尤嵩菀 , 王文龙 . 美俄军事智能化发展及启示 [J ] . 海军工程大学学报(综合版) , 2020 , 17 ( 2 ): 64 - 69 .

YOU S Y , WANG W L . Research on military intellectualization of United States and Russia and its enlightenment [J ] . Journal of Naval University of Engineering(Comprehensive Edition) , 2020 , 17 ( 2 ): 64 - 69 . (in Chinese)

XIE R L , MENG Z J , ZHOU Y M , et al . Heuristic Q-learning based on experience replay for three-dimensional path planning of the unmanned aerial vehicle [J ] . Science Progress , 2020 , 103 ( 1 ): 1 - 18 .

孙健 , 井立 , 刘朝君 . 突发威胁下的无人机航迹规划算法 [J ] . 飞行力学 , 2018 , 36 ( 3 ): 52 - 55 .

SUN J , JING L , LIU Z J . Route planning algorithm of UAV with unexpected threat [J ] . Flight Dynamics , 2018 , 36 ( 3 ): 52 - 55 . (in Chinese)

ALBERT A , LEIRA F S , IMSLAND L . UAV path planning using MILP with experiments [J ] . Modeling, Identification and Control , 2017 , 38 ( 1 ): 21 - 32 . DOI: 10.4173/mic.2017.1.3 http://doi.org/10.4173/mic.2017.1.3 http://www.mic-journal.no/ABS/MIC-2017-1-3.asp http://www.mic-journal.no/ABS/MIC-2017-1-3.asp

代进进 , 李相民 , 薄宁 , 等 . 基于模型预测控制的无人机避障路径规划方法 [J ] . 火力与指挥控制 , 2020 , 45 ( 1 ): 114 - 119 .

DAI J J , LI X M , BO N , et al . Study on UAV obstacle avoidance path planning based on model predictive control [J ] . Fire Control & Command Control , 2020 , 45 ( 1 ): 114 - 119 . (in Chinese)

王文彬 , 秦小林 , 张力戈 , 等 . 基于滚动时域的无人机动态航迹规划 [J ] . 智能系统学报 , 2018 , 13 ( 4 ): 524 - 533 .

WANG W B , QIN X L , ZHANG L G , et al . Dynamic UAV trajectory planning based on receding horizon [J ] . CAAI Transactions on Intelligent Systems , 2018 , 13 ( 4 ): 524 - 533 . (in Chinese)

LIU Q , SHI L , SUN L L , et al . Path planning for UAV-mounted mobile edge computing with deep reinforcement learning [J ] . IEEE Transactions on Vehicular Technology , 2020 , 69 ( 5 ): 5723 - 5728 . DOI: 10.1109/TVT.25 http://doi.org/10.1109/TVT.25 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=25 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=25

BLASI L , D AMATO E , MATTEI M , et al . Path planning and real-time collision avoidance based on the essential visibility graph [J ] . Applied Sciences , 2020 , 10 ( 16 ): 5613 . DOI: 10.3390/app10165613 http://doi.org/10.3390/app10165613 https://www.mdpi.com/2076-3417/10/16/5613 https://www.mdpi.com/2076-3417/10/16/5613 This paper deals with a novel procedure to generate optimum flight paths for multiple unmanned aircraft in the presence of obstacles and/or no-fly zones. A real-time collision avoidance algorithm solving the optimization problem as a minimum cost piecewise linear path search within the so-called Essential Visibility Graph (EVG) is first developed. Then, a re-planning procedure updating the EVG over a selected prediction time interval is proposed, accounting for the presence of multiple flying vehicles or movable obstacles. The use of Dubins curves allows obtaining smooth paths, compliant with flight mechanics constraints. In view of possible future applications in hybrid scenarios where both manned and unmanned aircraft share the airspace, visual flight rules compliant with International Civil Aviation Organization (ICAO) Annex II Right of Way were implemented. An extensive campaign of numerical simulations was carried out to test the effectiveness of the proposed technique by setting different operational scenarios of increasing complexity. Results show that the algorithm is always able to identify trajectories compliant with ICAO rules for avoiding collisions and assuring a minimum safety distance as well. Furthermore, the low computational burden suggests that the proposed procedure can be considered a promising approach for real-time applications.

