Research on multi-UAVs route planning method based on improved bat optimization algorithm

Abstract

In a complex navigation environment, it is very important to solve the problems of multiple constraints and complex calculations in the route planning process of multiple reconnaissance unmanned aerial vehicles (UAVs) to improve the flight reconnaissance effect, and the bat algorithm (BA) with simple parameters has a certain effect on it. Aiming at the problems of unbalanced global optimization and local optimization and slow convergence speed in the later iteration of the BA in the path planning of multi-reconnaissance UAVs, a Levy-based flight search strategy and an improved bat algorithm (IBA) with changing speed are designed. In order to solve the multi-UAV route planning problem, the 3D space is reduced to a divided two-dimensional space based on the “scatter plot” method, and the spatial encoding method is used. Finally, it is proved that the IBA is theoretically more concise and effective than other algorithms.

Keywords:

• Improved bat algorithm
• scatter plot
• Levy flight
• inertia weight

1. Introduction

1.1. Background

The problem of unmanned aerial vehicle (UAV) route planning was first proposed by the United States in the 1960s, and it has shown great importance in actual combat. The United Kingdom and France are also at the forefront of UAV route planning technology. China’s research in this field started relatively late, and research at the theoretical stage began in the 1990s. After 2000, dynamic programming (Eun & Bang, 2006), A* algorithm (Sun & Sun, 2022), particle swarm algorithm (K Liu et al., 2013), artificial field potential method (Redding et al., 2007), and other related algorithms have been applied to UAV route planning.

Multi-unmanned reconnaissance aircraft can better complete the task when there are many actual reconnaissance targets, but it also brings new challenges (De Moraes & de Freitas, 2018). For different problems, many researchers have proposed different methods. Liu (Liu, 2019) transformed the route planning problem of multi-reconnaissance UAVs into a multi-travel salesman problem and improved the operator of the genetic algorithm, but the overall flight distance is too large, and there are non-reconnaissance targets. Wang (Wang, 2011) adjusted the pheromone concentration for multi-reconnaissance UAVs to solve the problem of premature convergence of the algorithm, but when the scale of the reconnaissance environment expands, there will be reconnaissance deviations. Yang (Z J Li & Liu, 2015) used a co-evolutionary genetic algorithm to solve the cooperative path planning problem of multi-reconnaissance UAVs and completed time-domain coordination and air-space coordination, but there are many control variables, and the local search ability is weak.

The above methods can solve the route planning problem of multi-reconnaissance UAVs to a certain extent, but there are still the following shortcomings: 1) The coordination requirements between multi-aircraft are high, and the local search and global search are unbalanced; 2) The movement space is larger and more complex, and there are more control variables. In order to better solve the route planning problem of multi-reconnaissance UAVs, this paper will use the “scatter plot method” of dimensionality reduction to model the environment and propose an improved bat algorithm (IBA) to obtain better planning results.

1.2. Related Works

Bat algorithm (BA) is a kind of swarm intelligence optimization algorithm with high efficiency and fast convergence speed (Guo et al., 2015; Yuan et al., 2021). However, the BA also suffers from the disadvantages of easily falling into local extrema and low convergence accuracy. For this reason, many scholars have proposed improvement strategies from different perspectives (K Li et al., 2020; Lin et al., 2019; Xi et al., 2018; Zhou et al., 2021). Xi (Xi et al., 2018) presented an IBA for UAV path planning based on the crossover in genetic algorithm, which expanded the search space and achieved accelerated convergence. In UAV path planning, Lin (Lin et al., 2019) modified the artificial potential field approach to accomplish accelerated convergence of bat position update, developed the optimal success rate scheme to improve the inertia weight, and employed the chaotic method to prevent falling into the local optimum. Li (K Li et al., 2020) designed an IBA for UAV oilfield inspection dynamic intrusion target tracking to enhance the local search ability of the BA to overcome the shortcomings of easy fall into the local optimal and poor optimization stability. Zhou (Zhou et al., 2021) proposed a new IBA for UAV flight path planning in a static environment by integrating the basic BA into the artificial bee colony algorithm.

