无人机物流相比传统的物流具有高智能、低排放、低经济成本等优势，可畅通最后一公里，是智慧物流未来发展的重要方向之一，2023年12月召开的中央经济会议重点指出要发展低空经济等战略新兴产业。无人机物流产业就是低空经济的重要载体，同时也是下一代物流技术发展的关键组成部分，是空中交通的细分领域，具有巨大商用前景价值。按照中国民用驾驶航空器发展路线图V1.0的规划，无人驾驶航空器运输范围不断扩大，货物运输逐步覆盖低空短距离末端配送、中高空的支线和干线运输，无人运输系统的运输能力不断提升，逐渐融入综合运输体系并承担相应的市场份额。到2025年，城市短距离低速轻小型末端物流配送场景逐步成熟，城市中长距离物流配送逐步应用。因此，亟待解决面向城市低空物流场景中的无人机航迹规划问题，本文从无人机物流配送运行风险控制与运行效率角度出发，以多旋翼无人机的多点配送模式为研究对象，开展无人机航迹规划的建模与规划方法研究，重点解决了以下问题：

总结和分析了面向城市低空物流的无人机航迹规划研究基础。总结无人机物流航迹规划的相关内容，对物流无人机的类型、配送模式进行了说明，对无人机物流配送的影响因素进行了评估和分析；研究了城市低空环境建模方法以及航迹规划模型求解技术。

研究基于航迹双层规划模型的面向城市低空物流的无人机航迹规划建模构建，将无人机的路径规划作为上层模型，将航迹规划作为下层模型；在无人机路径上层规划模型中，根据物流公司的需求以及顾客对配送的需求建立目标函数，将无人机的电量约束和载重约束作为路径规划模型的约束条件；在下层规划模型中，根据无人机的航迹代价和运行安全代价构建目标函数，将无人机的性能约束作为航迹下层规划的约束条件。

研究面向城市低空物流的无人机航迹规划模型求解。选用三维栅格地图对城市低空环境进行建模，并将静态建筑障碍物、电磁干扰威胁以及无人机受横风影响坠落后对地面人员产生伤害的风险考虑在内；采用混沌理论、鲸鱼捕食策略和麻雀预警机制来对沙猫群算法（Sand Cat Swarm Optimization，SCSO）进行改进，提高模型求解效率与准确度，实现对上层规划模型的求解；运用混沌理论、北方苍鹰算法和t分布扰动策略来改进麻雀算法（Sparrow Search Algorithm，SSA），实现对下层规划模型的高效求解，为提升无人机物流运行安全和效率提供方法支持。

通过算例验证本文提出方法的有效性。首先生成出真实的城市低空环境模型；通过算例分析实验对无人机路径上层规划建模和沙猫群算法改进的有效性进行验证；通过在生成的城市低空环境模型中进行算例分析实验来验证对无人机航迹下层规划建模和麻雀算法改进的有效性；通过双层规划模型来构建面向城市低空物流的无人机航迹规划模型，通过改进算法对上下层模型进行求解，从而生成出城市低空物流配送无人机的航迹。

The development of UAV logistics is considered to be one of the important directions for the future intelligent logistics, as highlighted in the Central Economic Conference held in December 2023. Compared with the traditional logistics, UAV logistics has more advantages such as high intelligence, low emissions, and low economic costs, and can more effectively address the "terminal kilometer" delivery issue. According to the Development Blueprint Version 1.0 for Civil UAV in China, the scope of UAV logistics continues to expand, gradually covering short-distance terminal deliveries in urban low-altitude areas, as well as middle-to-high altitude branch and trunk line transportation. The transportation capacity of unmanned aerial systems is continuously improving, gradually integrating into comprehensive transportation systems and taking on corresponding market shares. By 2025, the urban short-distance, low-speed, light and small scale terminal logistics delivery scenarios are expected to mature gradually, the application of urban middle-to-long distance logistics delivery also making progress. Consequently, there is an urgent need to address the issue of drone path planning in urban low-altitude logistics scenarios. This paper focuses on the research for drone path planning for urban low-altitude logistics, with a specific emphasis on the risk control and operational efficiency of drone delivery operations. The study uses the multi-rotor UAV multi-point delivery mode as the research object and investigates the modeling and solution methods for drone path planning, addressing the following key issues:

Summarizing and analyzing the research basis for UAV path planning in urban low-altitude logistics. This includes summarizing relevant content on drone logistics path planning, explaining the types of logistics drones and delivery modes, assessing and analyzing the impact factors of UAV logistics delivery. The study also explores methods for modeling the urban low-altitude environment and solving path planning models.

