基于可达集的无人机低空飞行冲突解脱算法

杨建航; 张福彪; 王江

doi:10.13700/j.bh.1001-5965.2021.0542

基于可达集的无人机低空飞行冲突解脱算法

doi: 10.13700/j.bh.1001-5965.2021.0542

杨建航^{1, 2},
张福彪^{1, 2, ,},
王江^{1, 2}

1.
北京理工大学宇航学院，北京 100081
2.
无人机自主控制技术北京重点实验室，北京 100081

基金项目: 国家重点研发计划(2021YFF0601304)；国家自然科学基金(U1913602)；北京市科学技术委员会基金(Z181100003218013)

详细信息

通讯作者:
E-mail：fubiao.zhang@bit.edu.cn

中图分类号: V221⁺.3；TB553
计量
- 文章访问数: 415
- HTML全文浏览量: 53
- PDF下载量: 45
- 被引次数: 0
出版历程
- 收稿日期: 2021-09-09
- 录用日期: 2021-12-17
- 网络出版日期: 2022-01-12
- 整期出版日期: 2023-07-31

Conflict resolution algorithms for UAV low-altitude flight based on reachable set

YANG Jianhang^{1, 2},
ZHANG Fubiao^{1, 2
, ,},
WANG Jiang^{1, 2}

1.
School of Aerospace Engineering，Beijing institute of Technology，Beijing 100081，China
2.
Beijing Key Laboratory of UAV Autonomous Control Technology，Beijing 100081，China

Funds: National Key Research and Development Program of China (2021YFF0601304); National Natural Science Foundation of China (U1913602); Beijing Municipal Science & Technology Commission fund (Z181100003218013)

More Information

Corresponding author: E-mail：fubiao.zhang@bit.edu.cn

摘要

摘要:
针对无人空中交通管理（UTM）中的冲突解脱问题，提出了以可达集分析为基础的实时避撞算法。该算法可用于城市低空环境中的密集交通流空域，保证无人机（UAV）飞行过程的安全性。基于相对运动的概念，通过分析平面空域中的飞行博弈问题对避撞系统进行建模，同时利用水平集方法和最优控制理论对无人机的可达集进行分析和计算，使用机载传感器获取无人机与周围物体的信息，为每架无人机提供新的避撞策略。通过3种不同空域环境的飞行案例进行仿真实验，验证了该策略不仅可以得到平滑的飞行路径，实时安全地解决冲突解脱问题，而且针对合作/非合作目标均有效。
- 无人空中交通管理 /
- 冲突解脱 /
- 城市低空环境 /
- 可达集分析 /
- 避撞策略 /
- 平面空域
Abstract:
Aiming at the conflict resolution problem in unmanned air traffic management (UTM), real-time collision avoidance algorithms based on reachability set analysis are proposed. To assure the secure operation of unmanned aerial vehicles (UAV) in low-altitude urban environments with dense traffic flow, these algorithms can be deployed. Based on the relative motion between the UAVs, the collision avoidance problem is modeled as a dynamic game problem in the 2D horizontal airspace, further the key concept of the reachable set of the UAV can be analyzed and calculated using the level set method and optimal control theory. Aided by airborne sensors, a new collision avoidance strategy for each drone is proposed using information about drones and surrounding objects. The technique can safely resolve the conflict resolution problem in real-time with a smooth flight route, according to simulation findings from three examples in varied airspace settings, and it is also successful against both cooperative and non-cooperative UAVs.
- unmanned air traffic management /
- conflict resolution /
- low-altitude urban environment /
- reachability set analysis /
- collision avoidance strategy /
- 2D horizontal airspace

HTML全文

图 1 前向可达集与后向可达集^[30]

Figure 1. Forward reachable set and backward reachable set^[30]

下载: 全尺寸图片幻灯片

图 2 无人机前后向可达集确保安全方式

Figure 2. FRS and BRS ensure safety measures

下载: 全尺寸图片幻灯片

图 3 水平集方法的图示^[32]

Figure 3. Illustration of level set method^[32]