The acronyms used in this article are given in Table 1.

Table 1. Acronyms used in this paper

Center coordinates	Radius
BA	Bat algorithm
IBA	Improved Bat algorithm
PSOA	Particle swarm optimization algorithm
UAV	Unmanned aerial vehicle

2. Problem Analysis

2.1. Multi-Reconnaissance UAVs Flight Elements

The application scenario of the method proposed in this paper is the route planning and design of multi-reconnaissance UAVs in a single base, and the detailed descriptions of the problem are as follows: On the premise of satisfying the relevant constraints, multi-reconnaissance UAVs start from their respective starting points and follow the planned safe route to the target point to be reconnaissance.

As portrayed in Figures 1-2, each reconnaissance UAV satisfies performance constraints such as flight altitude, flight distance, and track turn angle, and environmental constraints such as evading missiles, radar, mountains, hills, etc. The relevant constraints are as follows (K Liu et al., 2013):

(1) $\min {\mathrm{y}}_{\mathrm{i}+1}\le y_{\mathit{i}+1}\le max{y}_{\mathit{i}+1}$(1)

(2) $\min {\mathrm{y}}_{\mathrm{i}+1}=\mathrm{d}\bullet \tan \left[\arctan \left(\frac{{\mathrm{y}}_{\mathrm{i}}-{\mathrm{y}}_{\mathrm{i}-1}}{\mathrm{d}}\right)-{\phi }_{\mathrm{m}}\right]$(2)

(3) $\max {\mathrm{y}}_{\mathrm{i}+1}=\mathrm{d}\bullet \tan \left[\arctan \left(\frac{{\mathrm{y}}_{\mathrm{i}}-{\mathrm{y}}_{\mathrm{i}-1}}{\mathrm{d}}\right)+{\phi }_{\mathrm{m}}\right]$(3)

Figure 1. UAV angle constraint.

Figure 2. UAV 3D angle constraint.

1. Time coordination and space coordination are satisfied among multi-reconnaissance UAVs.

2. Each reconnaissance target does not interfere with the other.

The above three constraints are the premise, and the final route planning result should be realized:

1. The reconnaissance target has a high degree of completion.

2. The total cost of executing the task is minimal.

2.2. Environmental Modeling of Multi-Reconnaissance UAVs

Environmental modeling is the primary problem of multi-reconnaissance UAV route planning. To make the model reflect the real situation and simplify the route planning method, a scatter-plot environment modeling method is proposed.

1. Basic idea

To let the UAV do fewer ascending and descending actions to save fuel, this paper relies on the contour map to obtain the real situation of a certain height plane. As exhibited in Figure 3, the environment model is constructed by a scatter plot at a certain height, and the height meets the performance of the UAV itself.

Figure 3. A scatter plot of a certain height.

1. Obstacle avoidance strategy

The environment model is divided into n line segments with equal intervals d along the horizontal axis, and the model of the environment to be planned is divided as shown in Figure 4.

Figure 4. A simulation map of a certain height.

• (2)Route plannable area

In the environment simulation diagram, the solid area is the area where mountains, buildings, etc., cannot be traversed through the middle, and the hollow area is the area that can be navigated but has threats such as radar radiation. The blank can be when regional drone routing can be used for routing. When planning a UAV route, the blank space is an area that can be used for route planning.

• (3)Route planning

The UAV can navigate above or below the obstacle/threat source, and it is stipulated that each interval can only be navigated once. That is, it cannot be turned back.

3. Improvement of BA

3.1. Basic BA

Bats have a keen auditory orientation (or echolocation) system that can pass through the throat of sound waves higher than 20,000 Hz, known as ultrasound. In searching to encounter obstacles, the loudness of the ultrasonic wave $\mathit{A}$ changes from high to low, and the pulse emission rate $\mathrm{r}$ changes from low frequency to high frequency. The bat analyzes the reflected ultrasonic wave through the brain to determine the appearance of the obstacle, distance, orientation, and type, etc., to judge whether to eat or run.

