# Proactive Mission Planning of Unmanned Aerial Vehicle Fleets Used in Offshore Wind Farm Maintenance
## 3 Model Formulation  
### Illustrative Example  
Consider an offshore wind farm with an area of 346.5 ha consisting of 100 WTs with a rotor diameter of 250 m; hereinafter, the turbines are denoted by \(T_{i}\). The turbines are arranged according to the scheme presented in Figure 1. It is assumed that the distance between the WTs is a multiple of the rotor diameter and is equal to 1500 m. Due to the coastal fauna as well as aesthetic conditions, the farm is located 12 km from the shore. Consider a situation in which 6 WTs, \(T=\{T_{10},T_{28},T_{50},T_{52},T_{68},T_{90}\}\), await technical inspection (repairs) and are located in the service area (marked as blue crossed circles in Figure 1). It is assumed that the servicing time is equal to 60 min: \(t=60\) min. There are 3 service teams available, \(W=\{W_{1},\ W_{2},\ W_{3}\}\), each consisting of a pair of employees. Each service team has different competences. The level of competence of the team has an impact on the service activities performed by them. The difference in competence is reflected in the cost of employing a given team for the service. The impact on the time-of-service task and the cost of a given group is presented in Table 1.  
It is required that all turbines of the \(T\) set undergo service within 1 working day, i.e., that the duration of the entire mission does not exceed \(H=8\) h (each WT can be serviced by any of the service teams, i.e., a subset of the set \(W\)). The transport of service teams to turbines is carried out via a vessel. The vessel sails at an average speed of 8 m/s. The cost of the vessel's operating hour is \(csa=120\) [u.m./h] (u.m. = units of money), while the cost of parking the vessel (e.g., when employees descend from the ship to the WT) \(csp=60\) [u.m./h]. Moreover, it is assumed that the time of descent of employees from the ship to the WT, as well as the time of return from the WT to the ship, is \(TI=15\) min. During a service operation, it may be necessary to deliver additional components (e.g., spare parts and tools) from the vessel to the WT. The vessel is equipped with a UAV,\(u_{1}\) (with the technical parameters described in Table 2), which is responsible for delivering the ordered goods. In this context, maintenance mission planning includes, on the one hand, ship mission planning and the assignment of service teams to WTs and, on the other hand, planning of the delivery of components (by the UAV) during the service of these WTs. Therefore, the problem of planning service missions can be reduced to the following two stages:  
1. Proactive planning: The pre-mission stage in which the vessel's route and the assignment of service teams to WTs are planned. Only teams responsible for servicing turbines are considered. The vessel's mission is determined, guaranteeing minimal cost of servicing a given set of WTs by a given set of service teams. 2. Reactive planning: This stage is carried out during the implementation of the mission. During the mission, requests are received from service teams (servicing WTs) regarding spare parts required for delivery to WT. A fleet of UAVs and service teams are available on the vessel. The position of the vessel, its route, and the weather conditions are known. \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 \(W_{1}\) & \(-15\) & 60 & 50 \\ \hline \(W_{2}\) & 0 & 40 & 30 \\ \hline \(W_{3}\) & 15 & 20 & 10 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Characteristics of the service teams. Figure 1: The assumed structure of the offshore wind farm. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**UAV** & **Max Speed [m/s]** & **Weight Capacity [kg]** & **Load/Unload Time [min]** & **Cost [u.m./h]** \\ \hline \(u_{1}\) & 16 & 120 & 10 & 50 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Technical parameters of the used UAV.