# Emergent Search of UAV Swarm Guided by the Target Probability Map
## 4 The Steps of ESUSTPM
In each step, the monomers can avoid collision when the distances between the agents or the distances between the agent and boundary are less than the set safe value. In order to simulate this searching behavior, a random direction is generated by Equation (12):

\[\stackrel{{\rightharpoonup}}{{dir}}=\frac{rnd(d,1)}{\|rnd(d,1) \|}, \tag{12}\]

where \(d\) is the dimension of the space, and it is 2 in this paper. \(rnd(\cdot)\) represents a function that produces a random number in [\(-1\),1]. \(\|\cdot\|\) indicates the norm. The position of the agent \(i\) is updated in Equation (13):

\[\stackrel{{\rightharpoonup}}{{P_{i}}}(t+1)=\stackrel{{ \rightharpoonup}}{{P_{i}}}(t)+\stackrel{{\rightharpoonup}}{{dir}} \cdot S\cdot\Delta t, \tag{13}\]

Figure 5: The emergent searching scenario of the single swarm at the initial time. Figure 6: Cooperative search results based on the proposed ESUSTPM model. where \(S\) is the constant step, and it equals 10 in this paper. \(\Delta t\) is the simulation interval. The experimental result at the 200 th time cycle is shown in Figure 7, and most grids are still blue. Compared with the proposed ESUSTPM algorithm, the cooperative searching algorithm based on the classical random algorithm cannot complete the full coverage of the mission area within 200 time cycles, and the reduction in the environmental uncertainty is also not sufficient. #### 5.1.3 Cooperative Search Based on the Mower Search

The mower searching algorithm is a classical searching algorithm [33], and UAV agents sweep the mission area back and forth at a certain speed. Figure 8 shows the mower searching result at the 200 th time cycle. The color of each grid becomes lighter at the 200 th time cycle, and this indicates that all grids have been visited, and the TEP decreases. In order to simulate this searching behavior clearly, the position of the UAV agent \(i\) is updated by the following Equation (14):

\[\overset{\rightarrow}{P}_{i}(t+1)=\overset{\rightarrow}{P}_{i}(t)+\overset{ \rightarrow}{b}\cdot l\cdot\Delta t, \tag{14}\]

where \(\overset{\rightarrow}{b}\) is the unit direction. This direction will reverse when the UAV meets the boundary. \(l\) is a certain step, and it equals 10 in this paper. \(\Delta t\) is the simulation interval. Figure 8: Cooperative search results based on the mower search. Figure 7: Cooperative search results based on the classical random searching algorithm. #### 5.1.4 Cooperative Search Based on the Boids Model without Guidance

The Boids model consists of three rules, including collision avoidance, velocity matching and flocking centering. Collision avoidance demonstrates that the monomer attempts to avoid collision with the nearby neighbors. Velocity matching means that each swarm monomer attempts to match the velocity with the nearby neighbors. The flock centering indicates that the agent attempts to stay close to the nearby neighbors. The monomers can realize a distributed synergy effect of UAV swarm by adopting the three principles to interact with each other. In the cooperative search based on the Boids model without guidance, the local rules only contain the above three rules for maintaining the flocking state and searching the grids. As the guiding rules are not used to guide the movement of UAV agents, the searching efficiency of this cooperative searching method will not be high in theory. Figure 9 is the simulation result, which indicates that the searching algorithm based on the Boids model without guidance is executed after 200 time cycles. The given safe distance between the agents is 120 m. As the monomer cannot acquire the environmental guidance in the searching process and the interactions between agents further restrict and disturb the movement of the nearby monomers, the swarm can only partially cover the mission area. #### 5.1.5 Cooperative Search Based on the Boids Model with Guidance

The Boids principles and the proposed guiding mechanism are adopted to perform the full coverage mission. The searching time is 200 time cycles.