## 3 System Model and Problem Statement
### System Model  
As illustrated in Figure 1, the SAG-MCS scenario is simplified to a 2-dimensional continuous square area with the size of \(L\times L\) pixels. The simulation area has fixed borders and multiple obstacles that UAVs cannot fly over. We assume that there are a set \(\mathcal{K}\triangleq\{k\mid k=1,2,\ldots,K\}\) of Pols, and each PoI is assigned a certain data amount \(d(k),\forall k\). Note that Pols are regarded as persistent information nodes and are not going to disappear after coverage. Additionally, we consider a set \(\mathcal{C}\triangleq\{c\mid c=1,2,\ldots,C\}\) of charging stations and a set \(\mathcal{B}\triangleq\{b\mid b=1,2,\ldots,B\}\) of round and rectangular obstacles. At the beginning of each simulation episode, the locations of all the Pols, charging stations, and obstacles are randomly distributed in the 2D map. Each PoI's data amount \(d(k),\forall k\) is randomly assigned in a certain range as well, but the total data volume \(\Sigma_{k}d(k)\) of different episodes remains consistent.  
Let \(\mathcal{U}\triangleq\{u\mid u=1,2,\ldots,U\}\) be \(U\) UAV agents deployed in the simulation area, where the UAVs can perform continuous and horizontal flying movements at a fixed altitude. We define \(R_{obs}\) as the observation range, and \(R_{cov}\) as the coverage range or sensing range of each UAV. Arbitrary UAV can observe the local map within the radius \(R_{obs}\) in real-time and receive \(L_{sat}\times L_{sat}\) fuzzy global map captured by satellites every some timesteps. Any PoI \(k\) within a UAV's \(R_{cov}\) is recognized as covered and all its data \(d(k)\) is collected once at each timestep \(t\). Note that \(R_{cov}\) is smaller than \(R_{obs}\), as UAVs can only collect data when approaching to Pols, but they can observe a wider range of area in general. Moreover, we consider the UAV swarm can autonomously form the ad-hoc network, and each pair of agents can be interconnected within communication range \(R_{comm}\) and exchange observed information for joint decision making. Considering the delays and packet losses in real-world ad-hoc networking, we set a communication dropout probability \(p\) between adjacent UAV nodes in training and evaluation. As for the energy consumption, we set the onboard battery status \(\phi(u)\in[0,100\%],\forall u\).  
For each simulation episode, the data collection task in SAG-MCS scenario will last for \(T\) timesteps in total. Each UAV's position is randomly assigned and their batteries are fully-charged in the beginning. At each timestep \(t\), UAV \(u\) can obtain local observation from embedded sensors; while every few timesteps, it can obtain fuzzy global observation from the satellite. Using the multi-scale observations \(\{\mathbf{o}_{t}^{u}\}_{u\in\mathcal{U}}\), UAV \(u\) performs an action \(\{\mathbf{a}_{t}^{u}\}_{u\in\mathcal{U}}\). We set the battery \(\phi(u)\) consumed at timestep \(t\) as \(\{e_{t}^{u}\}_{u\in\mathcal{U}}\), which is determined by the current flying speed \(\{v_{t}^{u}\}_{u\in\mathcal{U}}\) and will be introduced in Section 3.4. When flying close to charging stations, their batteries will be fully charged in next timestep, simulating the real-world battery replacement process on the ground.