3D Trajectory Planning of UAVs Based on Improved Dung Beetle Optimization Algorithm

doi:10.12382/bgxb.2024.1068

Abstract

Abstract:

The traditional dung beetle intelligent optimization algorithm has good global search capability,but its performance is affected by the initialization parameter settings,which can lead to problems suchas blind spots in the local search,and non-communication between populations,etc.To address the problem of search blind spots in identifying the threats or no-fly areas for 3D trajectory planning of UAVs,a multi-strategy improved dung beetle optimization algorithm is proposed to improve the global trajectory planning capability.The initialization parameters,dung beetle ball-rolling behavior,small dung beetle foraging behavior and dung beetle stealing behavior are improved by using a novel chaotic mapping,a novel Cauchy-Lorenz wandering strategy,an improved triangular wandering strategy,and a novel Cauchy's inverse cumulative distribution function wandering strategy,respectively.The dung beetles of each population are crossed by using an improved longitudinal and transversal crossover strategy,and the ability of the UAV to identify the threat areas and the global trajectory planning is enhanced by the improvement of the multi-strategy.The results show the superiority of theimproved dung beetle algorithm in UAV trajectory planning.The total cost of the improved optimization algorithm is only 57.88% of the cost of the traditional dung beetle intelligent optimization algorithm,which is reduced by 42.12%.Compared with the total costs of the sand cat swarm algorithm,the particle swarm algorithm,the hippopotamus algorithm,and the gray wolf algorithm,the total cost of the proposed algorithm is reduced by 38.37%,38.80%,44.17% and 41.80%,respectively.

Key words: trajectory planning, dung beetle optimization algorithm, novel chaotic mapping, novel Cauchy-Lorenz wandering strategy, novel Cauchy inverse cumulative distribution function wandering strategy

CLC Number:

TJ760.1

JI Lu, CHEN Chao, CHEN Heng. 3D Trajectory Planning of UAVs Based on Improved Dung Beetle Optimization Algorithm[J]. Acta Armamentarii, 2025, 46(9): 241068-.

Figures/Tables 15

Fig.1 Raster method of environmental modelling

Fig.2 Selection of six directions in three-dimensional space

Fig.3 Distribution of random points generated by different initial value mappings under 2000 iterations

Fig.4 Histograms generated by different initial value mappings under 2000 iterations

Fig.5 Flowchart of the improved DBO algorithm

Table 1 Parameter values of 6 algorithms

算法	参数设置
MSIDBO算法	K=0.1,b=0.3,S=0.5
DBO算法	K=0.1,b=0.3,S=0.5
SCSO算法	r_G=[2,0],R=[-r_G, r_G]
PSO算法	w=0.5,c₁=2,c₂=2
HO算法	T>0.6
GWO算法	a_max=2,a_min=0

Table 2 CEC2022 test function

类型	编号	函数	取值范围	维度	理论最优值
单峰函数	F1	$f 1 (x) = ∑ i = 1 D x i 2 + ∑ i = 1 D 0.5 x i 2 + ∑ i = 1 D 0.5 x i 4$	[-100,100]	20	300
基础函数	F2	$f 2 (x) = ∑ i = 1 D - 1 (100 (x i 2 - x i + 1) 2 + (x i + 1 - 1) 2)$	[-100,100]	20	400
基础函数	F4	$f 4 (x) = ∑ i = 1 D (x i 2 - 10 c o s (2 π x i) + 10)$	[-100,100]	20	800
混合函数	F6	$f 6 (x) = x i 2 + 106 ∑ i = 2 D x i 2$	[-100,100]	20	1800
混合函数	F8	$f 8 (x) = ∑ i = 1 D (106) i - 1 D - 1 x i 2$	[-100,100]	20	2200
组合函数	F10	$f 10 (x) = ∑ i = 1 D x i 2 - D 1 / 4 + 0.5 ∑ i = 1 D x i 2 + ∑ i = 1 D x i / D + 0.5$	[-100,100]	20	2400
组合函数	F12	$f 12 (x) = 418.9829 × D - ∑ i = 1 D g (z i) z i = x i + 4.209687462275036 E + 002 g (z i) = z i s i n (z i 1 / 2), z i ≤ 500 (500 - m o d (z i, 500)) s i n (500 - m o d (z i, 500)) - (z i - 500) 2 10000 D, z i 500 (m o d (z i, 500) - 500) s i n (m o d (z i, 500) - 500) - (z i + 500) 2 10000 D, z i - 500$	[-100,100]	20	2700

