Improved PID Search Algorithm for UAV Path Planning in Mountainous Environments

doi:10.16182/j.issn1004731x.joss.24-0721

Abstract

Abstract:

To address the challenges of UAV path planning in mountainous environments, including high computational complexity and suboptimal optimization performance, and the disadvantages of the PID-based search algorithm, such as low optimization accuracy and slow convergence rate, this paper proposed an improved PID search algorithm (IPSA). The method introduced a good point set to ensure a more uniform population distribution, thereby enhancing population diversity and global search capability. The Q-learning algorithm was employed to adapt PID parameter adjustments, incorporating an exploration rate factor to further improve the algorithm's exploration and computational capabilities. A lens imaging opposition-based learning mechanism was also integrated to help the algorithm effectively avoid local optima and accelerate the convergence rate. Experimental results have demonstrated that compared with the PSA algorithm, the convergence accuracy of the IPSA algorithm increases by 3.5% in sparse environments and by 3.5% in complex environments, while the stability increases by 33.1% and 53.7% respectively, thereby significantly boosting UAV path planning capability in mountainous environments.

Key words: UAV, path planning, PID search algorithm, good point set, Q-learning, lens imaging opposition-based learning

CLC Number:

TP391.9

Peng Yi, Lei Yunkui, Yang Qingqing, Li Hui, Wang Jianming. Improved PID Search Algorithm for UAV Path Planning in Mountainous Environments[J]. Journal of System Simulation, 2025, 37(12): 3075-3086.

Figures/Tables 13

Fig. 1

Fig. 2

Table 1

Algorithm parameters

参数名称	参数值
最低飞行高度 $H m i n$ /m	100
最高飞行高度 $H m a x$ /m	200
最大转弯角 $φ m a x$ /(°)	$45$
最大爬升角 $θ m a x$ /(°)	$45$
起点 $x 0$ /m	(50, 50, 100)
终点 $x F$ /m	(800, 800, 100)
初始学习率 $λ i$	0.9
最终学习率 $λ f$	0.1
探索率 $E$	0.9
折扣因子 $γ$	0.9
比例系数 $K p$	1
积分系数 $K i$	0.05
微分系数 $K d$	0.1
调整比例 $δ$ /%	5

Table 1

Table 2

Table 3

Fig. 3

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Table 4

Table 5

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Table 6

Fig. 7

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障碍区	位置	威胁半径
1	(300, 450, 150)	50
2	(350, 600, 150)	70
3	(450, 450, 150)	85
4	(550, 300, 150)	75

指标	IPSA	PSA	PSO	WOA
最优值	377.63	386.57	385.08	409.11
平均值	385.08	399.09	409.19	420.86
平均路径/m	1 198	1 203	1 209	1 242
标准差	6.18	9.24	10.80	17.30
平均收敛时间/s	1.73	2.25	3.57	1.99

障碍区	位置	威胁半径
1	(500, 100, 150)	70
2	(300, 500, 150)	70
3	(550, 300, 150)	70
4	(300, 250, 150)	70
5	(700, 650, 150)	70
6	(500, 700, 150)	70
7	(700, 400, 150)	70

指标	IPSA	PSA	PSO	WOA
最优值	384.96	394.44	397.32	422.97
平均值	398.10	412.47	421.06	463.59
平均路径/m	1 209	1 211	1 228	1 275
标准差	5.73	12.37	20.76	23.81
平均收敛时间/s	1.82	2.50	4.38	2.34

初始参数设置 (p, i, d)	目标函数值	标准差	飞行距离/m	高度变化/m	角度变化/(°)
(1, 0.05, 0.1)	398.10	5.73	1 207	122.11	116.72
(3, 0.05, 0.1)	430.34	10.12	1 233	234.19	183.88
(5, 0.05, 0.1)	443.37	16.28	1 233	279.41	226.52
(1, 0.05, 0.5)	403.34	10.12	1 213	186.35	118.08
(1, 0.05, 1.0)	430.26	16.92	1 227	241.18	190.23
(1, 0.50, 0.1)	402.63	9.45	1 212	150.52	119.92
(1, 1.00, 0.1)	407.83	16.75	1 216	190.82	118.74