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ZHANG W C . UAV application and thinking [J ] . Defence Science & Technology Industry , 2023 ( 4 ): 47 - 49 . (in Chinese)

RAGAB M , ALTALBE A , ALGHAMDI A M , et al. A drones optimal path planning based on swarm intelligence algorithms [J ] . Computers Materials & Continua , 2022 ( 7 ): 365 - 380 .

白玉 . 四旋翼无人机的应用与发展综述 [J ] . 广西农业机械化 , 2020 ( 2 ): 7 ,9.

BAI Y . A review of the application and development of four-rotor UAV [J ] . Guangxi Agricultural Mechanization , 2020 ( 2 ): 7 ,9. (in Chinese)

刘永琦 , 徐丹 , 程归 , 等 . 基于改进A * 算法的无人机快速轨迹规划方法 [J ] . 飞行力学 , 2020 , 38 ( 2 ): 40 - 46 .

LIU Y Q , XU D , CHEN G , et al. Fast trajectory planning method of UAV based on improved A * algorithm [J ] . Flight Mechanics , 2020 , 38 ( 2 ): 40 - 46 . (in Chinese)

AGGARWAL S , KUMAR N . Path planning techniques for unmanned aerial vehicles:a review, solutions, and challenges [J ] . Computer Communications , 2020 , 149 : 270 - 299 . DOI: 10.1016/j.comcom.2019.10.014 http://doi.org/10.1016/j.comcom.2019.10.014 https://linkinghub.elsevier.com/retrieve/pii/S0140366419308539 https://linkinghub.elsevier.com/retrieve/pii/S0140366419308539

尹依伊 , 王晓芳 , 周健 . 基于Q学习的多协同航迹规划方法 [J ] . 兵工学报 , 2023 , 44 ( 2 ): 484 - 495 . DOI: 10.12382/bgxb.2021.0606 http://doi.org/10.12382/bgxb.2021.0606 针对多无人机同时到达目标的航迹规划问题,建立战场环境模型和单无人机航迹规划的马尔可夫决策模型,基于Q学习算法解算航程最短的最优航迹,应用基于Q学习算法得到的经验矩阵快速解算各无人机的最短航迹并计算协同航程,通过调整绕行无人机的动作选择策略,得到各无人机满足时间协同的航迹组。考虑多无人机的避碰问题,通过设计后退参数确定局部重规划区域,基于深度Q学习理论,采用神经网络替代Q_table对局部多无人机航迹进行重规划,避免维度爆炸问题。对于先前未探明的障碍物,参考人工势场法思想设计障碍物Q矩阵,将其叠加至原Q矩阵,实现无人机的避碰。仿真结果表明:所提基于Q学习的多无人机协同航迹规划算法能够得到时间协同与碰撞避免的协同航迹,并对环境建模时所未探明的障碍物进行躲避;与A^*算法相比,针对在线应用问题,新算法具有更高的求解效率。

YIN Y Y , WANG X F , ZHOU J . Q-Learning-based Multi-UAV Cooperative Path Planning Method [J ] . Acta Armamentarii , 2023 , 44 ( 2 ): 484 - 495 . (in Chinese) DOI: 10.12382/bgxb.2021.0606 http://doi.org/10.12382/bgxb.2021.0606 To solve the path planning problem of mul tiple UAVs' synchronous arrival at the target, the battlefield environment model and the Markov decision process model of the path planning for a single UAV is established, and the optimal path is calculated based on the Q-learning algorithm. With this algorithm, the Q-table is obtained and used to calculate the shortest path of each UAV and the cooperative range. Then the time-coordinated paths is obtained by adjusting the action selection strategy of the circumventing UAVs. Considering the collision avoidance problem of multiple UAVs, the partical replanning area is determined by designing retreat parameters, and based on the deep reinforcement learning theory, the neural network is used to replace Q-table to re-plan the partical path for UAVs, which can avoid the problem of dimensional explosion. As for the previously unexplored obstacles, the obstacle matrix is designed based on the idea of the artificial potential field theory, which is then superimposed on the original Q-table to realize collision avoidance for the unexplored obstacle. The simulation results verify that with the proposed reinforcement learning path planning method, the coordinated paths with time coordination and collision avoidance can be obtained, and the previously unexplored obstacles in the simulation can be avoided as well. Compared with A * algorithm, the proposed method can achieve higher efficiency for online application problems.

