\({}^{\circ}\) N; \({}^{\circ}\) E)** \\ \hline
1 (NSo) & North-South & 29.60; \(-\)18.34 & 28.60; \(-\)18.00 & 29.40; \(-\)18.25 & 29.20; \(-\)18.25 \\
2 (SNo) & South-North & 28.60; \(-\)17.00 & 29.60; \(-\)17.30 & 28.80; \(-\)17.10 & 29.00; \(-\)17.10 \\
3 (EWo) & East-West & 28.82; \(-\)15.22 & 29.10; \(-\)16.38 & 28.90; \(-\)15.43 & 28.91; \(-\)15.65 \\
4 (WEo) & West-East & 29.70; \(-\)16.40 & 29.40; \(-\)15.20 & 29.60; \(-\)16.20 & 29.60; \(-\)15.98 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Scenarios coordinates (\({}^{\circ}\) N; \({}^{\circ}\) E) of the start point, target, and overlapping obstacles for the four directions. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Seen.Id.** & **Direction** & **Start (\({}^{\circ}\) N; \({}^{\circ}\) E)** & **Target (\({}^{\circ}\) N; \({}^{\circ}\) E)** & **Obstacle 1 (\({}^{\circ}\) N; \({}^{\circ}\) E)** & **Obstacle 2 (\({}^{\circ}\) N; \({}^{\circ}\) E)** \\ \hline
5 (NSs) & North-South & 29.60; \(-\)18.34 & 28.60; \(-\)18.00 & 29.37; \(-\)18.32 & 29.37; \(-\)17.96 \\
6 (SNs) & South-North & 28.60; \(-\)16.80 & 29.60; \(-\)17.15 & 28.90; \(-\)16.80 & 28.90; \(-\)17.15 \\
7 (EWs) & East-West & 28.80; \(-\)15.20 & 29.10; \(-\)16.40 & 29.10; \(-\)15.50 & 28.82; \(-\)15.50 \\
8 (WEs) & West-East & 29.70; \(-\)16.40 & 29.40; \(-\)15.20 & 29.70; \(-\)16.10 & 29.42; \(-\)16.10 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Scenarios coordinates (\({}^{\circ}\) N; \({}^{\circ}\) E) of the start point, target, and separated obstacles for the four directions. Figure 3: Scenario elements example: start point, target, and obstacle’s locations. Figure 2: Surface currents of the area of simulation (Canary Islands, NE Atlantic). Regarding the average direction of the 3D ocean currents, scenarios 1, 3, 5, and 7 correspond to favourable currents, while scenarios 2, 4, 6, and 8 represent against currents.