改进PID搜索算法的山地环境无人机路径规划

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

摘要/Abstract

摘要：

针对无人机在山地环境下路径规划时存在求解难度大、寻优效果不佳，PID搜索算法(PID-based search algorithm，PSA)在该场景中寻优精度低、收敛速度慢等问题，提出了一种改进PID搜索算法(IPSA)的山地无人机路径规划方法。引入佳点集使种群分布更均匀，增加了种群的多样性，提高算法的全局搜索能力；利用Q-learning算法将动作空间对应为PID参数调节的策略，设计了探索率因子，提高算法对不同策略的探索性和求解能力；加入透镜成像反向学习机制，帮助算法跳出局部最优，加快收敛速度。实验结果表明：与PSA算法相比，IPSA算法在稀疏环境和复杂环境下的收敛精度分别提高了3.5%和3.5%，稳定性分别提高了33.1%和53.7%，提升了山地环境中无人机路径规划的能力。

关键词: 无人机, 路径规划, PID搜索算法, 佳点集, Q-learning, 透镜成像反向学习

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

中图分类号:

TP391.9

彭艺,雷云揆,杨青青等 . 改进PID搜索算法的山地环境无人机路径规划[J]. 系统仿真学报, 2025, 37(12): 3075-3086.

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

图/表 13

图 1

图2

表1

算法参数

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

表1

表2

表3

图3

图4

表4

表5

图5

图6

表6

图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