ZHOU L T , WU N P , CHEN H . RRT*-fuzzy dynamic window approach (RRT*-FDWA) for collision-free path planning [J ] . Applied Sciences , 2023 , 13 ( 9 ): 5234 . DOI: 10.3390/app13095234 http://doi.org/10.3390/app13095234 https://www.mdpi.com/2076-3417/13/9/5234 https://www.mdpi.com/2076-3417/13/9/5234 Path planning is an important aspect and component in the research of mobile-robot-related technologies. Many path planning algorithms are only applicable to static environments, while in practical tasks, the uncertainty in dynamic environments increases the difficulty of path planning and obstacle avoidance compared with static environments. To address this problem, this paper proposes an RRT*-FDWA algorithm. RRT* first generates a global optimal path, and then, when obstacles exist nearby, an FDWA algorithm fixes the local path in real time. Compared with other path planning algorithms, RRT*-FDWA can avoid local minima, rapidly perform path replanning, generate a smooth optimal route, and improve the robot’s maneuvering amplitude. In this paper, the effectiveness of the algorithm is verified through experiments in dynamic environments.

郭晓静 , 杨卓橙 . 基于邻域拓展的静态路径规划A * 算法研究 [J ] . 计算机工程与应用 , 2022 , 58 ( 8 ): 168 - 174 . DOI: 10.3778/j.issn.1002-8331.2010-0222 http://doi.org/10.3778/j.issn.1002-8331.2010-0222 为了解决传统的A*算法搜索自由度低，规划出的路径长度长且转角大的问题，提出了一种改进的A*算法。改进算法将传统的8邻域搜索拓展到24邻域，并利用引导向量优化邻域数量，提升搜索效率；采用路径平滑算法消除路径中的冗余节点，优化平滑路径。在不同障碍率、不同栅格地图等12种模拟场景下的100次有效实验与真实地图下的20次有效实验中，改进后算法总体较好。在Matlab中的仿真结果表明，与8邻域A*算法、24邻域A*算法、Dijkstra算法、快速拓展随机树算法等传统方法比较，改进的A*算法搜索成功率、路径长度、搜索时间等指标明显优化，搜索出路径平滑，且在真实场景下该算法仍稳定有效。

GUO X J , YANG Z C . Research on A * algorithm of static path planning based on neighborhood extension [J ] . Computer Engineering and Applications , 2022 , 58 ( 8 ): 168 - 174 . (in Chinese)

陈智康 , 刘佳 , 王丹丹 , 等 . 改进Dijkstra机器人路径规划算法研究 [J ] . 天津职业技术师范大学学报 , 2020 , 30 ( 3 ): 30 - 35 .

CHEN Z K , LIU J , WANG D D , et al. Research on improved path planning algorithm of dijkstra robot [J ] . Journal of Tianjin University of Technical and Education , 2020 , 30 ( 3 ): 30 - 35 . (in Chinese)

傅亮 , 刘峰 , 刘书勇 , 等 . 基于改进D*Lite的二维路径连续动态规划算法 [J/OL ] . 无线电通信技术 , 2023 ( 2023-11-13 ).[ 2023-11-30 ] . http://kns.cnki.net/kcms/detail/13.1099.TN.20231101.1357.002.html http://kns.cnki.net/kcms/detail/13.1099.TN.20231101.1357.002.html http://kns.cnki.net/kcms/detail/13.1099.TN.20231101.1357.002.html.

FU L , LIU F , LIU S Y , et al. Two-dimensional path continuous dynamic programming algorithm based on improved D*Lite [J/OL ] . Radio Communications Technology , 2023 ( 2023-11-13 )..[ 2023-11-30 ] . http://kns.cnki.net/kcms/detail/13.1099.TN.20231101.1357.002.html http://kns.cnki.net/kcms/detail/13.1099.TN.20231101.1357.002.html http://kns.cnki.net/kcms/detail/13.1099.TN.20231101.1357.002.html. (in Chinese)

ZHANG H , LI Z M , JIANG X Y , et al. Beetle colony optimization algorithm and its application [J ] . IEEE Access , 2020 , 8 : 128416 - 128425 . 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

DEWANGAN R , SHUKLA A , GODFREY W . Three dimensional path planning using grey wolf optimizer for UAVs [J ] . Applied Intelligence , 2019 , 49 ( 6 ): 2201 - 2217 . DOI: 10.1007/s10489-018-1384-y http://doi.org/10.1007/s10489-018-1384-y

LI Y , LIN X X , LIU J S . An improved grey wolf optimization algorithm to solve engineering problems [J ] . Sustainability , 2021 , 13 ( 6 ): 3208 . DOI: 10.3390/su13063208 http://doi.org/10.3390/su13063208 https://www.mdpi.com/2071-1050/13/6/3208 https://www.mdpi.com/2071-1050/13/6/3208 With the rapid development of the economy, the disparity between supply and demand of resources is becoming increasingly prominent in engineering design. In this paper, an improved gray wolf optimization algorithm is proposed (IGWO) to optimize engineering design problems. First, a tent map is used to generate the initial location of the gray wolf population, which evenly distributes the gray wolf population and lays the foundation for a diversified global search process. Second, Gaussian mutation perturbation is used to perform various operations on the current optimal solution to avoid the algorithm falling into local optima. Finally, a cosine control factor is introduced to balance the global and local exploration capabilities of the algorithm and to improve the convergence speed. The IGWO algorithm is applied to four engineering optimization problems with different typical complexity, including a pressure vessel design, a tension spring design, a welding beam design and a three-truss design. The experimental results show that the IGWO algorithm is superior to other comparison algorithms in terms of optimal performance, solution stability, applicability and effectiveness; and can better solve the problem of resource waste in engineering design. The IGWO also optimizes 23 different types of function problems and uses Wilcoxon rank-sum test and Friedman test to verify the 23 test problems. The results show that the IGWO algorithm has higher convergence speed, convergence precision and robustness compared with other algorithms.