朱杰 , 鲁艺 , 张辉明 . 突发威胁情况下的无人机航迹重规划 [J ] . 计算机工程与应用 , 2018 , 54 ( 8 ): 255 - 259 . DOI: 10.3778/j.issn.1002-8331.1709-0345 http://doi.org/10.3778/j.issn.1002-8331.1709-0345 为了提高Voronoi图在航迹规划方面的实用性，提出了一种改进型的Voronoi图构造模型。该模型通过引入威胁源的不可穿越区域边界，利用折中原理，在Delaunay三角网的基础上构建航迹拓扑空间。改进型的Voronoi图模型拓展了传统模型的航迹段数量，提高了航迹段对威胁的敏感性，使规划的航迹更为合理。其次，在分析突发威胁对于航迹拓扑空间影响的基础上，提出了一种基于改进型Voronoi图的航迹重规划模型，并结合D*算法对突发情况下的航迹重规划进行了研究，规划出了理想航迹。

ZHU J , LU Y , ZHANG H M . Path replanning for UAV in emergent threats [J ] . Computer Engineering and Application , 2018 , 54 ( 8 ): 255 - 259 . (in Chinese)

吴云华 , 牛康 , 李磊 , 等 . 基于3D-APF和约束动力学的无人机编队飞行控制 [J ] . 系统工程与电子技术 , 2018 , 40 ( 5 ): 1104 - 1108 .

WU Y H , NIU K , LI L , et al . Formation flight control of UAV based on 3D-APF and constraint dynamics [J ] . Systems Engineering & Electronics , 2018 , 40 ( 5 ): 1104 - 1108 . (in Chinese)

陈天德 , 黄炎焱 , 沈炜 . 基于虚拟障碍物法的无震荡航路规划 [J ] . 兵工学报 , 2019 , 40 ( 3 ): 651 - 658 . DOI: 10.3969/j.issn.1000-1093.2019.03.025 http://doi.org/10.3969/j.issn.1000-1093.2019.03.025 人工势场法作为路径规划的一种算法，凭借其解算得到的平滑航路，特别适用于不够灵活的移动机器人、智能体的路径规划。由于人工势场法自身不可避免地存在局部极小值以及算法执行不可避免的离散化，导致航路点解算可能会陷入局部极小值陷阱而进入死循环以及出现航路点震荡问题。针对局部极小值陷阱问题，提出改进型虚拟障碍物法；对虚拟障碍物位置的确定，引入了威胁区的概念，并提出了一个确定标准。针对航路点震荡问题，提出过滤震荡点法。仿真实验证明：改进型虚拟障碍物法能够有效地使陷入局部极小值陷阱的航路点解算，成功逃出陷阱；过滤震荡点法能够有效地消除震荡航路点，得到相对平滑的航路。

CHEN T D , HUANG Y Y , SHEN W . Non-oscillation path planning based on virtual obstacle method [J ] . Acta Armamentarii , 2019 , 40 ( 3 ): 651 - 658 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2019.03.025 http://doi.org/10.3969/j.issn.1000-1093.2019.03.025 The artificial potential field method, as a path planning algorithm, is used for the path planning of clumsy mobile robots, agents and so on because it can provide a smooth route. Due to the inevitable existence of local minimum and discretization of algorithms during algorithm execution, the calculation of the route point may fall into the local minimum trap, which may result in the infinite loop of algorithmic program and the oscillation of path point. For local minimum trap, an improved virtual obstacle method is proposed to overcome this problem. The definition of threat area is introduced to determine the location of virtual obstacle, and a determining standard is put forward. A filtering oscillation point method is proposed to solve the problem of path point oscillation. The simulated results show that the route points which are stuck in local minimum trap can escape from the trap successfully using the improved virtual obstacle method. Additionally, the oscillation route points can be effectively eliminated to obtain a relatively smooth route by the filtering oscillation point method. Key

潘无为 , 姜大鹏 , 庞永杰 , 等 . 人工势场和虚拟结构相结合的多水下机器人编队控制 [J ] . 兵工学报 , 2017 , 38 ( 2 ): 326 - 334 . DOI: 10.3969/j.issn.1000-1093.2017.02.017 http://doi.org/10.3969/j.issn.1000-1093.2017.02.017 传统的多水下机器人（AUV）编队算法，例如领航跟随法、虚拟结构法，对编队形成过程中AUV间的避碰问题和编队行进过程中的避障问题，没有进行有效解决。人工势场法可利用势函数进行避碰、避障，但队形组织能力略显不足。针对上述问题，提出了一种人工势场和虚拟结构相结合的多AUV编队控制算法。将系统分为3个部分：编队参考点、虚拟结构质点和AUV. 以编队参考点为中心形成期望的虚拟结构以组织队形；虚拟结构质点以期望的虚拟结构为运动目标，并在运动的过程中，通过人工势场斥函数，实现避碰和避障；AUV对虚拟结构质点进行目标跟踪，从而渐进形成AUV的队形。通过编队路径跟踪、编队队形变换和编队避障等一系列仿真实验，对算法的可靠性和灵活性进行充分验证。实验结果表明：在随机的初始位置条件下，多AUV系统可以快速无碰撞地形成队形；在编队行进过程中进行灵活的队形变换，并对障碍物有效避碰。

