﻿ 角度测量下双机协同standoff目标跟踪
 文章快速检索 高级检索

1. 北京航空航天大学自动化科学与电气工程学院, 北京 100191;
2. 中航工业成都飞机设计研究所, 成都 610091

Coordinated standoff target tracking using two UAVs with only bearing measurement
ZHU Qian1, ZHOU Rui1, DONG Zhuoning1, LI Hao2
1. School of Automation Science and Electrical Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China;
2. AVIC Chengdu Aircraft Design & Research Institute, Chengdu 610091, China
Abstract: A novel method for a random moving target coordinated standoff tracking was proposed to maximize the target position estimation precision by two unmanned aerial vehicles (UAVs) equipped with only bearing sensor. The analytical relationship model between the UAV observation geometry configuration and the root mean square error (RMSE) of target position estimation, which is chosen as performance index, was established, and thus the optimal UAV observation geometry configuration was obtained. Extended information filter was used to implement target states fusion and estimation. The optimal cooperative observation geometry configuration was implemented using online distributed nonlinear model predictive control (NMPC), considering the constraints of UAV platform dynamic performances, collision avoiding, and security distance. The simulation results demonstrated the pair of UAV effectively maintained the optimal observation geometry configuration and coordinated standoff target tracking performance in real-time.
Key words: unmanned aerial vehicle (UAV)     standoff tracking     coordinated control     nonlinear model predictive control     root mean square error

1 目标跟踪问题描述 1.1 无人机动力学模型

1.2 目标运动模型

1.3 传感器测量模型

1.4 扩展信息滤波

2 目标位置估计精度分析 2.1 均方根误差模型

 图 1 角度测量下的协同目标观测 Fig. 1 Only bearing measurement cooperative target observation

2.2 standoff跟踪问题

UAV协同跟踪过程中,ri总会有一定的距离约束Rmin,称为standoff距离(rd),即ri≥Rmin=rd.分析可知:当$\sigma _{\theta i}^2$一定时,ri=Rmin=rd,且β=θ2-θ1=90°时RMSExy最小,对应目标位置误差δp越小,目标定位越准确.依据式(18)可知standoff跟踪最优观测构型如下:

3 非线性模型预测控制

(35)

WhileΔJ>ε do

If ΔJ<0

Else减少Δk来确保性能指标改善.

End If

End While

4 仿真结果与分析

 图 2 两架UAV与随机运动目标的绝对航迹 Fig. 2 Absolute trajectories of two UAVs and random moving target

 图 3 UAV与随机运动目标相对距离和相对角间距 Fig. 3 Relative distances and angle spacing between UAV and random moving target

 图 4 UAV与目标的瞬时相对轨迹和几何关系 Fig. 4 Relative trajectories between UAV and target and their instantaneous geometric relationships

 图 5 运动目标位置估计 Fig. 5 Position estimation of moving target

 图 6 目标位置估计的均方根误差 Fig. 6 Root mean square error of target position estimation

 参数 数值 TS/s 0.5 N 4 仿真时长/s 2 500 rd/m 500 α/(m·s-2) 0.3 vmax/(m·s-1) 10 ωmax/(rad·s-1) 0.15 τv,τω/s 0.33 v0/(m·s-1) 40 Δk 0.2 rc/m 40 误差限ε 0.8 优化参数μv,μw,μc,μr 1.0×10-3

UAV与目标之间绝对和相对运动轨迹分别如图 2图 4所示,可以看出:两架UAV实现了对随机运动目标的协同standoff跟踪,两架UAV与目标相对距离都收敛于standoff距离(rd=500 m).两架UAV实际角间距都收敛到期望角间距90°.双机为实现稳定协同standoff跟踪需动态调整与目标之间的距离和相对角间距.由于动态调整,在过渡阶段可能会出现较大波动,但很快会收敛到最优观测构型(即r1=r2=rd,β=θ2-θ1=90°),从而形成稳定双机协同standoff跟踪.稳定协同standoff跟踪过程中两架UAV与目标相对距离和角间距都在期望值附近小幅波动,分析其原因主要是由于目标随机运动的不确定性所造成.

 方法 平均跟踪距离误差/m 平均跟踪角间距误差/(°) 运行时间/s 本文方法 16.107 3.803 39.87 fmincon优化函数 12.258 2.017 1 371.2

5 结 论

1) UAV仅有角度测量时,最大化目标位置估计精度对应的UAV最优观测空间构型为:保持设定的standoff距离同时保持90°的观测视线角间距.

2) 分布式非线性模型预测控制算法能够实现UAV之间的综合最优控制,在满足各种约束和控制性能的前提下有效提高对随机运动目标的协同standoff跟踪性能.