Table 2 CEC2022 test function

类型	编号	函数	取值范围	维度	理论最优值
单峰函数	F1	$f 1 (x) = ∑ i = 1 D x i 2 + ∑ i = 1 D 0.5 x i 2 + ∑ i = 1 D 0.5 x i 4$	[-100,100]	20	300
基础函数	F2	$f 2 (x) = ∑ i = 1 D - 1 (100 (x i 2 - x i + 1) 2 + (x i + 1 - 1) 2)$	[-100,100]	20	400
基础函数	F4	$f 4 (x) = ∑ i = 1 D (x i 2 - 10 c o s (2 π x i) + 10)$	[-100,100]	20	800
混合函数	F6	$f 6 (x) = x i 2 + 106 ∑ i = 2 D x i 2$	[-100,100]	20	1800
混合函数	F8	$f 8 (x) = ∑ i = 1 D (106) i - 1 D - 1 x i 2$	[-100,100]	20	2200
组合函数	F10	$f 10 (x) = ∑ i = 1 D x i 2 - D 1 / 4 + 0.5 ∑ i = 1 D x i 2 + ∑ i = 1 D x i / D + 0.5$	[-100,100]	20	2400
组合函数	F12	$f 12 (x) = 418.9829 × D - ∑ i = 1 D g (z i) z i = x i + 4.209687462275036 E + 002 g (z i) = z i s i n (z i 1 / 2), z i ≤ 500 (500 - m o d (z i, 500)) s i n (500 - m o d (z i, 500)) - (z i - 500) 2 10000 D, z i 500 (m o d (z i, 500) - 500) s i n (m o d (z i, 500) - 500) - (z i + 500) 2 10000 D, z i - 500$	[-100,100]	20	2700

Table 3 Calculated results of different optimization algorithms for CEC2022 test function