王永琦 , 江潇潇 . 基于混合灰狼算法的机器人路径规划 [J ] . 计算机工程与科学 , 2020 , 42 ( 7 ): 1294 - 1301 .

WANG Y Q , JIANG X X . Robot path planning using a hybrid grey wolf optimization algorithm [J ] . Computer Engineering & Science , 2020 , 42 ( 7 ): 1294 - 1301 . (in Chinese)

CHEN Y , YU J , MEI Y , et al. Modifiedcentral force optimization (MCFO) algorithm for 3D UAV path planning [J ] . Neurocomputing , 2016 , 171 : 878 - 888 . DOI: 10.1016/j.neucom.2015.07.044 http://doi.org/10.1016/j.neucom.2015.07.044 https://linkinghub.elsevier.com/retrieve/pii/S0925231215010267 https://linkinghub.elsevier.com/retrieve/pii/S0925231215010267

XU C , DUAN H , LIU F . Chaotic artificial bee colony approach to uninhabited combat air vehicle (UCAV) path planning [J ] . Aerospaceence & Technology , 2010 , 14 ( 8 ): 535 - 541 .

MIRJALILI S , MIRJALILI S M , LEWIS A D . Grey wolf optimizer [J ] . Advances in Engineering Software , 2014 , 69 : 46 - 61 . DOI: 10.1016/j.advengsoft.2013.12.007 http://doi.org/10.1016/j.advengsoft.2013.12.007 https://linkinghub.elsevier.com/retrieve/pii/S0965997813001853 https://linkinghub.elsevier.com/retrieve/pii/S0965997813001853

GOLDANLOO , JAVANMARD M , GHAREHCHOPOGH , et al. A hybrid OBL-based firefly algorithm with symbiotic organisms search algorithm for solving continuous optimization problems [J ] . The Journal of Supercomputing , 2021 , 78 : 3998 - 4031 . DOI: 10.1007/s11227-021-04015-9 http://doi.org/10.1007/s11227-021-04015-9

李阳 , 李维刚 , 赵云涛 , 等 . 基于莱维飞行和随机游动策略的灰狼算法 [J ] . 计算机科学 , 2020 , 47 ( 8 ): 291 - 296 . DOI: 10.11896/jsjkx.190600107 http://doi.org/10.11896/jsjkx.190600107 在标准灰狼优化算法寻优的中后期, 由于衰减因子减小, 灰狼群体中的个体均向领导层灰狼所在区域靠近, 导致算法的全局寻优能力差, 降低了寻优精度。针对该问题, 提出了一种改进灰狼优化算法(Improved Grey Wolf Optimization, IGWO)。该算法首先分析了衰减因子对灰狼算法(Grey Wolf Optimization, GWO)的影响, 提出了一种分段可调节衰减因子, 用于平衡算法的勘探能力与开发能力。其可以根据不同优化问题来寻找适当的参数, 实现更高精度的寻优, 并且保证了在寻优过程的中后期, 算法也具有一定的全局搜索能力。数值仿真实验表明, 提高勘探比例有利于提高算法的收敛精度。同时, 在寻优过程中, 根据概率选择对领导层灰狼分别进行莱维飞行操作或随机游动操作。利用莱维飞行短距离搜索与偶尔较长距离行走相间的搜索特点, 提高算法的全局寻优能力;利用随机游动相对集中的搜索特性, 提高局部寻优能力。最后, 对8个标准测试函数进行仿真实验, 并与其他几种算法进行比较, 实验结果表明, 所提算法在寻优精度、算法稳定性及收敛速度上都有较大优势。

LI Y , LI W G , ZHAO Y T , et al. Grey wolf algorith-m based on Levy flight and random walk strategy [J ] . Computer Science , 2020 , 47 ( 8 ): 291 - 296 . (in Chinese)

GUERRERO M , CASTILLO O , GARCÍA M, Cuckoo search via Lévy flights and acomparison with genetic algorithms [J ] . Fuzzy Logic Augmentation of Nature-Inspired Optimization Metaheuristics. Berlin,Germany:Springer , 2015 , 574 : 91 - 103 .