Researching the construction of UAV path planning model based on a bi-level programming model for urban low-altitude logistics. This involves treating the drone's route planning as the upper-level model and the path planning as the lower-level model. In the upper-level model, the objective function is established based on the requirements of the logistics company and the customers' delivery needs, with the drone's battery and payload constraints serving as the constraints for the upper-level route planning model. In the lower-level model, the objective function is constructed based on the drone's path cost and operational safety cost, with the drone's performance constraints serving as the constraints for the lower-level path planning.

Researching the solution of the UAV path planning model for urban low-altitude logistics. This involves using a three-dimensional grid map to model the urban low-altitude environment and considering the risks posed by static building obstacles, electromagnetic interference threats, and the potential harm to ground personnel from drone crashes due to crosswinds. Improvements to the Sand Cat Swarm Optimization (SCSO) algorithm are made by chaos theory, whale predating strategy, and sparrow warning mechanism to enhance the model's solution efficiency and accuracy for the upper-level model. Similarly, improvements to the Sparrow Search Algorithm (SSA) are made by chaos theory, Northern Goshawk algorithm, and t-distribution disturbance strategy to achieve efficient solution for the lower-level model, thereby providing methodological support to enhance the safety and efficiency of drone logistics operations.

Validating the effectiveness of the proposed methods through case studies. This involves generating a realistic urban low-altitude environment model and conducting case study experiment analysis to validate the effectiveness of the upper-level modeling and the improved Sand Cat Swarm Optimization algorithm. Furthermore, case study experiment conducted within the generated urban low-altitude environment model are used to validate the lower-level modeling and the improved Sparrow Search Algorithm. Through the construction of a bi-level path planning model for urban low-altitude logistics and solving the upper and lower layer models by improved algorithms, the drone's path for urban low-altitude logistics delivery can be generated. Research results demonstrate that the proposed path planning method in this paper can effectively plan the total paths of logistics UAV in urban low-altitude environments, offering a scientific basis for the development of China's logistics and distribution industry.

[1] 中华人民共和国中央人民政府.无人驾驶航空器飞行管理暂行条例[EB/OL]. (2023-5-1) [2023-6-28]. https://www.gov.cn/zhengce/zhengceku/202306/content_6888800.

[2] 诺文. 美团自研无人机发布构建“天地人”完整配送生态[N]. 人民邮电, 2021-07-22(006).

[3] 林舒仪,张斌. 无人机物流配送行业未来发展研究——基于美团发布自研新型无人机的分析[J]. 物流工程与管理, 2022, 44(5): 104-106.

[4] 中国民用航空局. 民用无人驾驶航空器系统空中交通管理办法[EB/OL]. (2016-9-21) [2021-7-15]. http://www.caac.gov.cn/XXGK/XXGK/GFXWJ/201610/t20161008_40016.html.

[5] 中国民用航空局. 轻小型民用无人机飞行动态数据管理规定[EB/OL]. (2019-11-5) [2019-11-5]. http://www.caac.gov.cn/XXGK/XXGK/GFXWJ/201911/t20191120_199530.html.

[6] 中华人民共和国交通运输部. 无人机物流配送运行规范（征求意见稿）[EB/OL]. (2021-9) [2021-10-21]. https://jtst.mot.gov.cn/zxd/seekPublicAdvice/pagePublishAdviceStdList/373.

[7] 中国民用航空局.城市场景轻小型无人驾驶航空器物流航线划设规范[EB/OL]. (2022-7-29) [2022-8-1].http://www.caac.gov.cn/XXGK/XXGK/BZGF/HYBZ/202208/t20220811_214939.html.

[8] 中国民用航空局. “十四五”航空物流发展专项规划[EB/OL].(2022-2-16). https://www.caac.gov.cn/XXGK/XXGK/FZGH/202202/t20220216_211785.html.

[9] 中国民用航空局. 民用无人驾驶航空器系统物流运行通用要求第1部分：海岛场景[EB/OL].(2023-10-30)[2023-11-1].https://www.caac.gov.cn/XXGK/XXGK/BZGF/HYBZ/202310/t20231031_221872.html.

[10] 任新惠,王佳雪,王梦琦. 考虑动态能耗的无人机配送选址路径规划研究[J]. 计算机工程与应用, 2023, 59(13): 273-280.

[11] 张蓓蓓,靳舒葳,由嘉伟,等. 复杂环境下无人机配送路径优化[J]. 现代信息科技, 2023, 7(9): 121-126.