The BA (Yang, 2010) is an intelligent algorithm based on the biological characteristics of bats when they search for prey. The moving position of each bat in the BA is the solution of a certain dimension in the solution space of the optimization problem to be solved, and different bat populations have different solution spaces. The mathematical modeling of the position change of the bat in the BA is as follows:

(4) ${\mathrm{f}}_{\mathrm{i}}={\mathrm{f}}_{\min }+\left({\mathrm{f}}_{\max }-{\mathrm{f}}_{\min }\right)\mathit{\beta }$(4)

(5) ${\mathrm{v}}_{\mathrm{i}}^{\mathrm{t}}={\mathrm{v}}_{\mathrm{i}}^{\mathrm{t}-1}+\left({\mathrm{x}}_{\mathrm{i}}^{\mathrm{t}-1}-{\mathrm{x}}_{\ast }\right)\mathrm{f}$(5)

(6) ${\mathrm{x}}_{\mathrm{i}}^{\mathrm{t}}={\mathrm{x}}_{\mathrm{i}}^{\mathrm{t}-1}+{\mathrm{v}}_{\mathrm{i}}^{\mathrm{t}}$(6)

where ${\mathrm{f}}_{\mathrm{i}}$ is the search pulse frequency used by the i-th bat, ${\mathrm{f}}_{\mathrm{i}}\in \left[{\mathrm{f}}_{\min }-{\mathrm{f}}_{\max }\right]$; ${\mathrm{v}}_{\mathrm{i}}^{\mathrm{t}}$ and ${\mathrm{x}}_{\mathrm{i}}^{\mathrm{t}}$ represent the flight speed and position of the t-th generation bat, respectively, ${\mathrm{x}}_{\ast }$ is the current global optimal position. The relationship between the speed ${\mathrm{v}}_{\mathrm{i}}^{\mathrm{t}}$ of the t-th generation bat and the speed ${\mathrm{v}}_{\mathrm{i}}^{\mathrm{t}-1}$ of the t-1-th generation bat is shown in equation (5)(5) ${\mathrm{v}}_{\mathrm{i}}^{\mathrm{t}}={\mathrm{v}}_{\mathrm{i}}^{\mathrm{t}-1}+\left({\mathrm{x}}_{\mathrm{i}}^{\mathrm{t}-1}-{\mathrm{x}}_{\ast }\right)\mathrm{f}$(5) , and the relationship between the position ${\mathrm{x}}_{\mathrm{i}}^{\mathrm{t}}$ of the t-th generation bat and the position ${\mathrm{x}}_{\mathrm{i}}^{\mathrm{t}-1}$ of the t-1-th generation bat is shown in equation (6)(6) ${\mathrm{x}}_{\mathrm{i}}^{\mathrm{t}}={\mathrm{x}}_{\mathrm{i}}^{\mathrm{t}-1}+{\mathrm{v}}_{\mathrm{i}}^{\mathrm{t}}$(6) . The local random search of the BA occurs in any population in the iterative process, and the change of its position is related to a certain position currently searched, and the relationship between the two is shown in (7).

(7) ${\mathrm{x}}_{\mathrm{new}}={\mathrm{x}}_{\mathrm{old}}+\mathit{\varsigma }{A}_t$(7)

where ${\mathrm{x}}_{\mathrm{new}}$, ${\mathrm{x}}_{\mathrm{old}}$ represent the solution space in all dimensions of a population of bats, ${\mathrm{x}}_{\mathrm{old}}$ is a random solution in the current optimal solution set in this dimension, and $\mathit{\varsigma }$ is a random variable and belongs to $\left[0,1\right]$.

