# Adaptive Path Planning for UAV-Based Pollution Sampling
## 4 Experiments and Results
### Results of Pollution Sampling with Adaptive Path Planning
#### 4.6.1 Smog Profiling over Zywie
\begin{table}
\begin{tabular}{l l} \hline
**Scenario ID** & APPLLowEmissionZywiec \\ \hline
**Description** & Smog profiling over Zywiec \\ \hline
**Stages** & 1. & The aircraft begins its mission from the initial waypoint while airborne. \\  & 2. & The aircraft navigates to the area with the highest pollution. \\  & 3. & The aircraft measures pollution along a zigzag path. \\  & 4. & The UAV navigates to the goal waypoint. \\  & 5. & Communication is lost 1800 s after start. \\  & 6. & The path is recalculated locally, then the UAV executes a return-to-home \\  & 7. & The UAV proceeds seamlessly to the goal waypoint along new path. \\ \hline
**Map** & Rectangle area from (49.65000\({}^{\circ}\) N, 19.13000\({}^{\circ}\) E) to (49.82000\({}^{\circ}\)N, 19.28000\({}^{\circ}\) E), local origin (\(0,0,0\)) located at (49.68500\({}^{\circ}\) N, 19.19000\({}^{\circ}\) E, 0 m AMSL \({}^{\ddagger}\)), 12 h wind forecast \\ \hline
**Algorithms** & ACO\({}_{\mathbb{R}}\) (GPP), RRT* (LPP) \\ \hline
**Mission parameters** & Start waypoint = \((-400,-200,518,-\frac{3}{4}\pi)\) \\  & Goal waypoint = \((100,200,544,\frac{\pi}{4})\) \\  & Safety margin = \(100\) m vertically, 200 m horizontally \\  & Airspeed = \(22\)\(\frac{\pi}{8}\) \\  & Flight-path angle limits (ascend, descend) = \(\left\langle-\frac{\pi}{90},\frac{\pi}{12}\right\rangle\) rad \\  & Max roll angle (symmetrical) = \(\frac{\pi}{30}\) rad \\  & Safety margin = \(100\) m \\ \hline
**Pollution** & Linear cost growth from 0 at the center with rate = 0.005 m\({}^{-1}\) \\
**model** & Center at (49.68500\({}^{\circ}\) N, 19.19000\({}^{\circ}\) E, 348 m AMSL) \\ \hline
**Criteria** & max(CT) \(\leq\) 4.55 s (for LPP) \\
**of success** & FT \(\leq\) 2964 s \\  & NCOL = 0 (GPP and LPP) \\ \hline \end{tabular} \({}^{\dagger}\) The airport is located at 1291 ft (394.5 m) AMSL [49]; 0 m altitude was used to keep the vertical scale relative to sea level.  
\end{table} 
Table 7: Smog profiling over Zywiec—mission outline. Figure 5: Measurement mission over Zywiec. The mission is deemed successful if it fulfills all success criteria outlined in Table 7. The criterion for the maximum flight time is calculated as  
\[ \begin{split}\text{FT}&\leq\frac{s_{m}}{v_{a}}\sum_{n=1 }^{N-1}\biggl{(}\sqrt{(w_{n}^{x}-w_{n+1}^{x})^{2}+(w_{n}^{y}-w_{n+1}^{y})^{2}}+ \frac{1}{\sin(\gamma_{n})}(w_{n}^{z}-w_{n+1}^{z})\biggr{)}\\ \gamma_{n}&=\begin{cases}\gamma_{min}\text{ if }w_{n}^{z}-w_{n+1 }^{z}\\ \gamma_{max}\text{ otherwise}\end{cases}\quad,\end{split}  \tag{32}\]  
where \(w_{s}\) and \(w_{g}\) represent the start and goal waypoint positions, respectively, while \(v_{a}\) denotes a constant airspeed. The variable \(s_{m}\) is a safety multiplier depending on scenario, set empirically. Here, it starts at a base value of 2.0 to account for wind. For each measurement site encountered during the mission, \(s_{m}\) increases by 0.5, resulting in \(s_{m}=2.5\) for this case. The term FT refers to the total simulated flight duration--from the start point to the final destination. Parameters \(\gamma_{min}\) and \(\gamma_{max}\) represent the lowest and highest inertial-referenced flight-path angles, respectively. The maximum allowable CT is calculated by dividing the safety margin by the airspeed, rounding to two decimal places. Thus, using values from Table 7, we have \(\max(\text{CT})\) smaller than 4.55 s. Here, \(\max(\text{CT})\) refers to the computation time of the longest individual calculation within a given test case. To facilitate comparison between the paths planned by the APP with path designed by a human expert (reference path), the scenario outlined in Table 7 was modified by eliminating dynamic re-planning. As a result, the simplified scenario includes only steps 1 through 4. Figure 6 compares two paths: the manually created reference path (top) and the GPP-generated path with the longest FT (bottom). The thin yellow line indicates the theoretical planned route, while the thick red line shows the actual simulated trajectory.