[12] 林驿,吕靖,蒋永雷. 考虑交通时变特性的城乡快递无人机配送优化研究[J]. 计算机应用研究, 2020, 37(10): 2984-2989, 3013.

[13] 路世昌,邵旭伦,李丹. 卡车-无人机协同救灾物资避障配送问题研究[J]. 计算机工程与应用, 2023, 59(2): 289-298.

[14] 杨雷博,周俊. 限制区下货车联合无人机配送路径问题研究[J]. 计算机工程与应用, 2023, 59(12): 326-332.

[15] 陆玲玲,胡志华. 海岛无人机配送中继站选址-路径优化[J]. 大连理工大学学报, 2022, 62(3): 299-308.

[16] Pugliese LDP, Guerriero F, Macrina G. Using drones for parcels delivery process. Procedia Manufacturing, 2020, 42: 488-497．

[17] Kuru K, Ansell D, Khan W, el a1. Analysis and optimization of unmanned aerial vehicle swarms in logistics: An intelligent delivery platform. IEEE Access, 2019, 7: 15804-15831.

[18] Rabta B, Wankmtiller C, Reiner G. A drone fleet model for last-mile distribution in disaster relief operations. International Journal of Disaster Risk Reduction, 2018, 28: 107-112．

[19] Li Y S, Zhang G Z, Pang Z B, et al. Continuum approximation models for joint delivery systems using trucks and drones[J]. Enterprise information systems, 2020, 14(1/5): 406-435.

[20] Kim S, Moon I. Traveling salesman problem with a drone station[J]. IEEE Transaction on systems, Man, and Cybernetics: systems. 2019, 49(1): 12-52．

[21] Poikonen S, Wang X Y, Golden B. The vehicle routing problem with drones: Extended models and connections. Networks, 2017, 70(1): 34-43．

[22] Patchara K, Mario V, Mohammed M J, et al. Multiple traveling salesman problem with drones: mathematical model and heuristic approach[J]. Computers & Industrial Engineering, 2019, 129: 14-30．

[23] Kuo R J, Lu S H, Lai P Y, et al. Vehicle routing problem with drones considering time windows. Expert Systems with Applications, 2022, 191: 116264.

[24] 费毓晗, 张洪海, 张连东, 等. 城市物流无人机运输路径规划[J]. 武汉理工大学学报(交通科学与工程版), 2023, 47(01): 79-84,89.

[25] 李翰, 张洪海, 张连东, 等. 城市区域多物流无人机协同任务分配[J]. 系统工程与电子技术, 2021, 43(12): 3594-3602.

[26] 何宇翔. 基于蚁群算法的物流配送路径优化方法研究[J]. 电子设计工程, 2023, 31(20): 49-53.

[27] 宾厚, 张路行, 王素杰, 等. 基于改进多目标遗传算法的农村低碳物流配送路径优化[J].中国农业大学学报, 2023, 28(7): 224-237.

[28] 马成颖, 牟海波. 考虑路况、配送员与顾客满意度的冷链物流车辆配送路径优化方法[J].交通信息与安全, 2022, 40(5): 156-168.

[29] Liu G K, Hu J Y, Yu Y, et al. Vehicle routing problem in cold chain logistics: A joint distribution model with carbon trading mechanisms[J]. Resources, Conservation and Recycling, 2020, 156: 104715.

[30] Petr Stodola, Libor Kutˇej. Multi-Depot Vehicle Routing Problem with Drones: Mathematical

Formulation, solution algorithm and experiments[J]. Expert Systems With Applications, 2023, 241: 122483.

[31] Teng Y, Chen J B, Zhang S Y, et, al. Solving dynamic vehicle routing problem with time windows by ant colony system with bipartite graph matching[J]. Egyptian Informatics Journal, 2023, 25: 100421.

[32] Zakir Hussain Ahmed, Fateme Maleki, Majid Yousefikhoshbakht, et al. Solving the vehicle routing problem with time windows using modified football game algorithm[J]. Egyptian Informatics Journal, 2023, 24(4): 100403.

[33] Manolis N. Kritikos, Theocharis Metzidakis, George Ioannou. The cumulative vehicle routing problem with arc time windows[J]. Expert Systems With Applications, 2023, 240: 122447.

[34] Omer Ozkan. Optimization of the distance-constrained multi-based multi-UAV routing problem with simulated annealing and local search-based matheuristic to detect forest fires: The case of Turkey[J]. Applied Soft Computing, 2021, 113: 108015.

[35] Erdi Dasdemir, Murat Köksalan, Diclehan Tezcaner Öztürka. A flexible reference point-based multi-objective evolutionary algorithm: An application to the UAV route planning problem[J]. Computers and Operations Research, 2020, 114: 104811.