The mathematical modeling of the loudness variation and pulse firing rate variation of a single bat is as follows:

(8) $A_{\mathrm{i}}^{\mathrm{t}+1}=\mathit{\alpha }{A}_{\mathrm{i}}^{\mathrm{t}}$(8)

(9) ${\mathrm{r}}_{\mathrm{i}}^{\mathrm{t}+1}={\mathrm{r}}_{\mathrm{i}}^0\left[1-\exp \left(-\mathit{\gamma }\mathrm{t}\right)\right]$(9)

where $A_{\mathrm{i}}^{\mathrm{t}+1}$ is the sound intensity of the t + 1-th generation bat, $\mathit{\alpha }$ is the coefficient of sound intensity attenuation transformation and takes the constant on $\left[0,1\right]$; ${\mathrm{r}}_{\mathrm{i}}^{\mathrm{t}+1}$ is the pulse emissivity of the t + 1-th generation bat, ${\mathrm{r}}_{\mathrm{i}}^0$ represents the current maximum emissivity of the bat, and $\mathit{\gamma }$ is the emissivity change coefficient, which is the constant in $\left(0,+\mathrm{\infty }\right]$.

The BA is somewhat effective in solving multi-objective type problems (Gandomi & Yang, 2014). It has the advantages of less parameters, easy operation, and easy simulation, and has a strong global search ability (Fister et al., 2014). However, according to the pseudocode of the algorithm, it can be seen that the iterative operation of the algorithm relies on the interaction of individuals to optimize, and there are cases of dependence on individuals, and the more complex the complex space model is, the greater the convergence defect of the algorithm. Therefore, this paper proposes a bat optimization algorithm to increase population diversity by increasing the inertia weight decreasing strategy and the Levy flight strategy. The experimental results show that, compared with the basic BA and particle swarm algorithm, the IBA has better optimization balance and convergence accuracy.

3.2. Inertia Weight Decreasing Strategy

Although the basic BA has a fast search speed in the early stage (Chakri et al., 2017), as the number of iterations increases, it is easy to fall into the local optimum (G C Li & Xiao, 2014; Z Li et al., 2014), resulting in a slower convergence speed and lower solution accuracy in the late stage (Gangwar & Pathak, 2020; Pathak & Srivastava, 2020). Scholars Shi et al. proposed a decreasing weight inversely proportional to the number of iterations (Shi & Eberhart, 1999). The inertia weight ${\omega }_0$ will be set in the velocity equation (5)(5) ${\mathrm{v}}_{\mathrm{i}}^{\mathrm{t}}={\mathrm{v}}_{\mathrm{i}}^{\mathrm{t}-1}+\left({\mathrm{x}}_{\mathrm{i}}^{\mathrm{t}-1}-{\mathrm{x}}_{\ast }\right)\mathrm{f}$(5) to improve the convergence accuracy of the algorithm. The bat iterative change process is shown in equations (10)(10) ${\mathrm{v}}_{\mathrm{i}}^{\mathrm{t}}={\omega }_0{\mathrm{v}}_{\mathrm{i}}^{\mathrm{t}-1}+\left({\mathrm{x}}_{\mathrm{i}}^{\mathrm{t}-1}-{\mathrm{x}}_{\ast }\right)\mathrm{f}$(10) -(11(11) ${\mathrm{x}}_{\mathrm{i}}^{\mathrm{t}}={\mathrm{x}}_{\mathrm{i}}^{\mathrm{t}-1}+{\mathrm{v}}_{\mathrm{i}}^{\mathrm{t}}$(11) ).

(10) ${\mathrm{v}}_{\mathrm{i}}^{\mathrm{t}}={\omega }_0{\mathrm{v}}_{\mathrm{i}}^{\mathrm{t}-1}+\left({\mathrm{x}}_{\mathrm{i}}^{\mathrm{t}-1}-{\mathrm{x}}_{\ast }\right)\mathrm{f}$(10)

(11) ${\mathrm{x}}_{\mathrm{i}}^{\mathrm{t}}={\mathrm{x}}_{\mathrm{i}}^{\mathrm{t}-1}+{\mathrm{v}}_{\mathrm{i}}^{\mathrm{t}}$(11)

The experimental results of Shi show that a larger inertia weight ${\omega }_0$ allows the bat to have a larger speed at present, so it has a stronger global search ability. However, the smaller inertia weight ${\omega }_0$ enables bats have a strong ability to optimize in local search.

