多扩展目标跟踪优化中基于威胁规避的无人机路径规划策略

陈辉; 魏凤旗; 韩崇昭

doi:10.12000/JR22116

多扩展目标跟踪优化中基于威胁规避的无人机路径规划策略

DOI: 10.12000/JR22116

1.
兰州理工大学电气工程与信息工程学院兰州 730050
2.
西安交通大学自动化科学与工程学院西安 710049

基金项目: 国家自然科学基金项目(62163023, 62173266, 62103318, 61873116)，甘肃省教育厅产业支撑计划项目(2021CYZC-02)

详细信息

作者简介:
陈　辉，博士，教授，博士生导师，主要研究方向为雷达目标跟踪、数据融合与电子对抗等

魏凤旗，硕士生，研究方向为数据融合与多目标跟踪技术

韩崇昭，教授，主要研究方向为多源信息融合、随机控制与自适应控制、非线性频谱分析等

通讯作者:
陈辉 huich78@hotmail.com

责任主编：易伟 Corresponding Editor: YI Wei
中图分类号: TP274
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出版历程
- 收稿日期: 2022-06-17
- 修回日期: 2022-07-22
- 网络出版日期: 2022-08-11
- 刊出日期: 2023-06-28

UAV Path Planning Strategy Based on Threat Avoidance in Multiple Extended Target Tracking Optimization

1.
College of Electrical and Information Engineering, Lanzhou University of Technology, Lanzhou 730050, China
2.
College of Automation Science and Engineering, Xi’an Jiaotong University, Xi’an 710049, China

Funds: The National Natural Science Foundation of China (62163023, 62173266, 62103318, 61873116), The Industrial Support Project of Education Department of Gansu Province (2021CYZC-02)

More Information

Corresponding author: CHEN Hui, huich78@hotmail.com

摘要

摘要: 为了降低无人机执行侦察任务时被摧毁的概率，该文提出一种有效减少威胁的路径规划算法。首先利用高分辨率机载雷达对多扩展目标进行稳健的跟踪估计，然后根据三向决策规则对各目标按威胁进行分类，并利用模糊理想解相似性排序技术(TOPSIS)的方法计算目标威胁度，综合多任务决策联合优化(联合评估目标威胁度和目标跟踪质量)作为评价准则对无人机进行路径规划。仿真实验表明，模糊威胁度评估方法在多扩展目标跟踪环境下是有效的，所提无人机路径规划算法是合理的，在不损失目标跟踪精度的条件下有效降低了目标威胁度。
- 路径规划 /
- 目标威胁度 /
- 三向决策规则 /
- 扩展目标跟踪
Abstract: To reduce the probability of UAV (Unmanned Aerial Vehicle) being destroyed during a reconnaissance mission, this study proposes an effective path planning algorithm to reduce the target threat. First, high-resolution airborne radar is used for robust tracking and estimation of multiple extended targets. Subsequently, the targets are classified based on the threat degree calculated via fuzzy TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution). Next, path planning of a UAV is performed considering joint optimization of multiple task decision-making (the joint evaluation of the target threat degree and target tracking performance) as an evaluation criterion. The simulation results indicate that the fuzzy threat assessment method is effective in multiple extended target tracking, and the proposed UAV path planning algorithm is reasonable. Thus the target threat is efficiently reduced without losing the tracking accuracy.
- Path planning /
- Target threat degree /
- Three-way decision rule /
- Extended target tracking

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图 1 目标威胁评估过程

Figure 1. Target threat assessment process

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图 2 路径规划的基本原理图

Figure 2. Basic schematic diagram of path planning

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图 3 目标状态图示

Figure 3. Target status diagram

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图 4 目标威胁度评估

Figure 4. Target threat assessment

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图 5 目标实际轨迹与UAV原始轨迹

Figure 5. Actual target trajectory and UAV original trajectory

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图 6 穿越敌占区的UAV轨迹

Figure 6. UAV track crossing enemy occupied area

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图 7 完全自保的UAV轨迹

Figure 7. Fully self insured UAV trajectory

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图 8 MC实验中穿越敌占区的UAV轨迹分布

Figure 8. Trajectory distribution of UAV crossing enemy occupied area in MC experiment