[36] Shi J M, Mao H T, Zhou Z B, et al. Adaptive large neighborhood search algorithm for the Unmanned aerial vehicle routing problem with recharging[J]. Applied Soft Computing, 2023, 147: 110831.

[37] 李歆莹, 房建武. 城市环境下基于A*算法和DWA算法的无人机路径规划方法研究[J]. 无人系统技术, 2023, 6(2): 61-70.

[38] 罗冠辰, 于剑桥, 张思宇, 等. 穿越恶劣天气区域的无人机航迹规划[J]. 北京理工大学学报, 2014, 34(10): 1054-1059.

[39] 卢成阳, 王文格. 复杂城市环境下无人机三维路径规划[J]. 计算机系统应用, 2022, 31(5): 184-194.

[40] 司鹏搏, 吴兵, 杨睿哲, 等. 基于DDPG三维无人机路径规划[J]. 高技术通讯, 2022, 32(10): 1049-1057.

[41] 骆文冠, 于小兵. 基于强化学习布谷鸟搜索算法的应急无人机路径规划[J]. 灾害学, 2023, 38(2): 206-212.

[42] 丁敏, 夏兴宇, 邹永杰, 等. 基于改进蝴蝶优化算法的无人机3-D航迹规划方法[J]. 南京航空航天大学学报, 2023, 55(5): 851-858.

[43] Wu X L, Xu L, Zhen R, et al. Bi-directional adaptive A* algorithm toward optimal path planning for large-scale UAV under multi-constraints[J]. IEEE Access, 2020, 8: 85431-85440.

[44] MAUROVIĆ I, SEDER M, LENAC K, et al. Path planning for active SLAM based on the D* algorithm with negative edge weights[J]. IEEE Transaction on systems, Man and Cybernetics: systems, 2018, 48(8): 1321-1331.

[45] Aparajita Chowdhury, Debashis De. RGSO-UAV: Reverse Glowworm Swarm Optimization inspired UAV path-planning in a 3D dynamic environment[J]. Ad Hoc Networks, 2023, 140: 13068.

[46] Zhang W H, Peng C D, Yuan Y, et al. A novel multi-objective evolutionary algorithm with a two-fold constraint-handling mechanism for multiple UAV path planning[J]. Expert Systems With Applications, 2023, 38: 121862.

[47] GyeongTaek Lee, KangJin Kim, Jaeyeon Jang. Real-time path planning of controllable UAV by subgoals using goal-conditioned reinforcement learning[J]. Applied Soft Computing, 2023, 146: 110660.

[48] Sabitri Poudel, Sangman Moh. Priority-aware task assignment and path planning for efficient and load-balanced multi-UAV operation[J]. Vehicular Communications, 2023, 42: 100633.

[49] Shi J Q, Tan L, Zhang H T. Adaptive multi-UAV path planning method based on improved gray wolf algorithm[J]. Computers and Electrical Engineering, 2022, 104: 108377.

[50] Manh Duong Phung, Quang Phuc Ha. Safety-enhanced UAV path planning with spherical vector-based particle swarm optimization[J]. Applied Soft Computing, 2021, 107: 107376.

[51] 韦泽鹏, 王达磊, 陈艾荣. 基于伦理的桥梁施工决策模糊层次分析法[J]. 上海公路, 2016(3): 34-38.

[52] Amir Seyyedabbasi, Farzad Kian. Sand Cat Swarm Optimization: a nature-inspired algorithm to solve global optimization problems[J]. Engineering with Computers, 2022, 39: 2627-2651.

[53] HEIDARI A A, MIRJALILI S, FARIS H, et al. Harris hawks optimization: algorithm and applications[J]. Future Generation Computer Systems, 2019, 97: 849-872.

[54] Trojovský P, Dehghani, M. Subtraction-Average-Based Optimizer: A New Swarm-Inspired Metaheuristic Algorithm for Solving Optimization Problems[J]. Biomimetics, 2023, 8: 149.

[55] 薛建凯. 一种新型的群智能优化技术的研究与应用: 麻雀搜索算法[D], [硕士学位论文]. 上海: 东华大学, 2019.

[56] Mirjalili S, Mirjalili S M, Lewis A. Grey Wolf Optimizer[J]. Advances in Engineering Software, 2014, 69: 46-61.

[57] Xue J, Shen B. Dung beetle optimizer: a new meta-heuristic algorithm for global optimization[J]. The Journal of Supercomputing, 2022: 1-32.

[58] 赵帅. 低空空域下多无人机无冲突路径规划研究[D], [硕士学位论文]. 江苏: 南京航空航天大学, 2019.

