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1. 空军工程大学 航空航天工程学院, 西安 710038;
2. 空军工程大学 科研部, 西安 710051

UAV 3D real-time path planning based on dynamic step
ZHANG Shuai1 , LI Xueren1 , ZHANG Jianye2 , ZHANG Peng1 , LI Bo1 , ZHAO Xiaolin1
1. School of Aeronautics and Astronautics Engineering, Air Force Engineering University, Xi'an 710038, China ;
2. Department of Science Research, Air Force Engineering University, Xi'an 710051, China
Received: 2015-12-17; Accepted: 2016-03-18; Published online: 2016-04-13 15:37
Foundation item: Aviation Science Foundation of China (20145596024); Natural Science Foundation of Shanxi Province of China (2014JQ8331)
Corresponding author. LI Xueren, Tel.:029-84787712, E-mail:lixueren@126.com
Abstract: Because planning unmanned aerial vehicle (UAV) path directly in 3D space is difficult, we divide 3D path planning into 2D plane path planning and height planning, and then combine them to get the 3D path so that planning space is simplified and complexity is reduced. To search the path subtly in the region near threat, we propose a dynamic searching step strategy according to the distance between UAV and threat. Setting sub-goal helps UAV to quickly modify the path and realize path re-planning when UAV meets the unexpected threat. Simulation results demonstrate that the proposed method is effective. UAV can bypass the unexpected threat and plan 3D path successfully. The threat probability of path decreases through taking dynamic step.
Key words: unmanned aerial vehicle (UAV)     path planning     sub-goal     dynamic step     2D plane path planning     height planning

1 航迹规划建模 1.1 无人机约束条件

1)最大航程

 (1)

2)最小转弯半径

 (2)

3)最低飞行高度

 (3)

4)最大俯仰角

 (4)
1.2 威胁模型

1.2.1 山峰威胁

 (5)

 (6)

1.2.2 雷达威胁

 (7)

1.3 突发威胁规避策略

1.3.1 设置子目标点

 图 1 设置子目标点 Fig. 1 Sub-goal setting

1.3.2 子目标点位置计算

 (8)

 (9)

A的位置坐标(xA, yA)为

 (10)

θ-θB满足如下关系：

 (11)

 (12)

1.3.3 规避方向和子目标点的选择

1)如果θA>θB并且threat (A)>threat (B)，说明顺时针方向规避威胁比逆时针方向规避时航向调整小，航程更短，并且B点威胁概率小于A点，此时选择B点作为需要设置的子目标点。

2)如果θA < θB并且threat (A) < threat (B)，说明逆时针方向规避威胁比顺时针方向规避时航向调整小，航程更短，并且A点威胁概率小于B点，此时选择A点作为需要设置的子目标点。

3)如果θA>θB并且threat (A) < threat (B)，但是threat (B)-threat (A) < C，其中C为常值，表示无人机可接受的威胁阈值，则优先选择航向调整小，航程短的规避方向，此时选择B点作为需要设置的子目标点；如果threat (B)-threat (A)>C，则优先选择安全系数更高的规避方向，选择A点作为需要设置的子目标点。

4)如果θA < θB并且threat (A)>threat (B)，但是threat (A)-threat (B) < C，则优先选择航向调整角度小，航程短的规避方向，此时选择A点作为需要设置的子目标点；如果threat (A)-threat (B)>C，则优先选择安全系数更高的规避方向，选择B点作为需要设置的子目标点。

1.4 动态步长调整策略

 (13)

 图 2 小于安全距离时步长动态调整 Fig. 2 Step dynamic adjustment when distanceis less than safe distance

1.5 节点扩展

 图 3 圆形节点扩展示意图 Fig. 3 Schematic diagram of circular expanding nodes

 (14)

1.6 目标函数

 (15)

 (16)

 (17)

ω1ω2为比例系数，用于调节威胁代价和航程代价量纲不同的影响，通过调节权系数，可以实现规划安全优先或者是航程优先的航迹。

1.7 高度规划

 图 4 Hsafe的确定 Fig. 4 Determination of Hsafe

2 算法流程

2.1 静态二维参考航迹规划

2.2 二维实时航迹规划

2.3 三维航迹规划

3 仿真实验 3.1 规划空间

 威胁类型 中心坐标/km 中心点高度/km λ 山峰1 (10，6) 25 0.10 山峰2 (16，32) 28 0.08 山峰3 (36，22) 18 0.05 山峰4 (32，42) 30 0.10 雷达1 (47，40) 32 0.10 雷达2 (47，46) 32 0.08 雷达3 (50，10) 40 0.08

 图 5 航迹规划区域 Fig. 5 Path planning area
3.2 动态步长结果对比

 图 6 固定步长与动态步长航迹仿真 Fig. 6 Path simulation with fixed step and dynamic step

 S/km 步长策略 节点数 时间/s 航程/km 平均威胁概率 0.6 动态步长 217 2.177 99.459 0.034 固定步长 166 2.156 99.351 0.028 1.0 动态步长 129 2.076 99.472 0.038 固定步长 100 2.066 99.400 0.040 3.0 动态步长 42 1.988 98.943 0.099 固定步长 33 1.979 99.449 0.195 5.0 动态步长 25 1.971 98.263 0.269 固定步长 20 1.965 99.078 0.580

3.3 二维航迹规划

 图 7 等高线投影面静态规划航迹 Fig. 7 Static path planning on contour projective plane
 图 8 等高线投影面实时规划航迹 Fig. 8 Real-time path planning on contour projective plane

3.4 高度规划

 图 9 静态规划航迹高度剖面图 Fig. 9 Height profile map of static path planning
 图 10 实时规划航迹高度剖面图 Fig. 10 Height profile map of real-time path planning
3.5 三维航迹规划

 图 11 静态规划三维航迹 Fig. 11 Static 3D path planning
 图 12 实时规划三维航迹 Fig. 12 Real-time 3D path planning

4 结论

1)当基准步长为大步长时，采用动态步长进行航迹规划，航程更短，威胁程度降低。

2)可以实现对地形的跟踪，有利于低空突防，求解的复杂度降低，得到较为满意的航迹。

3)可以成功规避突发威胁，实现实时规划。

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#### 文章信息

ZHANG Shuai, LI Xueren, ZHANG Jianye, ZHANG Peng, LI Bo, ZHAO Xiaolin

UAV 3D real-time path planning based on dynamic step

Journal of Beijing University of Aeronautics and Astronsutics, 2016, 42(12): 2745-2754
http://dx.doi.org/10.13700/j.bh.1001-5965.2015.0821