下载: 全尺寸图片幻灯片

图 4 2架飞机相对运动系统模型

Figure 4. Two aircraft relative motion system model

下载: 全尺寸图片幻灯片

图 5 目标集与后向可达集

Figure 5. Target set and backward reachable set

下载: 全尺寸图片幻灯片

图 6 可达集随时间变化

Figure 6. Reachable set changes over time

下载: 全尺寸图片幻灯片

图 7 避撞动画的注释帧

Figure 7. Comment frame of collision avoidance animation

下载: 全尺寸图片幻灯片

图 8 飞机Ⅱ避撞示意图

Figure 8. Aircraft Ⅱ cannot enter the reachable set, thus avoiding collision

下载: 全尺寸图片幻灯片

图 9 无人机与障碍物模型

Figure 9. UAV and obstacle model

下载: 全尺寸图片幻灯片

图 10 可达集与3种区域的关系

Figure 10. Relation between reachable set and three areas

下载: 全尺寸图片幻灯片

图 11 UAV避障模型

Figure 11. UAV collision avoidance model

下载: 全尺寸图片幻灯片

图 12 本文算法工作流程

Figure 12. Work flow of proposed algorithm

下载: 全尺寸图片幻灯片

图 13 用于仿真的3种案例

Figure 13. Three cases for simulation

下载: 全尺寸图片幻灯片

图 14 案例1的可达集

Figure 14. Reachable set of case 1

下载: 全尺寸图片幻灯片

图 15 无人机躲避多个静态障碍物的过程

Figure 15. Process of UAV avoiding multiple static obstacles

下载: 全尺寸图片幻灯片

图 16 无人机与静态障碍物之间的距离

Figure 16. Distance between UAV and static obstacles

下载: 全尺寸图片幻灯片

图 17 无人机速度和飞行平面内推力（案例1）

Figure 17. UAV speed and thrust in flight plane (case 1)

下载: 全尺寸图片幻灯片

图 18 案例2的可达集

Figure 18. Reachable set of case 2

下载: 全尺寸图片幻灯片

图 19 2架无人机相互避撞的过程

Figure 19. Process of two UAVs avoiding each other

下载: 全尺寸图片幻灯片

图 20 2架无人机之间的距离

Figure 20. Distance between two UAVs

下载: 全尺寸图片幻灯片

图 21 无人机1速度和飞行平面内推力（案例2）

Figure 21. UAV 1 speed and thrust in flight plane (case 2)

下载: 全尺寸图片幻灯片

图 22 无人机2速度和飞行平面内推力（案例2）

Figure 22. UAV 2 speed and thrust in flight plane (case 2)

下载: 全尺寸图片幻灯片

图 23 案例3的可达集

Figure 23. Reachable set of case 3

下载: 全尺寸图片幻灯片

图 24 无人机躲避多个动态障碍物的过程

Figure 24. Process of UAV avoiding multiple dynamic objects

下载: 全尺寸图片幻灯片

图 25 无人机速度和飞行平面内推力（案例3）

Figure 25. UAV speed and thrust in flight plane (case 3)

下载: 全尺寸图片幻灯片

图 26 无人机与动态物体之间的距离

Figure 26. Distance between UAV and dynamic objects

下载: 全尺寸图片幻灯片

表 1 仿真参数

Table 1. Simulation parameters

参数	数值
无人机初始位置${ {\boldsymbol{p} }_{\text{0} } }/{\rm{m}}$	[0 , 0]
反应时间/s	1
无人机质量$ m $/kg	20
无人机半径$ r $/m	1.5
无人机的初始速度${\boldsymbol{v} }/({\rm{m}} \cdot {{\rm{s}}}^{-1})$	[40 , 0]
冲突探测半径$ R $/m	120
障碍物半径${r_{{\rm{obs}}} }$/m	15
可达集获取时间/s	0.097

下载: 导出CSV

参考文献(39)