[59] 胡莘婷, 吴宇. 面向城市飞行安全的无人机离散型多路径规划方法[J]. 航空学报, 2021, 42(06): 463-474.

[60] Choon Hian Koh, K.H.Low, Lei Li, et al. Weight threshold estimation of falling UAVs (Unmanned Aerial Vehicles) based on impact energy[J]. Transportation Research Part C: Emerging Technologies, 2018, 93: 228-255.

[61] Dalamagkidis K, Valavanis K P, Piegl L A. On integrating unmanned aircraft systems into the national airspace system[M]. Berlin: Springer Press, 2009.

[62] 胡莘婷. 城市环境下无人机运行风险评估及路径规划[D], [硕士学位论文]. 天津: 中国民航大学, 2021.

[63] 张洪海, 张连东, 刘皞等. 城市低空物流无人机航迹规划模型研究[J]. 交通运输系统工程与信息, 2022, 22(01): 256-264.

[64] 王飞龙, 赵佳敏, 李红启. 考虑能耗和时间窗的物流无人机路径问题及求解[J]. 供应链管理, 2021, 2(7): 91-110.

[65] 汤小华. 第三方物流顾客满意度影响因素研究[J]. 物流技术, 2009, 28(5): 28-31.

[66] 费毓晗, 张洪海, 张连东, 等. 城市物流无人机运输路径规划[J]. 武汉理工大学学报(交通科学与工程版), 2023, 47(1): 79-84, 89.

[67] 李尤, 董增寿, 郑宇佳. 考虑客户满意度的生鲜冷链路径优化研究[J]. 物流工程与管理, 2023, 45(6): 12-17. 

[68] 户佐安, 贾叶子, 李博威, 等. 考虑客户满意度的车辆路径优化研究[J]. 工业工程, 2019, 22(1): 100-107. 

[69] 聊士超. 物流无人机城市区域配送航迹规划[D], [硕士学位论文]. 云南: 昆明理工大学, 2023.

[70] 贾鹤鸣, 王琢, 文昌盛, 等. 改进沙猫群优化算法的无人机三维路径规划[J]. 宁德师范学院学报(自然科学版), 2023, 35(2): 171-179.

[71] 王康, 司鹏, 陈莉等 .基于改进沙猫群算法的无人机三维航迹规划[J/OL]. 兵工学报, 2023, 44(11): 1-10.

[72] 贾鹤鸣, 李永超, 游进华, 等. 改进沙猫群优化算法的机器人路径规划[J]. 福建工程学院学报, 2023, 21(1): 72-77. 

[73] 李翰. 城市区域物流无人机路径规划方法研究[D]，[硕士学位论文]. 江苏: 南京航空航天大学, 2021.

[74] 回立川, 陈雪莲, 孟嗣博. 多策略混合的改进麻雀搜索算法[J]. 计算机工程与应用, 2022, 58(16): 71-83.

[75] Seyedali Mirjalili, Andrew Lewis. The whale optimization algorithm[J]. Advances in Engineering Software, 2016, 95: 51-67.

[76] Xue J, Shen B. A novel swarm intelligence optimization approach: sparrow search algorithm[J]. Systems science & control engineering, 2020, 8: 22-34.

[77] 张孟健, 张浩, 陈曦, 等. 基于Cubic映射的灰狼优化算法及应用[J]. 计算机工程与科学, 2021, 43(11): 2035-2042.

[78] M. Dehghani, Š. Hubálovský, P. Trojovský. Northern Goshawk Optimization: A New Swarm-Based Algorithm for Solving Optimization Problems[J]. IEEE Access, 2021, 9: 162059-162080.

[79] 舒聪. 面向无人机航迹规划的改进麻雀搜索算法及应用[D], [硕士学位论文]. 广东: 广州大学, 2022.

[80] 胡中华,许昕,陈中. 无人机三维航迹非均匀三次B样条平滑算法[J]. 控制工程, 2020, 27(7): 1259-1266.

[81] 黄书召, 田军委, 乔路, 等. 基于改进遗传算法的无人机路径规划[J]. 计算机应用, 2021, 41(2): 390-397.

[82] 郑锴, 郑献民, 殷少锋, 等. 基于改进A*算法的无人机任务分配和航迹规划优化方法[J]. 电光与控制, 2022, 29(10): 7-11, 101.

[83] 曾德全, 余卓平, 张培志, 等. 三次B样条曲线的无人车避障轨迹规划[J]. 同济大学学报(自然科学版), 2019, 47(z1): 159-163.