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图 9 MC实验中完全自保的UAV轨迹分布

Figure 9. Trajectory distribution of fully self protected UAV in MC experiment

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图 10 目标威胁度评估统计均值

Figure 10. Statistical mean value of target threat assessment

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图 11 多扩展目标跟踪效果图

Figure 11. Multi-extended target tracking rendering

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图 12 目标质心位置GOSPA距离统计

Figure 12. GOSPA distance statistics of target centroid position

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图 13 目标形状(椭圆长短轴)估计GOSPA距离统计

Figure 13. Target shape (major and minor axes of ellipse) estimation GOSPA distance statistics

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图 14 多目标势估计

Figure 14. Multi-objective cardinality estimation

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表 1 分类风险函数

Table 1. Classification risk function

分类行为	$ A({\text{P}}) $	$ \neg A({\text{N}}) $
$ {a_{\text{P}}} $	$ {\lambda _{{\text{PP}}}} $	$ {\lambda _{{\text{PN}}}} $
$ {a_{\text{B}}} $	$ {\lambda _{{\text{BP}}}} $	$ {\lambda _{{\text{BN}}}} $
$ {a_{\text{N}}} $	$ {\lambda _{{\text{NP}}}} $	$ {\lambda _{{\text{NN}}}} $

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表 2 GIW-MBer预测过程

Table 2. GIW-MBer prediction process

输入：${\boldsymbol{\zeta}} _{k - 1}^{\left( {i,j} \right)}$。
预测第j个GIW分量的参数：
${\boldsymbol{m}}_{k\|k - 1}^{\left( {i,j} \right)} = {\boldsymbol{F}}_{k\|k - 1}^i{\boldsymbol{m}}_{k - 1}^{\left( {i,j} \right)}$
${\boldsymbol{P}}_{k\|k - 1}^{\left( {i,j} \right)} = {\boldsymbol{F}}_{k\|k - 1}^i{\boldsymbol{P}}_{k - 1}^{\left( {i,j} \right)}{\left( {{\boldsymbol{F}}_{k\|k - 1}^i} \right)^{\rm T} } + {{\boldsymbol{Q}}_k}$
$v_{k\|k - 1}^{\left( {i,j} \right)} = {{\rm{e}}^{ - \frac{ { {T_s} } }{\tau } } }v_{k - 1}^{\left( {i,j} \right)}$，其中$ \tau $为时间衰减常数
${\boldsymbol{V} }_{k\|k - 1}^{\left( {i,j} \right)} = \dfrac{ {v_{k\|k - 1}^{\left( {i,j} \right)} - d - 1} }{ {v_{k - 1}^{\left( {i,j} \right)} - d - 1} }{\boldsymbol{V}}_{k - 1}^{\left( {i,j} \right)}$
${\boldsymbol{X}}_{k\|k - 1}^{\left( {i,j} \right)} = \dfrac{ {{\boldsymbol{V}}_{k\|k - 1}^{\left( {i,j} \right)} } }{ {v_{k\|k - 1}^{\left( {i,j} \right)} - 2d - 2} }$
输出：${\boldsymbol{\zeta}} _{k\|k - 1}^{\left( {i,j} \right)}$。

