# Proactive Mission Planning of Unmanned Aerial Vehicle Fleets Used in Offshore Wind Farm Maintenance
## 4 Case Study
### Spare-Part Distribution  
The proactive planning process used the proactive plan set out in the previous section (see Figure 6). It is assumed that the required equipment should be delivered to each of the serviced WTs during the mission. For this purpose, a UAV with the parameters presented in Table 2 is used. It is also assumed that the UAV has a battery with a capacity \(CAP=7500\) kJ. Flights take place in changing weather conditions. The weather forecast presented in the form of the function \(\mathcal{F}(\theta)\) illustrated in Figure 7 is known in advance. The function \(\mathcal{F}(\theta)\) is expressed in the polar coordinate system. The values describing the outer circle represent the wind direction \(\theta\), while the radii of circles describe the wind speed \(vw\). The wind blows mainly in a southwesterly direction and its gusts are forecasted to reach speeds \(vw=10\) m/s. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Effect on Nominal** & **Cost of an Employee** & **The Cost of an Employee** \\  & **Operation Time [min]** & **Performing a Service** & **Waiting for a Service** \\  & & **Order [u.m./h]** & **Order [u.m./h]** \\ \hline \(W_{1}\) & 0 & 40 & 30 \\ \hline \(W_{2}\) & 0 & 40 & 30 \\ \hline \(W_{3}\) & 0 & 40 & 30 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Characteristics of the service teams in the considered example. Figure 5: Solution guaranteeing service of \(T=\{T_{10},T_{28},T_{50},T_{52},T_{68},T_{90},\ T_{47}\}\) WTs within 466 min: schedule (**a**), vessel route (**b**). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**No. of** & **Mission Duration \(MD\)** & **Acceptable Solution** & **Mission Cost** & **Sum of Service Team’s** \\
**Service Teams** & **[min]** & \(MD\leq 420\) & **C [u.m.]** & **Wait Times [min]** \\ \hline
1 & 734 & NO & 1174 & 0 \\
2 & 457 & NO & 1448 & 140 \\ \hline
3 & 466 & NO & 1618 & 222 \\ \hline
4 & 420 & YES & 1817 & 289 \\ \hline
5 & 394 & YES & 1952 & 512 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Solving the synthesis problem for \(T=\{T_{10},T_{28},T_{50},T_{52},T_{68},T_{90},T_{47}\}\). Figure 6: Solution guaranteeing service of \(T=\{T_{10},T_{28},T_{50},T_{52},T_{68},T_{90},T_{47}\}\) WTs within 420 min: schedule (**a**), vessel route (**b**). For the presented data, a proactive UAV mission plan is sought to guarantee timely delivery of the expected equipment. In other words, the answer to the following question is sought: Does the available UAV allow us to deliver the required equipment in the assumed time horizon \(H=420\) min (\(7\) h)? The solution of the relevant \(CP_{AR}\) problem in (67) implemented in the IBM ILOG is shown in Figure 8.  
As shown in Figure 8, the reactive UAV flight mission plan guarantees timely delivery of the required parts to each \(Ts\). As can be seen, the entire UAV mission consists of three stages. * Stage 1: The UAV takes off from the vessel at the 94 th minute and flies to \(T_{28}\); after unloading the equipment, it flies on to \(T_{47}\) and \(T_{68}\) and then returns to the vessel. * Stage 2: The UAV takes off from the vessel at the 182 nd minute and flies to \(T_{10}\); after unloading the equipment, it flies on to \(T_{52}\) and then returns to the vessel. * Stage 3: The UAV takes off from the vessel at the 294 th minutes and flies to \(T_{50}\); after unloading the equipment, it flies on to \(T_{90}\) and then returns to the vessel. All three stages guarantee delivery of the required equipment during the WT service period. Delivery is also realizable in forecasted weather conditions, i.e., there is no threat of premature battery depletion. The battery levels at the end of these missions are 24%, 58%, and 63%. The cost of the entire mission (including the cost of the proactive and reactive stages) is \(C=1897\) u.m. The presented cases correspond to real situations encountered during the servicing of OWFs.