﻿ 低空自由飞行短期冲突探测算法<sup>*</sup>
 文章快速检索 高级检索

Short-term conflict detection algorithm for free flight in low-altitude airspace
LIU Yang, XIANG Jinwu, LUO Zhangping, JIN Wanzeng
School of Aeronautic Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
Received: 2016-08-25; Accepted: 2016-11-18; Published online: 2017-01-06 11:03
Foundation item: National Basic Research Program of China (2011CB707002)
Corresponding author. XIANG Jinwu, E-mail: xiangjw@buaa.edu.cn
Abstract: Considering the autonomous route of free flight in low-altitude airspace, a probabilistic short-term conflict detection algorithm is proposed. The trajectory prediction error caused by navigation error, control error and wind disturbance was taken into account. A reasonable error model was constructed to compute the conflict probability between aircraft in the short term. By using coordinate transformation and extending the conflict zone, an approximate analytical expression was presented to estimate the conflict probability of maneuvering flight in three-dimensional airspace. By comparison with Paielli and Erzberger (P&E) approximation algorithm and the Monte Carlo simulation algorithm, the presented algorithm was proved to increase the accuracy of conflict probability estimation and decrease the computational consumption. The result shows that this algorithm can reach the real-time requirement of free flight in low-altitude airspace and realize the conflict detection in complex environment.
Key words: free flight     trajectory prediction     conflict detection     conflict probability     Brownian motion

1 飞行冲突保护区

 (1)

 (2)
 图 1 低空自由飞行的保护区 Fig. 1 Protection zone of aircraft for free flight in low-altitude airspace

2 航迹预估模型

 (3)

t时刻预测位置可由当前时刻的位置信息、运动信息、控制信息外推得到：

 (4)
 (5)

 (6)

 (7)

 (8)

 (9)

 (10)

 (11)

 (12)

 (13)

 (14)

 (15)

 (16)

 (17)

 (18)

 (19)

Blin等[21]推导了二维平面内随机风扰动引起的交叉相关项。将其扩展为三维情况:

 (20)

3 冲突探测算法

Paielli和Erzberger[2-3]基于常速度和直线飞行假设，使用平行于相对速度方向的无限延长的条形扩展区域计算冲突概率，这种方法得到直线航路内冲突概率的上限值，高估了冲突概率且无法用于机动飞行情况。其他学者使用Monto Carlo算法计算冲突概率，虽然适用于计算机动情况下的冲突概率，但计算量大，计算过程复杂，无法满足实时性要求，本文仅使用Monto Carlo算法作为对比算法验证。

εi(t)为新坐标系O-ξηγ中的位置向量，T为从地面坐标系O-xyz到新坐标系O-ξηγ的旋转矩阵：

 (21)

 (22)

 (23)

 (24)

 (25)

 (26)

 (27)

 (28)

 (29)
 图 2 二维平面冲突概率计算示意图 Fig. 2 Schematic diagram of calculation of conflict probability in two-dimensional plane

 (30)

(ξi, ηi)、δξiδηi可由式(31) 和式(32) 确定:

 (31)
 (32)

 (33)

 (34)

 (35)

 图 3 三维空间冲突概率计算示意图 Fig. 3 Schematic diagram of calculation of conflict probability in three-dimensional airspace

 (36)

 (37)

 (38)

(ξi, ηi, γi)、δξiδηiδγi可由式(39) 确定:

 (39)
 (40)

 (41)

4 算例仿真 4.1 直线相向飞行

 图 4 直线相向飞行结果比较 Fig. 4 Result comparison of straight toward flight
4.2 转弯机动飞行

 图 5 二维情况转弯机动飞行结果比较 Fig. 5 Result comparison of turning maneuver flight in two-dimensional case
4.3 三维机动飞行

 图 6 三维情况爬升转弯机动飞行结果比较 Fig. 6 Result comparison of climbing turning maneuver flight in three-dimensional case

 算法 计算时间/ms 直线相向飞行 转弯机动飞行 三维机动飞行 Monte Carlo仿真算法 7.039×103 7.039×103 1.047×104 P&E近似算法 0.06 0.48 本文算法 2.58 2.58 3.72

5 结论

1) 分析了航迹预估中导航误差、控制误差以风扰动3种误差来源并分别进行了建模，建立了适当的误差模型，提高了航迹预估的精度。

2) 提出了低空自由飞行下冲突概率探测方法的近似解析算法，可用于计算三维空间内的冲突概率。仿真结果表明，本文算法适用于机动飞行的情况，可实现复杂环境下的冲突探测，具有足够的计算精度并满足实时性要求。