(12) ${\omega }_0={\omega }_2={\omega }_{\mathrm{e}}{\left(\frac{{\mathit{\omega }}_{\mathrm{s}}}{{\omega }_{\mathrm{e}}}\right)}^{\left(1-\frac{{\mathrm{c}}_2\mathrm{t}}{{\mathrm{t}}_{\max }}\right)}$(12)

where ${\mathrm{c}}_2$ is a parameter for adjusting ${\omega }_2$, and ${\omega }_{\mathrm{s}}$ and ${\omega }_{\mathrm{e}}$ are the inertia values after the initial and maximum iterations, respectively. ${\mathrm{t}}_{\max }$ is the maximum number of iterations, and $\mathrm{t}$ is the current number of iterations. After multiple tests in this article, select ${\omega }_{\mathrm{s}}=0.9$, ${\omega }_{\mathrm{e}}=0.2$.

3.3. Levy Flight Strategy

Levy flight search can move in a short distance for a long time, during which there will be occasional long-distance movement, to ensure that the flight will not be trapped in a local range (Wang et al., 2013). Therefore, adding the Levy flight strategy can make the bat jump out of the local optimum during the search process. In MATLAB, the Mantegna method is used to simulate the two-dimensional plane Levy flight, and the final effect is shown in Figure 5.

Figure 5. Levy flight.

According to the application of Levy flight in the cuckoo search algorithm, the probability density function is obtained:

(13) $\mathrm{Levy}\left(\mathit{\delta }\right)\sim \mathit{\mu }={\mathrm{t}}^{-1-\delta }$(13)

where $\mathit{\delta }$ belongs to (1, 3]. The cuckoo search algorithm adopts the formula to calculate the Levy random number (Wang et al., 2013)

(14) $\mathrm{Levy}\left(\mathit{\delta }\right)\sim \frac{\mathit{\varphi \mu }}{{\left|\mathit{\nu }\right|}^{1/{\beta }_0}}$(14)

where $\mathit{\mu }$, $\mathit{\nu }$ are normal distributions, ${\beta }_0$ belonging to (1, 3), and the definition of $\mathit{\varphi }$ is

(15) $\mathit{\varphi }={\left[\frac{\mathrm{\Gamma }\left(1+{\beta }_0\right)\sin \left(\mathit{\pi }{\beta }_0/2\right)}{\mathrm{\Gamma }\left(\left(\frac{1+{\beta }_0}{2}\right){\beta }_0{2}^{\left({\beta }_0-1\right)/2}\right)}\right]}^{1/{\beta }_0}$(15)

where $\mathrm{\Gamma }$ is a standard function of $\mathit{Gamma}$.

Then, the iterative change process of the BA through Levy flight is shown in equation (16)(16) ${\mathrm{x}}_{\mathrm{i}}^{\mathrm{t}}={\mathrm{x}}_{\mathrm{i}}^{\mathrm{t}-1}+{\mathrm{v}}_{\mathrm{i}}+\mathrm{Levy}\left(\mathit{\delta }\right)\otimes \left({\mathrm{x}}_{\mathrm{i}}^{\mathrm{t}-1}-{\mathrm{x}}_{\ast }\right)$(16) .

(16) ${\mathrm{x}}_{\mathrm{i}}^{\mathrm{t}}={\mathrm{x}}_{\mathrm{i}}^{\mathrm{t}-1}+{\mathrm{v}}_{\mathrm{i}}+\mathrm{Levy}\left(\mathit{\delta }\right)\otimes \left({\mathrm{x}}_{\mathrm{i}}^{\mathrm{t}-1}-{\mathrm{x}}_{\ast }\right)$(16)

where $\mathrm{Levy}\left(\mathit{\delta }\right)$ is the moving step size and obeys the Levy distribution with parameter $\mathit{\delta }$, and $\otimes$ its the dot product vector operation.

