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浙江大学学报(工学版)  2025, Vol. 59 Issue (7): 1481-1491    DOI: 10.3785/j.issn.1008-973X.2025.07.016
机械与能源工程     
基于多目标约束的无人机光顺路径生成全局优化方法
廖榆信1(),王伟1,*(),滕卫明2,贺海晏2,王战3,王进4
1. 浙江理工大学 机械工程学院,浙江 杭州 310018
2. 浙江省白马湖实验室有限公司,浙江 杭州 310051
3. 浙江浙能数字科技有限公司,浙江 杭州 310012
4. 浙江大学 流体动力与机电系统国家重点实验室,浙江 杭州 310027
Multi-objective constraint-based smooth path generation for UAVs global optimization method
Yuxin LIAO1(),Wei WANG1,*(),Weiming TENG2,Haiyan HE2,Zhan WANG3,Jin WANG4
1. School of Mechanical Engineering, Zhejiang Sci-Tech University, Hangzhou 310018, China
2. Zhejiang Baima Lake Laboratory Limited Company, Hangzhou 310051, China
3. Zhejiang Energy Digital Technology Limited Company, Hangzhou 310012, China
4. State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou 310027, China
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摘要:

复杂环境中的路径规划是无人机安全作业的基础,为此提出综合考虑避障能力、飞行效率和稳定性约束的全局优化方法. 采用柱面包络法对环境信息及障碍物进行规则化处理,分析无人机姿态变化对运动稳定性和飞行效率的潜在影响. 建立效率、避障和稳定性3个优化目标,将优化空间从传统的一维或二维提升到三维. 引入基于参考点的第三代非支配排序遗传算法 (NSGA-III)加速高维空间中的搜索过程,与改进的A*算法相比,收敛速度提高约49%. 针对障碍物设计潜在风险点判断机制,结合五次B样条对初始最优路径进行二次优化,改善无人机轨迹的几何特性及光顺性,使飞行稳定性及效率分别提高66.7%和25%. 通过仿真和实验验证NSGA-III在轨迹规划方面的有效性.

关键词: 路径规划多目标样条曲线轨迹平滑无人机    
Abstract:

Path planning in complex environments is fundamental to ensuring safe UAV operations. A global optimization method was proposed that comprehensively considered obstacle avoidance capability, flight efficiency, and stability constraints. The cylindrical envelope method was employed to standardize environmental data and obstacles, and the impact of UAV attitude variations on motion stability and flight efficiency was analyzed. Three optimization objectives—efficiency, obstacle avoidance, and stability—were established, expanding the optimization space from traditional one-dimensional or two-dimensional to three-dimensional. A reference-point-based non-dominated sorting genetic algorithm III (NSGA-III) was introduced to accelerate the search process in high-dimensional space, achieving approximately 49% faster convergence compared to the improved A* algorithm. A potential risk point detection mechanism was designed for obstacle avoidance, and a quintic B-spline was used to perform secondary optimization on the initial optimal path, enhancing the geometric characteristics and smoothness of the UAV trajectory. As a result, flight stability and efficiency were improved by 66.7% and 25%, respectively. The effectiveness of NSGA-III in trajectory planning was validated through simulations and experiments.

Key words: path planning    multiple objectives    spline curve    trajectory smoothness    UAV
收稿日期: 2024-06-11 出版日期: 2025-07-25
CLC:  TP 242  
基金资助: 国家自然科学基金资助项目(52405041);浙江省“尖兵领雁”资助项目(2023C01180);浙江省自然科学基金资助项目(LQ22E050022).
通讯作者: 王伟     E-mail: lyxzstu@163.com;wangw@zstu.edu.cn
作者简介: 廖榆信(2000—),男,硕士生,从事无人机轨迹规划技术研究. orcid.org/0009-0005-3339-5197. E-mail:lyxzstu@163.com
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引用本文:

廖榆信,王伟,滕卫明,贺海晏,王战,王进. 基于多目标约束的无人机光顺路径生成全局优化方法[J]. 浙江大学学报(工学版), 2025, 59(7): 1481-1491.

Yuxin LIAO,Wei WANG,Weiming TENG,Haiyan HE,Zhan WANG,Jin WANG. Multi-objective constraint-based smooth path generation for UAVs global optimization method. Journal of ZheJiang University (Engineering Science), 2025, 59(7): 1481-1491.

链接本文:

https://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2025.07.016        https://www.zjujournals.com/eng/CN/Y2025/V59/I7/1481

图 1  飞行路径成本示意图
图 2  无人机碰撞风险
图 3  无人机飞行的2个关键参数
图 4  基于支配排序的个体分类
图 5  基于超平面的参考点构造
图 6  新种群的产生过程
图 7  第三代非支配排序遗传算法的优化流程图
图 8  以潜在风险点为过渡路径的插值方法
图 9  路径点与障碍物的几何关系
编号坐标编号坐标编号坐标
Pr1(0.0,0.0,2.0)Pr6(0.5,0.0,1.5)Pr11(1.0,0.5,0.5)
Pr2(0.0,0.5,1.5)Pr7(0.5,0.5,1.0)Pr12(1.0,1.0,0.0)
Pr3(0.0,1.0,1.0)Pr8(0.5,1.0,0.5)Pr13(1.5,0.0,0.5)
Pr4(0.0,1.5,0.5)Pr9(0.5,1.5,0.0)Pr14(1.5,0.5,0.0)
Pr5(0.0,2.0,0.0)Pr10(1.0,1.0,0.0)Pr15(2.0,0.0,0.0)
表 1  超平面的参考点坐标
图 10  参考点的设计
图 11  仿真场景图
场景算法$ {L}_{t,i} $/m$ {\varphi }_{L} $/%$ {N}_{t,i} $/s$ {\varphi }_{t} $/%$ {R}_{t,i} $$ {\varphi }_{r} $/%
场景一改进RRT*164.937.8348.43259.0871.68
改进A*156.25.2873.36914.93
NSGA-Ⅱ154.66.2535.7651.25108.2588.17
NSGA-Ⅲ149.79.2237.0349.52101.8588.87
场景二改进RRT*158.936.4333.08178.8943.96
改进A*157.50.8854.44319.23
NSGA-Ⅱ144.88.8724.0855.7629.0490.90
NSGA-Ⅲ144.09.3718.1666.6425.1992.11
场景三改进RRT*166.4237.3650.07262.9655.55
改进A*162.422.4074.83591.59
NSGA-Ⅱ153.917.5227.5963.1374.9787.33
NSGA-Ⅲ152.808.1824.2467.6170.2088.13
表 2  不同算法在3种场景中的优化性能对比
图 12  非支配排序遗传算法的优化迭代过程
图 13  不同算法在3种场景中的无人机飞行路径三维视图
图 14  不同算法在3种场景中的无人机飞行路径俯视图
算法计算复杂度求解效率最优解搜寻能力
改进RRT*++++
改进A*+++++
NSGA-II+++++++++
NSGA-III++++++++++++
表 3  不同算法特点的定性描述
图 15  不同非支配排序遗传算法的最优结果分布
图 16  二次优化后的无人机飞行轨迹(场景一)
图 17  初始最优路径的飞行时间变化曲线
图 18  平滑轨迹的飞行时间变化曲线
图 19  无人机飞行路径的位置变化曲线
图 20  无人机实验平台
图 21  无人机控制系统图
图 22  第三代非支配排序遗传算法优化前后的无人机飞行实验结果
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