## 4 ST Approach  
Inspired by the knowledge of cooperative search and trajectory tracking [34; 35], we propose the ST approach. The lowest \(path_{a}\) without the OC of motion is mapped to a trajectory to be followed, and the cells it passes through are modeled as the key regions. Other blank cells are shaped as non-key regions, and obstacles are designed as no-fly zones. The input signal is the orientation sequence to maximize the search rewards of \(UAV_{i}\). The process of tracking \(path_{a}\) is the same as that of a UAV searching from the starting cell to the goal cell. Since the ST approach is only applied to a single UAV, there is no need to consider the cooperation-competition relationship between UAVs. ST approach based on basic PIO algorithm consists of four operators. **Operator 1: Obtain \(path_{a}\)**  
We use A* algorithm [23] to find \(path_{a}\), and A* algorithm can be simplified as the following steps:  
Step 1: Specify the OC for the UAV. Step 2: Design a cost function \(f(m,n)=g(m,n)+h(m,n)\), where \(g(m,n)\) denotes the movement cost: corresponds to the expenditure of moving the current position \((m,n)\) to other cell moved into the neighbor. \(h(m,n)\) denotes the heuristic cost: corresponds to the expenditure of changing from current cell to goal cell. When \(g(m,n)=0\), A* algorithm degenerates to Dijkstra algorithm. When \(h(m,n)=0\), A * algorithm degenerates to greedy best first search algorithm. Step 3: Estimate total expenditure \(h(m,n)\) and change to the cell with the least cost. Step 4: Repeat Step 3 until the goal cell is reached. Step 5: When reaching the goal, choose the final path with least cost. **Operator 2: Mark key cells**  
Referring to the concept of the TEP in the region searching, the blank cells are set as the non-key regions, which implies \(P_{e,i}^{m,n}(k)=0\). The cells that the path of \(UAV_{i}\)\(path_{a,i}\) passes through are marked as the key regions, and their \(P_{e,i}^{m,n}(k)\) are denoted as follows:  
\[P_{e,i}^{m,n}(k)=\begin{cases}\dfrac{1}{5},&1<s_{i}<N_{m,i},N_{f,i}=0,\\ 1,&s_{i}=  
**Remark 2**.: _As shown in the fourth term of Equation (20), UAV\({}_{i}\) will only track path\({}_{a,i}\). The key cells marked for other UAVs are non-key cells for UAV\({}_{i}\). This ensures that the tracking process of the UAVs does not affect each other._  
**Operator 3: Design fitness function**  
The reward function of the ST approach relates only to the TEP for every cell in Operation 2:  
\[J_{1}=\sum_{q=1}^{N_{p}}P_{e}^{m,n}(k+q). \tag{21}\]  
The original cell of \(path_{a}\) is the starting position of the ST approach. And its initial flight orientation is pointed from the starting position to the second cell of \(path_{a}\). **Operator 4: Track \(path_{a}\)**  
The process of tracking is similar to that of Algorithm 1 and can be described as the following steps:  
Step 1: Initialize the information of the region to be searched and the pose of the UAVs. Step 2: Execute \(N_{p}\)SAP, and then get the predicted state sequence \(\mathcal{E}_{i}(k)\). Step 3: Let \(fitness(\cdot)=J_{2}\), the path \(p_{i}^{l}(k)\) corresponding to the sequence with the greatest fitness in \(\mathcal{E}_{i}(k)\) solved by basic PIO. Step 4: \(UAV_{i}\) flies forward for a time step. Step 5: Repeat Step 2 to Step 4 until the goal cell is searched. Step 6: When reaching the goal, choose the final path with least cost and OC, as well as the total time steps \(T_{i,2}(k)\) from the starting point to the goal point. In light of the knowledge of graph theory, the key cells included by \(path_{a}\) is the only directed connection sequence from the starting position to the goal cell, which is equivalent to a directed path. Through the four operations described above, we can obtain a lowest path that satisfies 3 OC. ST approach as opposed to path following or trajectory tracking. The errors of the latter two are the absolute errors between the actual tracking trajectory and the ideal trajectory.