﻿ 基于速度障碍法的飞行冲突解脱与恢复策略<sup>*</sup>
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1. 空军工程大学 空管领航学院, 西安 710051;
2. 国家空管防相撞技术重点实验室, 西安 710051;
3. 中国人民解放军94116部队, 和田 848000;
4. 中国人民解放军93175部队, 长春 130051

Flight collision resolution and recovery strategy based on velocity obstacle method
WANG Zekun1,2, WU Minggong1,2, WEN Xiangxi1,2, JIANG Xurui3, GAO Yangyang4
1. Air Traffic Control and Navigation College, Air Force Engineering University, Xi'an 710051, China;
2. National Key Laboratory of Air Traffic Collision Prevention, Xi'an 710051, China;
3. Unit 94116 of the PLA, Hetian 848000, China;
4. Unit 93175 of the PLA, Changchun 130051, China
Received: 2018-11-12; Accepted: 2019-03-22; Published online: 2019-04-16 17:50
Foundation item: National Natural Science Foundation of China (71801221); Natural Science Basic Research Plan in Shaanxi Province of China (2018JQ7004)
Corresponding author. WEN Xiangxi, E-mail: wxxajy@163.com
Abstract: A geometric optimization algorithm is proposed based on velocity obstacle method to solve the problem of flight collision resolution and track recovery. We gave a rigorous mathematical description of the problem. Firstly, according to the relative position and speed relationship between the aircraft, the collision type and whether the conditions of each release strategy are met are determined, and the corresponding resolution strategy is adopted. After the collision was resolved, the plane resumed its flight on the original route. The model can effectively solve flight collision through geometric analysis and theoretical derivation. In addition, the track recovery point and the parameter solving process involved are given in detail. Finally, in the simulation, the algorithm chooses the collision resolution strategy independently according to different scenes. The results show that this method is simple and efficient, and the track recovery redirects the ownership to its original target waypoint without introducing new flight collision.
Keywords: velocity obstacles     air traffic control     collision detection     collision resolution     track recovery     geometric optimization algorithm

1 模型简化

1) 航路飞行过程中，飞机速度基本保持不变，即在冲突解脱时，假设飞机速度相同(同向飞行除外)。

2) 飞机在爬升和下降阶段地速保持不变。

3) 由于本文冲突解脱过程中飞机速度和航向改变量都较小，视其为瞬间改变。

4) 雷达管制条件下，航路航线飞行中，为了防止飞行冲突，保证飞行安全，提高飞行空间和时间利用率，规定的航空器之间应当保持最小安全距离。飞行间隔包括垂直间隔和水平间隔。其中水平间隔dl=10 km，垂直间隔dv=300 m，并且水平和垂直方向上的安全间隔至少要满足一项。因此，本文采取圆柱形安全保护区模型，如图 1所示。

 图 1 安全保护区模型 Fig. 1 Safety protection zone model

 (1)

2 探测模型 2.1 速度障碍模型

 图 2 速度障碍模型 Fig. 2 Velocity obstacle model

 (2)

αγ的大小可以分别由式(3)和式(4)给出：

 (3)
 (4)
2.2 有时间约束的速度障碍模型

 图 3 有时间约束的速度障碍模型 Fig. 3 Velocity obstacle model with time constraints

AC1相对于AC2的速度障碍区可表示为

 (5)

3 双机冲突解脱模型

3.1 高度解脱

AC1与AC2两架飞机处于同高度层，起始坐标分别为(x1, y1)、(x2, y2)，AC1若想超越AC2飞行，则可以采取改变高度层的策略解决飞行冲突，如图 4所示。在高度层改变的过程中，需要一直保持两机之间在水平和垂直方向上，至少有一个间隔满足最小安全间隔(水平安全间隔为10 km，垂直安全间隔为300 m)，假设在整个过程中，飞机的地速始终保持不变。为了简化计算过程，将AC2作为参考系，则AC1的相对速度vR=v1-v2，给定AC1的上升/下降率为v

 图 4 高度解脱 Fig. 4 Elevation resolution

TCP1→TCP2：结合两机速度以及安全间隔，可以得到该段航迹：

 (6)