算法	F1			F2			F4			F6
算法	平均值	标准差	最优值	平均值	标准差	最优值	平均值	标准差	最优值	平均值						标准差					最优值
MSIDBO 算法	3.61×10²	2.08×10²	3.00×10²	4.48×10²	1.55×10¹	3.95×10²	6.04×10²	1.21×10²	8.01×10²	9.05×10²						2.19×10³					1.90×10³
DBO 算法	1.27×10⁴	8.54×10³	4.47×10³	4.71×10²	3.69×10¹	4.07×10²	9.09×10²	2.86×10¹	8.64×10²	5.46×10⁴						1.30×10⁵					2.16×10³
SCSO 算法	9.25×10³	3.84×10³	1.27×10³	5.24×10²	4.73×10¹	4.65×10²	8.85×10²	1.08×10¹	8.77×10²	2.48×10⁶						6.43×10⁵					2.04×10³
PSO 算法	6.41×10²	4.34×10²	3.80×10²	4.66×10²	4.45×10¹	4.10×10²	8.41×10²	1.15×10¹	8.16×10²	1.03×10⁶						5.07×10⁵					1.98×10³
HO算法	6.56×10⁴	2.00×10⁴	2.93×10⁴	2.47×10³	6.73×10²	1.71×10³	9.85×10²	2.09×10¹	9.28×10²	1.68×10⁹						8.56×10⁸					8.04×10⁸
GWO算法	1.00×10⁴	3.76×10⁴	4.41×10³	4.86×10²	3.43×10¹	4.49×10²	8.49×10²	2.72×10²	8.19×10²	7.33×10⁵						2.17×10⁵					2.67×10³
算法	F8			F10			F12				评价																总排名
	平均值	标准差	最优值	平均值	标准差	最优值	平均值	标准差	最优值		各个测试函数平均值排名
	平均值	标准差	最优值	平均值	标准差	最优值	平均值	标准差	最优值		F1		F2		F4			F6		F8			F10		F12
MSIDBO 算法	2.22×10³	1.22×10¹	2.20×10³	2.71×10³	1.31×10²	1.43×10³	2.01×10³	2.69×10¹	1.05×10³	1		1		1			1		1			1		1		1
DBO算法	2.30×10³	7.01×10¹	2.22×10³	2.85×10³	6.63×10²	2.50×10³	2.99×10³	5.51×10¹	2.95×10³	5		3		5			2		5			2		4		4
SCSO算法	2.26×10³	5.86×10¹	2.22×10³	3.09×10³	1.04×10³	2.50×10³	3.00×10³	3.5×10¹	2.97×10¹	3		4		4			5		4			4		5		5
PSO算法	2.25×10³	5.50×10¹	2.22×10³	2.89×10³	4.58×10²	2.50×10³	2.98×10³	3.26×10¹	2.95×10¹	2		2		2			4		2			3		3		2
HO算法	2.72×10³	5.78×10²	2.29×10³	6.61×10³	1.52×10⁴	2.83×10³	3.86×10³	3.24×10²	3.66×10²	6		6		6			6		6			6		6		6
GWO算法	2.25×10³	4.84×10¹	2.22×10³	3.34×10³	8.04×10²	2.50×10³	2.95×10³	1.15×10¹	2.04×10¹	4		3		3			3		2			5		2		3

Table 3 Calculated results of different optimization algorithms for CEC2022 test function

算法	F1			F2			F4			F6
算法	平均值	标准差	最优值	平均值	标准差	最优值	平均值	标准差	最优值	平均值						标准差					最优值
MSIDBO 算法	3.61×10²	2.08×10²	3.00×10²	4.48×10²	1.55×10¹	3.95×10²	6.04×10²	1.21×10²	8.01×10²	9.05×10²						2.19×10³					1.90×10³
DBO 算法	1.27×10⁴	8.54×10³	4.47×10³	4.71×10²	3.69×10¹	4.07×10²	9.09×10²	2.86×10¹	8.64×10²	5.46×10⁴						1.30×10⁵					2.16×10³
SCSO 算法	9.25×10³	3.84×10³	1.27×10³	5.24×10²	4.73×10¹	4.65×10²	8.85×10²	1.08×10¹	8.77×10²	2.48×10⁶						6.43×10⁵					2.04×10³
PSO 算法	6.41×10²	4.34×10²	3.80×10²	4.66×10²	4.45×10¹	4.10×10²	8.41×10²	1.15×10¹	8.16×10²	1.03×10⁶						5.07×10⁵					1.98×10³
HO算法	6.56×10⁴	2.00×10⁴	2.93×10⁴	2.47×10³	6.73×10²	1.71×10³	9.85×10²	2.09×10¹	9.28×10²	1.68×10⁹						8.56×10⁸					8.04×10⁸
GWO算法	1.00×10⁴	3.76×10⁴	4.41×10³	4.86×10²	3.43×10¹	4.49×10²	8.49×10²	2.72×10²	8.19×10²	7.33×10⁵						2.17×10⁵					2.67×10³
算法	F8			F10			F12				评价																总排名
	平均值	标准差	最优值	平均值	标准差	最优值	平均值	标准差	最优值		各个测试函数平均值排名
	平均值	标准差	最优值	平均值	标准差	最优值	平均值	标准差	最优值		F1		F2		F4			F6		F8			F10		F12
MSIDBO 算法	2.22×10³	1.22×10¹	2.20×10³	2.71×10³	1.31×10²	1.43×10³	2.01×10³	2.69×10¹	1.05×10³	1		1		1			1		1			1		1		1
DBO算法	2.30×10³	7.01×10¹	2.22×10³	2.85×10³	6.63×10²	2.50×10³	2.99×10³	5.51×10¹	2.95×10³	5		3		5			2		5			2		4		4
SCSO算法	2.26×10³	5.86×10¹	2.22×10³	3.09×10³	1.04×10³	2.50×10³	3.00×10³	3.5×10¹	2.97×10¹	3		4		4			5		4			4		5		5
PSO算法	2.25×10³	5.50×10¹	2.22×10³	2.89×10³	4.58×10²	2.50×10³	2.98×10³	3.26×10¹	2.95×10¹	2		2		2			4		2			3		3		2
HO算法	2.72×10³	5.78×10²	2.29×10³	6.61×10³	1.52×10⁴	2.83×10³	3.86×10³	3.24×10²	3.66×10²	6		6		6			6		6			6		6		6
GWO算法	2.25×10³	4.84×10¹	2.22×10³	3.34×10³	8.04×10²	2.50×10³	2.95×10³	1.15×10¹	2.04×10¹	4		3		3			3		2			5		2		3