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表 3 GIW-MBer更新过程

Table 3. GIW-MBer update process

输入：${\boldsymbol{\zeta}} _{k\|k - 1}^{\left( {i,j} \right)}$，量测集划分W。
更新第j个GIW分量的参数：　　　　$\bar {\boldsymbol{z} }_k^{\boldsymbol{W} } = \dfrac{1}{ {\left\| {\boldsymbol{W} } \right\|} }\displaystyle\sum\limits_{{\boldsymbol{z}}_k^{\left( i \right)} \in {\boldsymbol{W}}} { {\boldsymbol{z} }_k^{\left( i \right)} }$
${\boldsymbol{X} }_{k\|k - 1}^{\left( {i,j} \right)} = \dfrac{ { {\boldsymbol{V} }_{k\|k - 1}^{\left( {i,j} \right)} } }{ {v_{k\|k - 1}^{\left( {i,j} \right)} - 2d - 2} }$
${\boldsymbol{S} }_{k\|k - 1}^{\left( {i,j,W} \right)} = { {\boldsymbol{H} }_k}{\boldsymbol{P} }_{k\|k - 1}^{\left( {i,j} \right)}{\boldsymbol{H} }_k^{\text{T} } + \dfrac{ { {\boldsymbol{X} }_{k\|k - 1}^{\left( {i,j} \right)} } }{ {\left\| {\boldsymbol{W} } \right\|} }$
${\boldsymbol{K}}_{k\|k - 1}^{\left( {i,j,{\boldsymbol{W}}} \right)} = {\boldsymbol{P}}_{k\|k - 1}^{\left( {i,j} \right)}{\boldsymbol{H}}_k^{\text{T} }{\left( {{\boldsymbol{S}}_{k\|k - 1}^{\left( {i,j,{\boldsymbol{W}}} \right)} } \right)^{ - 1} }$
${\boldsymbol{\varepsilon} } _{k\|k - 1}^{\left( {i,j,{\boldsymbol{W} } } \right)} = \bar {\boldsymbol{z} }_k^{\boldsymbol{W} } - { {\boldsymbol{H} }_k}{\boldsymbol{m} }_{k\|k - 1}^{\left( {i,j} \right)}$
${\boldsymbol{m}}_k^{\left( {i,j} \right)} = {\boldsymbol{m}}_{k\|k - 1}^{\left( {i,j} \right)} + {\boldsymbol{K}}_{k\|k - 1}^{\left( {i,j,{\boldsymbol{W}}} \right)}{\boldsymbol{\varepsilon}} _{k\|k - 1}^{\left( {i,j,{\boldsymbol{W}}} \right)}$
${\boldsymbol{P} }_k^{\left( {i,j} \right)} = {\boldsymbol{P} }_{k\|k - 1}^{\left( {i,j} \right)} - {\boldsymbol{K} }_{k\|k - 1}^{\left( {i,j,{\boldsymbol{W} } } \right)}{\boldsymbol{S}}_{k\|k - 1}^{\left( {i,j,{\boldsymbol{W} } } \right)}{\left( { {\boldsymbol{K} }_{k\|k - 1}^{\left( {i,j,{\boldsymbol{W} } } \right)} } \right)^{\text{T} } }$ 　　　　${\boldsymbol{Z} }_k^{\boldsymbol{W}} = \displaystyle\sum\limits_{ {\boldsymbol{z} }_k^{\left( i \right)} \in {\boldsymbol{W} } } {\left( { {\boldsymbol{z} }_k^{\left( i \right)} - \bar {\boldsymbol{z} }_k^{\boldsymbol{W}}} \right){ {\left( { {\boldsymbol{z} }_k^{\left( i \right)} - \bar {\boldsymbol{z} }_k^{\boldsymbol{W}}} \right)}^{\text{T} } } }$
$\begin{aligned} {\boldsymbol{N} }_{k\|k - 1}^{\left( {i,j,{\boldsymbol{W}}} \right)} =& {\left( { {\boldsymbol{X} }_{k\|k - 1}^{\left( {i,j} \right)} } \right)^{\frac{1}{2} } }{\left( { {\boldsymbol{S} }_{k\|k - 1}^{\left( {i,j,{\boldsymbol{W}}} \right)} } \right)^{ - \frac{1}{2} } }{\boldsymbol{\varepsilon} } _{k\|k - 1}^{\left( {i,j,{\boldsymbol{W} } } \right)} \\ & \times {\left( { {\boldsymbol{\varepsilon} } _{k\|k - 1}^{\left( {i,j,{\boldsymbol{W} } } \right)} } \right)^{\text{T} } }{\left( { {\boldsymbol{S} }_{k\|k - 1}^{\left( {i,j,{\boldsymbol{W} } } \right)} } \right)^{ - \frac{ {\text{T} } }{2} } }{\left( { {\boldsymbol{X} }_{k\|k - 1}^{\left( {i,j} \right)} } \right)^{\frac{ {\text{T} } }{2} } } \end{aligned}$
$v_k^{\left( {i,j,{\boldsymbol{W}}} \right)} = v_{k\|k - 1}^{\left( {i,j,{\boldsymbol{W}}} \right)} + \left\| {\boldsymbol{W} } \right\|$
${\boldsymbol{V} }_k^{\left( {i,j,{\boldsymbol{W} } } \right)} = {\boldsymbol{V} }_{k\|k - 1}^{\left( {i,j,{\boldsymbol{W} } } \right)} + {\boldsymbol{N} }_{k\|k - 1}^{\left( {i,j,{\boldsymbol{W}}} \right)} + {\boldsymbol{Z} }_k^{\boldsymbol{W} }$
${\boldsymbol{X} }_k^{\left( {i,j,{\boldsymbol{W} } } \right)} = \dfrac{ { {\boldsymbol{V} }_k^{\left( {i,j,{\boldsymbol{W} } } \right)} } }{ {v_k^{\left( {i,j,{\boldsymbol{W} } } \right)} - 2d - 2} }$
输出：${\boldsymbol{\zeta}} _k^{\left( {i,j} \right)}$。