AC1与AC2之间的距离为l时，开始上升高度(TCP1)，当上升高度为两机之间的垂直安全间隔时改为平飞(TCP2)。

TCP2→TCP3：为满足AC1与AC2之间始终保持安全间隔，当水平方向上两机之间的间隔为dl时，AC1开始下降高度(TCP3)。

 (7)

TCP3→TCP4：该段为下降阶段，AC1按给定的下降率下降高度至原飞行高度层。

 (8)

 (9)
3.2 速度解脱

3.2.1 解脱冲突

 图 5 速度解脱 Fig. 5 Speed resolution

 (10)

 (11)

AC1和AC2的初始位置分别为(x1, y1)、(x2, y2)，即两机在进行冲突解脱瞬间的距离为

 (12)

 (13)

 图 6 飞机相对位置示意图 Fig. 6 Schematic diagram of relative position of aircraft

 (14)

 (15)

 (16)

P点坐标(xP, yP)可以由以下推导得出：

 (17)

 (18)

3.2.2 恢复航迹

 (19)
 (20)
 图 7 速度解脱航迹恢复 Fig. 7 Track recovery with speed resolution

 (21)

3.3 航向解脱

3.3.1 解脱冲突

 图 8 航向解脱 Fig. 8 Heading resolution

 (22)

 (23)

3.3.2 恢复航迹

 (24)
 图 9 航向解脱航迹恢复 Fig. 9 Track recovery with heading resolution

4 双机冲突解脱策略

 图 10 双机冲突解脱流程 Fig. 10 Collision resolution process of two aircraft
4.1 同向航迹飞行冲突(0°~45°)

 (25)

 (26)
4.2 交叉航迹飞行冲突(45°~135°)

4.3 逆向航迹飞行冲突(135°~180°)

5 算例分析

 场景 起点/km 航向/(°) 速度/(km·h-1) 仿真步长/h 1 (0, 200, 4.2) 90 800 0.001 (110, 200, 4.2) 90 700 2 (200, 200, 4.2) 90 800 0.001 (250, 200, 4.2) 270 800 3 (0, 100, 4.2) 90 800 0.001 (100, 0, 4.2) 0 800 4 (0, 100, 4.2) 75 800 0.01 (100, 0, 4.2) 15 800

 场景 类型 冲突解脱所需速度/(km·h-1) 间隔s/km 距离l/km 判断 冲突解脱方式 小速度解脱 大速度解脱 1 同向 110 12.78 s≥l ER 2 逆向 50 53.25 s＜l HR 3 交叉 465.4 1 208.9 141.42 41.43 v′1∉[600, 900] km/h & v″1∉[600, 900] km/h ER 4 交叉 631.3 609.8 141.42 32.22 v′1∈[600, 900] km/h & v″1∈[600, 900] km/h SR

 图 11 同向飞行高度解脱(场景1) Fig. 11 Elevation resolution for the same track of flight (Scene 1)

 图 12 逆向飞行航向解脱(场景2) Fig. 12 Heading resolution for opposite track of flight (Scene 2)

 图 13 交叉飞行高度解脱(场景3) Fig. 13 Elevation resolution for cross track of flight (Scene 3)

 图 14 交叉飞行速度解脱(场景4) Fig. 14 Speed resolution for cross track of flight (Scene 4)

 场景 冲突解脱点/km 航迹恢复点/km 切入原航迹点/km 1 (778.4, 200, 4.2) (960.8, 200, 4.5) (983.2, 200, 4.2) 2 (200, 200, 4.2) (226.5, 211.3, 4.2) (253, 200, 4.2) 3 (71.2, 100, 4.2) (110.4, 100, 4.5) (132.8, 100, 4.2) 4 (88.3, 123.7, 4.2) (132.8, 135.6, 4.2) (200.1, 153.6, 4.2)

6 结论

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#### 文章信息

WANG Zekun, WU Minggong, WEN Xiangxi, JIANG Xurui, GAO Yangyang

Flight collision resolution and recovery strategy based on velocity obstacle method

Journal of Beijing University of Aeronautics and Astronsutics, 2019, 45(7): 1294-1302
http://dx.doi.org/10.13700/j.bh.1001-5965.2018.0650