3.4. IBA

In this paper, the inertia weight strategy is used to improve the bat individual speed variation method of the BA, so that the bat can navigate dynamically within the range and improve the bat convergence and convergence accuracy. The change of bat position relies on the Levy flight method to achieve a balance between local and global. The algorithm is described as follows

Algorithm 1 IBA

Initialize the population position, speed, pulse firing rate, loudness and other parameters of the IBA

while (k< Kmax)

Adjust the frequency to get a random solution

Update bat population speed

Bats constantly update their positions by flying through Levy

If (rand>Ai)

Choose a solution from the optimal solution set

Generate a local solution around the selected optimal solution

end

if ((rand<Ai) & (f(x)<f(x*)))

Accept this new solution

Reduce the pulse sound intensity

Increase adjustment pulse emissivity

end if

Get a series of optimal solutions

end while

3.5. Result Analysis

In the parameter settings of the BA and the IBA, the population size is 10, Ai = ri = 0.75, a = 0.9, s = ws = 0.9, we = 0.2, c2 = 1, p0 = 1.5, and the parameter of particle swarm optimization algorithm (PSOA) is set to w = 0.8, c1 = c2 = 0.9, run 30 times independently.

Comparing Figure 6 and Figure 7, the IBA has a smoother fitness curve and fewer inflection points than the basic BA in (Wang et al., 2013) and the particle swarm algorithm in (K Liu et al., 2013), which shows the local and global optimization balance of the algorithm better.

Figure 6. Z₁ fitness curve.

Figure 7. Z₂ fitness curve.

The test functions employed in the simulation are given in Table 2, and the test results are provided in Table 3. Table 3 shows that the final result is closer to the theoretical optimum of the fitness function, which shows that the algorithm has higher convergence accuracy in the later stage and is not easy to fall into the local optimum.

Table 2. Test function

Function name	Function expression	x scope	y scope
Scahfr	$z_1=21.5+\mathit{x}sin4\mathit{\pi }\mathrm{x}+\mathit{y}sin20\mathit{\pi }\mathrm{y}$	[−3,12.1]	[4.1,5.8]
Bohachevsky	${\mathrm{z}}_2=0.3\cos 3\mathit{\pi }\mathrm{x}-0.3\cos 4\mathit{\pi }\mathrm{x}-{\mathrm{x}}^2-{\mathrm{y}}^2-0.3$	[−1,1]	[−1,1]

Table 3. Test Results

Function number	Algorithm name	x	y	minz
Z1	BA	11.132	5.224	36.652
	IBA	9.141	4.812	35.723
	PSO	11.633	5.731	38.851
Z2	BA	0.162	−0.03	−0.1785
	IBA	−0.172	0.042	−0.1798
	PSO	0.177	−0.016	−0.1775

4. BA for Route Planning of Multi-Reconnaissance UAVs

4.1. Encoding

The BA is applied to the route planning of multi-reconnaissance UAVs. To facilitate the operation of the algorithm, the bats of each dimension in each population will be encoded with symbols. $A_{\hspace{0.17em}}^{\mathrm{m}}=\left(A_1^{\mathrm{m}},A_2^{\mathrm{m}},A_3^{\mathrm{m}},\dots \dots ,A_{\mathrm{n}}^{\mathrm{m}}\right)$ represents the m-th route planning scheme consisting of n waypoints, where 1, 2 … n are the sequence numbers of the moving positions in each dimension from the start point to the end point.

There are m kinds of flight routes decoded as the x-th UAV, and the m-th scheme is to reach the end point after passing through xA_m, xA_m2, xA_m3 from the starting point.

4.2. Fitness Function

Evaluating whether a route is optimal includes the degree of satisfaction and safety capability. The distance between the start and end points of the drone path should be short, and the overall path should be safe and short enough.

