# Reactive Planning-Driven Approach to Online UAVs Mission Rerouting and Rescheduling
## 3 Approach to UAV Fleet Online Routing
An example illustrating the course of the UAVs fleet mission, \({}^{1}S\), and the values of the resistance functions, \(Y_{1,1}(\theta)\), \(Y_{2,1}(\theta)\), \(Y_{3,1}(\theta)\), \(Y_{4,1}(\theta)\), is shown in Figure 2. It is worth noting that the UAVs' routing for mission \({}^{1}S\) is weatherproof for a given weather forecast (i.e., \(Y_{k,l}(\theta)\geq\mathcal{F}(\theta)\)) :  
\[{}^{1}\pi_{1}=(\text{N}_{1},\,\text{N}_{14},\,\text{N}_{6},\text{N}_{3},\text {N}_{13},\,\text{N}_{11},\text{N}_{1});\ ^{1}\pi_{2}=(\text{N}_{1},\text{N}_{24},\text{N}_{30},\text{N}_{12},\text{N}_ {20},\text{N}_{12},\text{N}_{1}):\]  
\[{}^{1}\pi_{3}=(\text{N}_{2},\text{N}_{32},\text{N}_{40},\text{N}_{26},\text{N }_{22},\text{N}_{23},\text{N}_{2});\ ^{1}\pi_{4}=(\text{N}_{2},\text{N}_{5},\text{N}_{31},\text{N}_{36},\text{N}_{12 },\text{N}_{15},\text{N}_{2})\]  
Figure 1: Graphical illustration of distributed delivery problem: distribution network (**a**) forecasted weather conditions (**b**) parameters of the UAVs (**c**). All goods should be delivered within a time horizon not exceeding 2.5 h (\(T=9000\) [s]). The deliveries are made under various weather conditions (set \(\mathbb{F}\)), which are illustrated in Figure 1b. According to the forecast, the wind speed does not exceed \(vw=9\frac{m}{s}\) in a direction of \(\theta=0^{\circ}\)-\(360^{\circ}\). Introducing of the additional base in node \(N_{2}\) allows the delivery problem to be split into two sub-problems with one transportation network. As a result, this means that each base has its own unique parameters, e.g., the width of the time horizon for a given iteration, which can be overlapping. This approach can be used in real world applications, e.g., when two companies have the same transportation network, their own fleet of UAV's, etc., they need to coordinate the transportation of goods between customers and avoid collisions. We consider a situation in which the weather conditions of the mission carried out rapidly changed at the time \(t^{*}=3000\) [s], i.e., during the execution of the sub-mission \({}^{2}S\), the wind speed increased to \(vw~{}=~{}11\) m/s with the same intensity and direction \(\theta=110^{\circ}\)-\(130^{\circ}\). Such a change means that this mission cannot be continued due to too much energy consumption (the mission's resistance function \(Y_{3,2}(\theta)\) values are below the level corresponding to speed \(11\frac{m}{s}\)-see Figure 3). Figure 3 shows the location of the UAVs  
Figure 2: Examples of delivery missions for the fleet \(\mathcal{U}=\{U_{1},U_{2},U_{3},U_{4}\}\). at time \(t^{*}=3000\)\([\)s\(]\), i.e., upon receipt of information about a change in weather and marking the place where the battery of \(U_{3}\) will be discharged in the event of continuation of deliveries in accordance with the current plan \({}^{2}S\). In this situation, the route of the sub-mission \({}^{2}S\) being carried out needs to be corrected, requiring the below question to be answered. Given a UAV fleet \(\mathcal{U}=\{U_{1},U_{2},U_{3},U_{4}\) } providing deliveries to the delivery points allocated in the network \(G\) from Figure 1. The UAVs fleet carries out delivery mission plan \(S^{*}\) from Figure 2. At the time \(t^{*}=3000\), there is a sudden change in the weather conditions, i.e., disturbance \(IS\) occurs, resulting in \(vw\ =\ 11\frac{n}{s};\theta=110^{\circ}-130^{\circ}\). This leads to a new question: Does a rerouting plan exist for mission \(S^{*}\) that guarantees the timely delivery of the ordered supplies in a given time horizon \(H=9000\)\([\)s\(]\) and at an acceptable battery level?