[1]	BALACHANDRAN S, MUNOZ C, CONSIGLIO M C. Implicitly coordinated detect and avoid capability for safe autonomous operation of small UAS[C]//17th AIAA Aviation Technology, Integration, and Operations Conference. Reston: AIAA, 2017: 1-10.
[2]	WU Y, LOW K H, HU X T. Trajectory-based flight scheduling for AirMetro in urban environments by conflict resolution[J]. Transportation Research Part C: Emerging Technologies, 2021, 131: 103355.
[3]	LUNDBERG J, ARVOLA M, WESTIN C, et al. Cognitive work analysis in the conceptual design of first-of-a-kind systems—Designing urban air traffic management[J]. Behaviour & Information Technology, 2018, 37(9): 904-925.
[4]	SCOTT D, RADMANESH M, SARIM M, et al. Distributed bidding-based detect-and-avoid for multiple unmanned aerial vehicles in national airspace[C]//2019 International Conference on Unmanned Aircraft Systems (ICUAS). Piscataway: IEEE Press, 2019: 930-936.
[5]	ALI B S. Traffic management for drones flying in the city[J]. International Journal of Critical Infrastructure Protection, 2019, 26: 100310. doi: 10.1016/j.ijcip.2019.100310
[6]	BIJJAHALLI S, SABATINI R, GARDI A. Advances in intelligent and autonomous navigation systems for small UAS[J]. Progress in Aerospace Sciences, 2020, 115: 100617. doi: 10.1016/j.paerosci.2020.100617
[7]	HO F, GERALDES R, GONÇALVES A, et al. Pre-flight conflict detection and resolution for UAV integration in shared airspace: Sendai 2030 model case[J]. IEEE Access, 2019, 7: 170226-170237. doi: 10.1109/ACCESS.2019.2954987
[8]	HU J M, YANG X X, WANG W C, et al. UAS conflict resolution in continuous action space using deep reinforcement learning[C]//AIAA aviation 2020 FORUM. Reston: AIAA, 2020.
[9]	ZHAO P, ERZBERGER H, LIU Y M. Multiple-aircraft-conflict resolution under uncertainties[J]. Journal of Guidance, Control, and Dynamics, 2021, 44(11): 2031-2049. doi: 10.2514/1.G005825
[10]	王泽坤, 吴明功, 温祥西, 等. 基于速度障碍法的飞行冲突解脱与恢复策略[J]. 北京航空航天大学学报, 2019, 45(7): 1294-1302. doi: 10.13700/j.bh.1001-5965.2018.0650 WANG Z K, WU M G, WEN X X, et al. Flight collision resolution and recovery strategy based on velocity obstacle method[J]. Journal of Beijing University of Aeronautics and Astronautics, 2019, 45(7): 1294-1302(in Chinese). doi: 10.13700/j.bh.1001-5965.2018.0650
[11]	DUCHAMP V, JOSEFSSON B, POLISHCHUK T, et al. Air traffic deconfliction using sum coloring[C]//2019 IEEE/AIAA 38th Digital Avionics Systems Conference (DASC). Piscataway: IEEE Press, 2020: 1-6.
[12]	MU L F, HAN S C. Satisficing game approach to conflict resolution for cooperative aircraft sharing airspace[J]. Big Data, 2021, 9(1): 53-62. doi: 10.1089/big.2020.0155
[13]	黄洋, 汤俊, 老松杨. 基于复杂网络的无人机飞行冲突解脱算法[J]. 航空学报, 2018, 39(12): 262-274. HUANG Y, TANG J, LAO S Y. UAV flight conflict resolution algorithm based on complex network[J]. Acta Aeronautica et Astronautica Sinica, 2018, 39(12): 262-274(in Chinese).
[14]	MIGLIACCIO G, MENGALI G, GALATOLO R, et al. A solution to detect and avoid conflicts for civil remotely piloted aircraft systems into non-segregated airspaces[J]. Proceedings of the Institution of Mechanical Engineers Part G:Journal of Aerospace Engineering, 2016, 230(9): 1655-1667. doi: 10.1177/0954410015625664
[15]	JOHNSON S C, PETZEN A, TOKOTCH D. Exploration of detect-and-avoid and well-clear requirements for small UAS maneuvering in an urban environment[C]//17th AIAA Aviation Technology, Integration, and Operations Conference. Reston: AIAA, 2017: 1-19.
[16]	GREBE T, KUNZI F. Applications of conflict probes for detect and avoid systems[C]//2019 IEEE/AIAA 38th Digital Avionics Systems Conference (DASC). Piscataway: IEEE Press, 2020: 1-5.
[17]	刘畅, 王宏伦, 姚鹏, 等. 面向空中威胁的无人机动态碰撞区建模与分析[J]. 北京航空航天大学学报, 2015, 41(7): 1231-1238. doi: 10.13700/j.bh.1001-5965.2014.0497 LIU C, WANG H L, YAO P, et al. Modeling and analysis of dynamic collision region for UAV avoiding aerial intruders[J]. Journal of Beijing University of Aeronautics and Astronautics, 2015, 41(7): 1231-1238(in Chinese). doi: 10.13700/j.bh.1001-5965.2014.0497
[18]	KUCHAR J K, YANG L C. A review of conflict detection and resolution modeling methods[J]. IEEE Transactions on Intelligent Transportation Systems, 2000, 1(4): 179-189. doi: 10.1109/6979.898217