(17) $C_{\mathrm{fuel}}^{\mathrm{i}}=\sqrt{{\left({\mathrm{x}}_1-{\mathrm{x}}_{\mathrm{s}}\right)}^2+{\left({\mathrm{y}}_1-{\mathrm{y}}_{\mathrm{s}}\right)}^2}+\sum _{\mathrm{i}=2}^{\mathrm{n}-1}\sqrt{{\left({\mathrm{x}}_{\mathrm{i}+1}-{\mathrm{x}}_{\mathrm{i}}\right)}^2+{\left({\mathrm{y}}_{\mathrm{i}+1}-{\mathrm{y}}_{\mathrm{i}}\right)}^2}+\sqrt{{\left({\mathrm{x}}_{\mathrm{n}}-{\mathrm{x}}_{\mathrm{e}}\right)}^2+{\left({\mathrm{y}}_{\mathrm{n}}-{\mathrm{y}}_{\mathrm{e}}\right)}^2}$(17)

where (x_s,y_s) is the starting position of the drone, and (x_e,y_e) represents the position of the target point. The security capability is inversely proportional to the distance of the UAV (bats are not in the threat) from the threat source S_g.

(18) ${\mathrm{C}}_{\mathrm{threat}}^{\mathrm{i}}=\int { }_0^{\mathrm{i}}\sum _{\mathrm{g}=1}^N\frac{{\mathit{S}}_{\mathrm{g}}}{{\left[{\left(\mathrm{x}-{\mathrm{x}}_{\mathrm{g}}\right)}^2+{\left(\mathrm{y}-{\mathrm{y}}_{\mathrm{g}}\right)}^2\right]}^2}\mathrm{dl}$(18)

where S_g is the g-th threat source S with the coordinates (x_g,y_g), and its actual meaning is the risk level coefficient of the hazard source to the navigation of the UAV.

To sum up, the fitness function of multi-UAV route planning, namely the route planning evaluation method, is shown in equation (19)(19) $\mathrm{minC}=\mathit{\eta }{C}_{\mathrm{fuel}}^{\mathrm{i}}+\left(1-\mathit{\eta }\right)C_{\mathrm{threat}}^{\mathrm{i}}$(19) .

(19) $\mathrm{minC}=\mathit{\eta }{C}_{\mathrm{fuel}}^{\mathrm{i}}+\left(1-\mathit{\eta }\right)C_{\mathrm{threat}}^{\mathrm{i}}$(19)

where $\mathit{\eta }$ is the current cost coefficient of the evaluation index, which can be increased if the navigation distance is more needed and can be reduced if the safety of the UAV is more needed.

5. Simulation

5.1. Simulation Verification of Route Planning for Multi-Reconnaissance UAVs

The number of designed multi-reconnaissance UAVs is three, of which the starting point or the end point is the same, and the performance of the UAV is the same, the flight speed remains unchanged, and the speed is 215 m/s. To verify the ability to avoid danger on the route (R Liu et al., 2018), the direct connection between the target point and the end point of each UAV will pass through the obstacle or the inside of the threat source, and the environment simulation range is 4.5*4.5 km.

In the simulation, the bat coding are shown in Table 4, and the parameter settings of environmental obstacles and environmental threat sources are illustrated in Table 5 and Table 6, respectively. When planning the route, set the distance between the obstacles and the vertical line segment of the divided space so that the direction can be changed within the maximum deflection angle. The parameters of the BA and the BOA are set as: Ai = ri = 0.75, a = 0.9, s = ws = 0.9, we = 0.2, c2 = 1, p0 = 1.5, the parameters of the PSOA are set as: w = 0.8, c1 = c2 = 0.9. The number of algorithm population is 30, and the number of iterations is 100. The comparison of UAV1 route results under the three algorithms is shown in Figure 8.

Figure 8. UAV 1 route under three algorithms.