PAN W W , JIANG D P , PANG Y J , et al . A multi-AUV formation algorithm combining artificial potential field and virtual structure [J ] . Acta Armamentarii , 2017 , 38 ( 2 ): 326 - 334 . (in Chinese)

梁宵 , 王宏伦 , 李大伟 , 等 . 基于流水避石原理的无人机三维航路规划方法 [J ] . 航空学报 , 2013 , 34 ( 7 ): 1670 - 1681 .

LIANG X , WANG H L , LI D W , et al . Three dimensional path planning for unmanned aerial vehicles based on principles of stream avoiding obstacles [J ] . Acta Aeronautica et Astronautica Sinica , 2013 , 34 ( 7 ): 1670 - 1681 . (in Chinese)

王宏伦 , 吴健发 , 姚鹏 . 基于扰动流体动态系统的无人机三维航路规划:方法与应用 [J ] . 无人系统技术 , 2018 , 1 ( 1 ): 72 - 82 .

WANG H L , WU J F , YAO P . UAV three-dimensional path planning based on interfered fluid dynamical system: methodology and application [J ] . Unmanned Systems Technology , 2018 , 1 ( 1 ): 72 - 82 . (in Chinese)

FAROOQ M U , ZHEN Z , EJAZ M , et al . Quadrotor UAVs flying formation reconfiguration with collision avoidance using probabilistic roadmap algorithm [C ] //Proceedings of International Conference on Computer Systems, Electronics and Control. Dalian,Liaoning,China:ICCSEC,2017 , 2017 : 866 - 870 .

高升 , 艾剑良 , 王之豪 . 混合种群RRT无人机航迹规划方法 [J ] . 系统工程与电子技术 , 2020 , 42 ( 1 ): 101 - 107 . DOI: 10.3969/j.issn.1001-506X.2020.01.14 http://doi.org/10.3969/j.issn.1001-506X.2020.01.14 快速扩展随机树（rapidly-exploring random tree，RRT）无人机航迹规划方法能够快速获得满足约束要求的可行航迹，但是无法获得接近最短航迹的较优航迹。针对航迹的最优性问题，提出了混合种群RRT无人机航迹规划方法。在基于环境势场的RRT算法的基础上，设计了一种种群优化方法，通过引入自优化种群和协同优化种群改善航迹段，使算法同时具有局部和全局寻优能力。在得到航迹节点的基础上，采用B样条曲线的平滑方法生成曲率连续的可跟踪航迹。仿真结果表明，所提算法能够综合考虑无人机航程代价和雷达威胁代价，快速地收敛得到接近最优且满足无人机动力学约束的可行航迹，在不同环境下也能有满意的收敛效率。

GAO S , AI J L , WANG Z H . Mixed population RRT algorithm for UAV path planning [J ] . Systems Engineering & Electronics , 2020 , 42 ( 1 ): 101 - 107 . (in Chinese)

王生印 , 龙腾 , 王祝 , 等 . 基于即时修复式稀疏A * 算法的动态航迹规划 [J ] . 系统工程与电子技术 , 2018 , 40 ( 12 ): 2714 - 2721 .

WANG S Y , LONG T , WANG Z , et al . Dynamic path planning using anytime repairing sparse A * algorithm [J ] . Systems Engineering & Electronics , 2018 , 40 ( 12 ): 2714 - 2721 . (in Chinese)

张韬 , 项祺 , 郑婉文 , 等 . 基于改进A * 算法的路径规划在海战兵棋推演中的应用 [J ] . 兵工学报 , 2022 , 43 ( 4 ): 960 - 968 . DOI: 10.12382/bgxb.2021.0209 http://doi.org/10.12382/bgxb.2021.0209 为满足海战兵棋推演中多目标路径规划的需求，解决传统A^*算法无法在兵棋推演中直接运用的问题，提出一种可供类似兵棋推演环境参考、基于改进A^*算法的路径规划方法。建立一种映 射机制，实现了A^*算法在兵棋推演环境中的初步运用。构建一种既能满足多目标需求又能保证生成最优路径的估价函数。为验证算法有效性，在实际推演平台上进行了相关实验。结果表明，改进A^*算法可较好地统筹多个决策目标之间的关系，有效提升路径方案的质量，解决使用A^*算法在海战兵棋推演中进行最优路径规划的实际问题。