[19]	刘慧颖, 白存儒, 杨广珺. 无人机自主防撞关键技术与应用分析[J]. 航空工程进展, 2014, 5(2): 141-147. doi: 10.3969/j.issn.1674-8190.2014.02.002 LIU H Y, BAI C R, YANG G J. Application and analysis and discussion of autonomous collision avoidance techniques for unmanned aerial vehicle[J]. Advances in Aeronautical Science and Engineering, 2014, 5(2): 141-147(in Chinese). doi: 10.3969/j.issn.1674-8190.2014.02.002
[20]	YU X, ZHANG Y M. Sense and avoid technologies with applications to unmanned aircraft systems: Review and prospects[J]. Progress in Aerospace Sciences, 2015, 74: 152-166.
[21]	PARK J W, OH H D, TAHK M J. UAV collision avoidance based on geometric approach[C]//2008 SICE Annual Conference. Piscataway: IEEE Press, 2008: 2122-2126.
[22]	WOLF T B, KOCHENDERFER M J. Aircraft collision avoidance using Monte Carlo real-time belief space search[J]. Journal of Intelligent & Robotic Systems, 2011, 64(2): 277-298.
[23]	CETIN O, ZAGLI I, YILMAZ G. Establishing obstacle and collision free communication relay for UAVs with artificial potential fields[J]. Journal of Intelligent & Robotic Systems, 2013, 69(1): 361-372.
[24]	YANG H, ZHAO Y J. Trajectory planning for autonomous aerospace vehicles amid known obstacles and conflicts[J]. Journal of Guidance, Control, and Dynamics, 2004, 27(6): 997-1008. doi: 10.2514/1.12514
[25]	FU S Y, HAN L W, TIAN Y, et al. Path planning for unmanned aerial vehicle based on genetic algorithm[C]//IEEE 11th International Conference on Cognitive Informatics and Cognitive Computing. Piscataway: IEEE Press, 2012: 140-144.
[26]	CEKMEZ U, OZSIGINAN M, SAHINGOZ O K. Multi colony ant optimization for UAV path planning with obstacle avoidance[C]//2016 International Conference on Unmanned Aircraft Systems (ICUAS). Piscataway: IEEE Press, 2016: 47-52.
[27]	KARIMI J, POURTAKDOUST S H. Optimal maneuver-based motion planning over terrain and threats using a dynamic hybrid PSO algorithm[J]. Aerospace Science and Technology, 2013, 26(1): 60-71. doi: 10.1016/j.ast.2012.02.014
[28]	LIN Y C, SARIPALLI S. Collision avoidance for UAVs using reachable sets[C]//2015 International Conference on Unmanned Aircraft Systems (ICUAS). Piscataway: IEEE Press, 2015: 226-235.
[29]	王亮, 魏铂淞, 熊瑜, 等. 基于边界归一化的低空无人机实时避撞路径规划[J]. 西北工业大学学报, 2017, 35(2): 213-219. doi: 10.3969/j.issn.1000-2758.2017.02.007 WANG L, WEI B S, XIONG Y, et al. Real-time route plan for UAV lower aerial collision avoidance based on boundary normalization[J]. Journal of Northwestern Polytechnical University, 2017, 35(2): 213-219(in Chinese). doi: 10.3969/j.issn.1000-2758.2017.02.007
[30]	VANOORT E R. Adaptive back stepping control and safety analysis for modern fighter aircraft[D]. Delft: Delft University of Technology, 2011.
[31]	LEUNG K, SCHMERLING E, ZHENG M X, et al. On infusing reachability-based safety assurance within probabilistic planning frameworks for human-robot vehicle interactions[J]. International Journal of Robotics Research, 2020, 39(10-11): 1326-1345. doi: 10.1177/0278364920950795
[32]	陈文. 混合系统可达集计算方法研究[J]. 科技传播, 2012, 4(22): 125-126. CHEN W. Research on computing method of reachable set of hybrid system[J]. Public Communication of Science & Technology, 2012, 4(22): 125-126(in Chinese).
[33]	OSHER S, FEDKIW R. Level set methods and dynamic implicit surfaces[M]. Berlin: Springer, 2003.
[34]	MITCHELL I M, BAYEN A M, TOMLIN C J. A time-dependent Hamilton-Jacobi formulation of reachable sets for continuous dynamic games[J]. IEEE Transactions on Automatic Control, 2005, 50(7): 947-957. doi: 10.1109/TAC.2005.851439
[35]	MITCHELL I M, TOMLIN C J. Overapproximating reachable sets by Hamilton-Jacobi projections[J]. Journal of Scientific Computing, 2003, 19(1-3): 323-346.
[36]	MITCHELL I. Games of two identical vehicles[R]. Stanford: Stanford University,2001.
[37]	MITCHELL I. A toolbox of level set methods[R]. Vancouver: The University of British Columbia, 2007.
[38]	管祥民, 吕人力. 基于满意博弈论的复杂低空飞行冲突解脱方法[J]. 航空学报, 2017, 38(S1): 120-128. doi: 10.7527/S1000-6893.2017.721475 GUAN X M, LYU R L. Aircraft conflict resolution method based on satisfying game theory[J]. Acta Aeronautica et Astronautica Sinica, 2017, 38(S1): 120-128(in Chinese). doi: 10.7527/S1000-6893.2017.721475
[39]	WANG J, XIN M. Integrated optimal formation control of multiple unmanned aerial vehicles[J]. IEEE Transactions on Control Systems Technology, 2013, 21(5): 1731-1744. doi: 10.1109/TCST.2012.2218815