Table 4 Parameters of mountain model and threat model

模型	(x_M,_i,x_M,_i)/ km	(x_Md,_i, x_Md,_i)/km	h_i/ km	(x_men,_i, y_men,_i)/km	r_men,1 km	h_men,1/ km
1	(12,25)	(8.2,9.6)	5.2	(10,12)	6.0	6.0
	(13,41)	(4.7,6.1)	3.1	(20,45)	4.5	6.0
	(27,09)	(6.4,5.0)	3.5	(25,15)	5.5	6.0
	(37,10)	(7.2,8.0)	4.0	(28,35)	5.0	6.0
	(39,32)	(6.0,10)	6.0	(35,45)	4.0	6.0
2	(10,17)	(6.0,8.0)	4.0	(15,45)	4.5	6.0
	(15,30)	(8.0,10.0)	6.0	(18,07)	5.0	6.0
	(25,40)	(5.0,7.0)	4.5	(28,15)	5.5	6.0
	(35,25)	(9.1,8.5)	6.0	(35,45)	4.5	6.0
	(40,10)	(6.0,7.0)	5.5	(43,35)	5.0	6.0
3	(12,23)	(8.5,7.0)	6.0	(13,10)	5.5	6.0
	(23,34)	(8.0,9.0)	5.0	(15,40)	4.5	6.0
	(25,15)	(6.5,8.0)	3.0	(25,15)	6.0	6.0
	(35,12)	(7.0,7.0)	6.0	(32,35)	5.0	6.0
	(35,41)	(5.0,7.5)	4.0	(40,25)	4.0	6.0

Fig.6 Three-dimensional diagrams of three models

Fig.7 Top views of three models

Fig.8 3D comparison of trajectory planning under three models

Fig.9 Top views of trajectory planning under three models

Table 5 Total cost values under three models

算法	模型	最优值	平均值	总平均值
MSIDBO算法	1	37.458	42.216	48.901
	2	45.295	54.056
	3	48.453	50.432
DBO算法	1	68.456	72.317	84.487
	2	82.709	108.189
	3	66.485	72.966
SCSO算法	1	58.756	61.085	79.354
	2	73.490	95.312
	3	69.237	81.664
PSO算法	1	678.892	53.877	79.904
	2	630.456	76.100
	3	620.678	109.733
HO算法	1	70.589	79.593	87.594
	2	83.780	89.260
	3	95.678	93.931
GWO算法	1	50.287	59.196	84.022
	2	98.125	106.277
	3	80.765	86.594

Fig.10 Comparison of trajectory planning path,altitude and corner costs under three models

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