ZHANG T , XIANG Q , ZHENG W W , et al . Application of path planning based on improved A * algorithm in war gaming of naval warfare [J ] . Acta Armamentarii , 2022 , 43 ( 4 ): 960 - 968 . (in Chinese)

HUANG Y , CHEN J G , WANG H L , et al . A method of 3D path planning for solar-powered UAV with fixed target and solar tracking [J ] . Aerospace Science and Technology , 2019 , 92 ( 9 ): 831 - 838 . DOI: 10.1016/j.ast.2019.06.027 http://doi.org/10.1016/j.ast.2019.06.027 https://linkinghub.elsevier.com/retrieve/pii/S127096381930389X https://linkinghub.elsevier.com/retrieve/pii/S127096381930389X

李文博 , 秦小林 , 罗刚 . 基于无障碍凸区域的无人机在线航迹规划 [J ] . 系统科学与数学 , 2021 , 41 ( 6 ): 1493 - 1506 .

LI W B , QIN X L , LUO G . Online trajectory planning of UAV based on convex obstacle-free area [J ] . Journal of Systems Science and Mathematical Sciences , 2021 , 41 ( 6 ): 1493 - 1506 . (in Chinese) DOI: 10.12341/jssms20355 http://doi.org/10.12341/jssms20355 A method based on obstacle-free convex area is proposed to solve the problem of UAV (Unmanned Aerial Vehicle) online trajectory planning. Firstly, A* algorithm based on probabilistic roadmap (PRM) is used to plan a global path off-line. Then, the path planned above is used for local planning by IRIS-Astar algorithm proposed in this paper. The large convex obstacle-free area of the current position is calculated by IRIS (Iterative Regional Inflation By Semidefinite Programming) algorithm, which is used to find a global path point farthest from the current track point to be taken as the local target point. As the UAV travels towards the local target point, the large convex area of the current position is calculated in real time, at the same time, whether the local target point is in this area is judged. If it is, continue to travel towards the local target point; otherwise, the local target point is recalculated. Experimental results show that compared with traditional algorithms, the proposed method can effectively solve the collision avoidance problem of UAV and greatly reduce the energy consumption of UAV.

WU Y , WU S , HU X . Multi-constrained cooperative path planning of multiple drones for persistent surveillance in urban environments [J ] . Complex & Intelligent Systems , 2021 , 7 ( 3 ): 1633 - 1647 .

ZHANG Z , WU J , DAI J Y , et al . Optimal path planning with modified A-Star algorithm for stealth unmanned aerial vehicles in 3D network radar environment [J ] . Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering , 2022 , 236 ( 1 ): 72 - 81 . DOI: 10.1177/09544100211007381 http://doi.org/10.1177/09544100211007381 http://journals.sagepub.com/doi/10.1177/09544100211007381 http://journals.sagepub.com/doi/10.1177/09544100211007381 For stealth unmanned aerial vehicles (UAVs), path security and search efficiency of penetration paths are the two most important factors in performing missions. This article investigates an optimal penetration path planning method that simultaneously considers the principles of kinematics, the dynamic radar cross-section of stealth UAVs, and the network radar system. By introducing the radar threat estimation function and a 3D bidirectional sector multilayer variable step search strategy into the conventional A-Star algorithm, a modified A-Star algorithm was proposed which aims to satisfy waypoint accuracy and the algorithm searching efficiency. Next, using the proposed penetration path planning method, new waypoints were selected simultaneously which satisfy the attitude angle constraints and rank-K fusion criterion of the radar system. Furthermore, for comparative analysis of different algorithms, the conventional A-Star algorithm, bidirectional multilayer A-Star algorithm, and modified A-Star algorithm were utilized to settle the penetration path problem that UAVs experience under various threat scenarios. Finally, the simulation results indicate that the paths obtained by employing the modified algorithm have optimal path costs and higher safety in a 3D complex network radar environment, which show the effectiveness of the proposed path planning scheme.

ZHANG Z , WU J , DAI J Y , et al . A novel real-time penetration path planning algorithm for stealth UAV in 3D complex dynamic environment [J ] . IEEE Access , 2020 , 8 : 122757 - 122771 . DOI: 10.1109/Access.6287639 http://doi.org/10.1109/Access.6287639 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639

GAO F X , DING J F , LIU Z C , et al . An improved A * algorithm for UAV path planning [C ] //Proceedings of 2021 IEEE International Conference on Electrical Engineering and Mechatronics Technology.Qingdao,Shandong, China:ICEEMT , 2021 : 772 - 776 .