 [1] KUCHAR J, YANG L. 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 [2] PAIELLI R, ERZBERGER H. Conflict probability estimation for free flight[J]. Journal of Guidance, Control, and Dynamics, 1997, 20 (3): 588–596. DOI:10.2514/2.4081 [3] PAIELLI R, ERZBERGER H. Conflict probability estimation generalized to non-level flight[J]. Air Traffic Control Quarterly, 1999, 7 (3): 195–222. DOI:10.2514/atcq.7.3.195 [4] 邓炜, 张军, 吴限, 等. 一种适用于航路改变情况的冲突概率探测算法[J]. 北京航空航天大学学报, 2005, 31 (12): 1327–1332. DENG W, ZHANG J, WU X, et al. Algorithm of conflict probability prediction for the case of trajectory change[J]. Journal of Beijing University of Aeronautics and Astronautics, 2005, 31 (12): 1327–1332. DOI:10.3969/j.issn.1001-5965.2005.12.013 (in Chinese) [5] 高杨, 徐浩军, 郑海峰. 计算航路上飞行冲突概率的一种方法[J]. 飞行力学, 2009, 27 (2): 50–53. GAO Y, XU H J, ZHENG H F. Algorithm to estimate the conflict probability on the airway[J]. Flight Dynamics, 2009, 27 (2): 50–53. (in Chinese) [6] 沈笑云, 周波, 曹博, 等. 基于冲突概率的低空自由飞行冲突检测算法[J]. 电光与控制, 2014, 21 (6): 43–47. SHEN X Y, ZHOU B, CAO B, et al. A free flight conflict detection algorithm of low-altitude airspace based on conflict probability[J]. Electronics Optics & Control, 2014, 21 (6): 43–47. (in Chinese) [7] PRANDINI M, HU J. A probabilistic approach to aircraft conflict detection[J]. IEEE Transactions on Intelligent Transportation Systems, 2001, 1 (4): 199–220. [8] PRANDINI M, PUTTA V. A probabilistic measure of air traffic complexity in three-dimensional airspace[J]. International Journal of Adaptive Control and Signal Processing, 2010, 24 (10): 813–829. DOI:10.1002/acs.1192 [9] 李丹, 崔德光. 基于布朗运动的空中交通短期冲突探测[J]. 清华大学学报(自然科学版), 2008, 48 (4): 477–481. LI D, CUI D G. Air traffic control conflict detection algorithm based on Brownian motion[J]. Journal of Tsinghua University(Science and Technology), 2008, 48 (4): 477–481. (in Chinese) [10] 刘小龙, 罗以宁, 赵喜求, 等. 一种改进的Prandini概率型中期冲突探测方法[J]. 计算机技术与发展, 2013, 23 (1): 214–216. LIU X L, LUO Y N, ZHAO X Q, et al. An improved medium-term conflict detection methods of Prandini probability type[J]. Computer Technology and Development, 2013, 23 (1): 214–216. (in Chinese) [11] 石磊, 吴仁彪, 黄晓晓. 基于总体冲突概率和三维布朗运动的冲突探测算法[J]. 电子与信息学报, 2015, 37 (2): 360–366. SHI L, WU R B, HUANG X X. Conflict detection algorithm based on overall conflict probability and three dimensional Brownian motion[J]. Journal of Electronics & Information Technology, 2015, 37 (2): 360–366. DOI:10.11999/JEIT140363 (in Chinese) [12] JILKOV V P, LI X R, LEDET J H.Improved estimation of conflict probability for aircraft collision avoidance[C]//17th International Conference on Information Fusion.Piscataway, NJ:IEEE Press, 2014:1-7. [13] BLOM H, BAKKER G.Conflict probability and incrossing probability in air traffic management[C]//Proceedings of the 41st IEEE Conference on Decision and Control.Piscataway, NJ:IEEE Press, 2002, 3:2421-2426. [14] JACQUEMART D, MORIO J. Adaptive interacting particle system algorithm for aircraft conflict probability estimation[J]. Aerospace Science and Technology, 2016, 55 (5): 431–438. [15] VISINTINI A, GLOVER W, LYGEROS J. Monte Carlo optimization for conflict resolution in air traffic control[J]. IEEE Transactions on Intelligent Transportation Systems, 2006, 7 (4): 470–482. DOI:10.1109/TITS.2006.883108 [16] 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. [17] BELKHOUCHE F. Modeling and calculating the collision risk for air vehicles[J]. IEEE Transactions on Vehicular Technology, 2013, 62 (5): 2031–2041. DOI:10.1109/TVT.2013.2238265 [18] LAMBERT A, GRUYER D.A fast Monte Carlo algorithm for collision probability estimation[C]//10th International Conference on Control, Automation, Robotics and Vision.Piscataway, NJ:IEEE Press, 2008:406-411. [19] KARLIN S, TAYLOR H M. 随机过程初级教程[M]. 庄无兴, 陈宗洵, 陈庆华, 译. 北京: 人民邮电出版社, 2007: 306-351. KARLIN S, TAYLOR H M.A first course in stochastic processess[M].ZHUANG W X, CHEN Z X, CHEN Q H, translated.Beijing:Posts & Telecom Press, 2007:306-351(in Chinese). http://210.37.2.189/opac/item.php?marc_no=0000326501 [20] HU J H, PRANDINI M, SASTRY S. Aircraft conflict prediction in the presence of a spatially correlated wind field[J]. IEEE Transactions on Intelligent Transportation Systems, 2005, 6 (3): 326–340. DOI:10.1109/TITS.2005.853699 [21] BLIN K, AKIAN M, BONNANS F, et al.A stochastic conflict detection method integrating planned heading and velocity changes[C]//Proceedings of 39th IEEE Conference on Decision and Control.Piscataway, NJ:IEEE Press, 2000, 5:4717-4722.

#### 文章信息

LIU Yang, XIANG Jinwu, LUO Zhangping, JIN Wanzeng

Short-term conflict detection algorithm for free flight in low-altitude airspace

Journal of Beijing University of Aeronautics and Astronsutics, 2017, 43(9): 1873-1881
http://dx.doi.org/10.13700/j.bh.1001-5965.2016.0687