Table 4. Bat coding

		d	2d	3d	… …	n
UAVx	1	xA1	xA12	xA13	… …	n
	… …	… …	… …	… …	… …	… …
	1	xAm	xAm2	xAm3	… …	n

Table 5. Simulation environment obstacle parameter setting

	Center coordinates	Radius
Obstacle 1	(3.5,3.25,0.27)	0.5
Obstacle 2	(3.5,2.5,0.27)	0.25
Obstacle 3	(1.5,3,0.27)	0.15
Obstacle 4	(2.5,3,0.27)	0.125
Obstacle 5	(2.8,2.8,0.7)	0.125
Obstacle 6	(3.5,3.95,0.27)	0.125

Table 6. Simulation environment threat source parameter settings

	Center coordinates	Long radius	Short radius
Threat source 1	(1.75,3.37,0.27)	0.35	0.15
Threat source 2	(1.5,2.25,0.27)	0.25	0.15

To avoid accidental collisions between multi-UAVs, and according to the safe distance to be maintained between UAVs, and taking the UAV 1 route as a reference, a certain number and position of artificial labor are designed in the divided fifth and sixth spaces. Obstacles, and the final planning results are shown in Figure 9 and Figure 10.

Figure 9. IBA planning route.

Figure 10. IBA planning route.

5.2. Simulation Analysis

Comparing the planned route in Figure 8, it can be found that the IBA, compared with the BA and the PSOA, makes the moving position of each part as close as possible to the next position and the target point in the route planning. Compared with the data in Tables 7-9, the IBA can reach the target point more accurately in terms of the degree of completing the reconnaissance target point, and the IBA has higher stability and higher precision when planning the path of multi-unmanned reconnaissance aircraft.

Table 7. UAV 1 route planning results under three algorithms

		1	2	3	4	5	6	7	8	minC
UAV 1	BA	3	2.62	2.26	2.68	2	2	2.01	2.7	79.21
	IBA	3	2.52	2.58	2.54	2	2	2.02	2.5	109.59
	PSOA	3	2.5	2.66	2.83	2.47	2.22	2.14	2.5	236.54

Table 8. UAV 2 route planning results under three algorithms

		1	2	3	4	5	6	7	8	minC
UAV 2	BA	3	3.49	3.68	3.86	3.87	4.49	4.1	4	116.87
	IBA	3	3.41	3.45	3.8	3.89	4.47	4.16	4	59.17
	PSOA	3	3.28	3.58	3.78	3.98	4.21	4.15	4	334.04

Table 9. UAV 3 route planning results under three algorithms

		1	2	3	4	5	6	7	8	9	minC
UAV 3	BA	2	2.39	1.83	1.82	1.87	2	2.07	2.16	2.5	76.57
	IBA	2	1.95	1.98	1.82	1.89	2	2.27	2.33	2.5	22.81
	PSOA	2	1.98	2.04	1.96	1.98	2.1	2.1	2.26	2.5	171.65

Comparing the data in Table 10, it can be found that in the multi-UAV route planning, the planned route of the IBA can better meet the preset route fitness requirements than the BA and the PSOA, and the size of its minC. The result of the route planned by the BA and the PSOA is smaller.

Table 10. Three Algorithms Route Planning Results

Algorithm name	Total distance fitness value	Total operation time (s)
BA	272.64	13.13
IBA	191.57	24.53
PSOA	642.23	9.18

However, it is found from Table 10 that the running time of the BA is relatively long, while the IBA has a longer time, and the PSOA has the shortest time. This has a certain relationship with the excessive number of loops of the algorithm itself and the randomness of the search space, which can be continued in future areas for improvement.

6. Conclusion

In summary, the “scatter plot” method to divide the space to be planned can properly screen the complex three-dimensional real environment according to the needs of the target, thereby reducing the number of parameters and simplifying the operation process, and the BA and the PSOA can plan more The UAV is theoretically suitable for the better route, but the optimized IBA can increase the accuracy of the route design purpose, thereby improving the applicability of route planning in the real environment. Future work will focus on employing cosine control factors and other methods to further improve the performance of BA and apply it to multi-UAV path planning.

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the The National Natural Science Foundation of China [61973164].