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表 4 基于威胁规避的UAV路径规划算法

Table 4. UAV path planning algorithm for threat avoidance

输入：$ k - 1 $时刻多扩展目标多特征信息${{\boldsymbol{\zeta}} _{k - 1} }$与UAV坐标　　　${{\boldsymbol{x}}_{s,k - 1} }$，其中${{\boldsymbol{\zeta}} _{k - 1} } = \left\{ { { {\boldsymbol{m} }_{k - 1} },{ {\boldsymbol{P} }_{k - 1} },{v_{k - 1} },{ {\boldsymbol{V} }_{k - 1} } } \right\}$。
步骤1 多扩展目标跟踪的预测过程，得到$ {f_{k\|k - 1}}\left( { \cdot \| \cdot } \right) $。　步骤2 路径规划：
${\hat {\boldsymbol{\xi}} _{k\|k - 1} } = {\text{Sfun} }\left\{ { {f_{k\|k - 1} }\left( { \cdot \| \cdot } \right)} \right\}$，
确定所有可能的路径规划方案${{\boldsymbol{C}}_k}$。
${\text{for all } }c \in {{\boldsymbol{C}}_k}{\text{ do} }$
生成PIMS：${{\boldsymbol{Z}}_k}\left( u \right)$，
量测集划分：${\boldsymbol{\rho}} \angle {{\boldsymbol{Z}}_k}\left( u \right)$，
计算伪更新后验密度$ {f_{k,c}}\left( { \cdot \| \cdot } \right) $，
提取状态的统计平均：${\hat {\boldsymbol{\xi}} _{k,c} } \leftarrow {\text{Sfun} }\left\{ { {f_{k,c} }\left( { \cdot \| \cdot } \right)} \right\}$，
计算$\mathcal{D}\left( { {{\boldsymbol{\xi}} _{k,c} },{ {\bar {\boldsymbol{\xi}} }_{k,c} } } \right)$和$ \mathcal{V}\left( c \right) $。
$ {\text{end for}} $ 　　　　求解控制方案：${\hat c_k} = \mathop {\arg \min }\limits_{c \in {{\boldsymbol{C}}_k} } \{ {w_\mathcal{V} }\mathcal{V}\left( c \right)$ 　　　　$+ {w_\mathcal{D} }\mathcal{D}({{\boldsymbol{\xi}} _{k,c} },{\bar {\boldsymbol{\xi}} _{k,c} })\}$。
步骤3 多扩展目标跟踪的更新过程，得到$ {f_{k\|k}}\left( { \cdot \| \cdot } \right) $。
步骤4 提取多扩展目标状态信息${{\boldsymbol{\xi}} _k}$，计算目标势${N_k} = \left\| { {{\boldsymbol{\xi}} _k} } \right\|$。
输出：k时刻UAV坐标${{\boldsymbol{x}}_{s,k} }$，目标势$ {N_k} $，多扩展目标状态集${{\boldsymbol{\xi}} _k}$。

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表 5 硬件配置

Table 5. Hardware configuration

参数	数值
CPU主频	3.1 GHz
最高睿频	5.2 GHz
内存类型	DDR4 3200 MHz
最大内存带宽	76.8 GB/s

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表 6 目标状态

Table 6. Target status

目标编号	位置(m; m)	速度(m/s; m/s)	运动方向(°)
1	[100; 100]	[–10; –10]	0
2	[200; 200]	[–10; –10]	0
3	[100; 100]	[–5; –5]	0
4	[–100; 100]	[10; –10]	0
5	[100; 100]	[5; 5]	180
6	[100; 100]	[–10; 10]	90

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表 7 各运动体的初始状态

Table 7. Initial state of each moving object

目标	出生时刻 (s)	消亡时刻 (s)	初始状态 (m; m; m/s; m/s)
目标1	1	40	[–300; 100; 30; –10]
目标2	11	40	[100; 200; –15; –30]
目标3	16	35	[50; –600; –20; 30]
目标4	21	35	[–600; –200; 10; 35]
目标5	26	30	[200; 500; –50; 20]
目标6	26	30	[–600; 600; 40; –30]
UAV	/	/	[600; –800; –30; 40]

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