 [1] Yang K, Kang Y, Sukkarieh S.Adaptive nonlinear model predictive path-following control for a fixed-wing unmanned aerial vehicle[J].International Journal of Control, Automation and Systems, 2013, 11(1):65-74. Click to display the text [2] Lawrence D A.Lyapunov vector fields for UAV flock coordination[C]//2nd AIAA Unmanned Unlimited Conference, Workshop, and Exhibit.Reston:AIAA, 2003. Click to display the text [3] Frew E W, Lawrence D A, Morris S.Coordinated standoff tracking of moving targets using Lyapunov guidance vector fields[J].Journal of Guidance, Control, and Dynamics, 2008, 31(2):290-306. Click to display the text [4] Summers T H, Akella M R, Mears M J.Coordinated standoff tracking of moving targets:Control laws and information architectures[J].Journal of Guidance, Control, and Dynamics, 2009, 32(1):56-69. Click to display the text [5] Chen H, Chang K, Agate C S.UAV path planning with tangent-plus-Lyapunov vector field guidance and obstacle avoidance[J].IEEE Transactions on Aerospace and Electronic Systems, 2013, 49(2):840-856. Click to display the text [6] Oh H, Kim S, Shin H S, et al.Rendezvous and standoff target tracking guidance using differential geometry[J].Journal of Intelligent & Robotic Systems, 2013, 69(1-4):389-405. Click to display the text [7] Ma L, Hovakimyan N.Cooperative target tracking in balanced circular formation:Multiple UAVs tracking a ground vehicle[C]//American Control Conference (ACC).Piscataway, NJ:IEEE Press, 2013:5386-5391. Click to display the text [8] Oh H, Turchi D, Kim S, et al.Coordinated standoff tracking using path shaping for multiple UAV[J].IEEE Transactions on Aerospace and Electronic Systems, 2014, 50(1):348-363. Click to display the text [9] 王树磊,魏瑞轩,郭庆,等.面向协同standoff跟踪问题的无人机制导律[J].航空学报, 2014, 35(6):1684-1693. Wang S L, Wei R X, Guo Q, et al.UAV guidance law for coordinated standoff target tracking[J].Acta Aeronautica et Astronautica Sinica, 2014, 35(6):1684-1693(in Chinese). Cited By in Cnki (1) [10] Ponda S S, Kolacinski R M, Frazzoli E.Trajectory optimization for target localization using small unmanned aerial vehicles[C]//AIAA Guidance, Navigation, and Control Conference.Reston:AIAA, 2009:10-13. Click to display the text [11] Lee W, Bang H, Leeghim H.A cooperative guidance law for target estimation by multiple unmanned aerial vehicles[J].Proceedings of the Institution of Mechanical Engineers, Part G:Journal of Aerospace Engineering, 2011, 225(12):1322-1335. Click to display the text [12] Kim S, Oh H, Tsourdos A.Nonlinear model predictive coordinated standoff tracking of a moving ground vehicle[J].Journal of Guidance, Control, and Dynamics, 2013, 36(2):557-566. Click to display the text [13] Zhu S, Wang D.Adversarial ground target tracking using UAV with input constraints[J].Journal of Intelligent & Robotic Systems, 2012, 65(1-4):521-532. Click to display the text [14] Mehrotra K, Mahapatra P R.A jerk model for tracking highly maneuvering targets[J].IEEE Transactions on Aerospace and Electronic Systems, 1997, 33(4):1094-1105. Click to display the text [15] 葛泉波,李文斌,孙若愚,等.基于EKF的集中式融合估计研究[J].自动化学报, 2013, 39(6):816-825. Ge Q B, Li W B, Sun R Y, et al.Centralized fusion algorithms based on EKF for multisensor non-linear systems[J].Acta Automatica Sinica, 2013, 39(6):816-825(in Chinese). Cited By in Cnki (15) [16] Gasparri A, Pascucci F.An interlaced extended information filter for self-localization in sensor networks[J].IEEE Transactions on Mobile Computing, 2010, 9(10):1491-1504. Click to display the text [17] Purvis K B, Astrom K J, Khammash M.Estimation and optimal configurations for localization using cooperative UAV[J].IEEE Transactions on Control Systems Technology, 2008, 16(5):947-958. Click to display the text [18] Sutton G J, Bitmead R R.Performance and computational implementation of nonlinear model predictive control on a submarine[M]//Nonlinear Model Predictive Control.Berlin:Springer, 2000:461-472. Click to display the text [19] Shin J, Kim H J.Nonlinear model predictive formation flight[J].IEEE Transactions on Systems, Man and Cybernetics, Part A:Systems and Humans, 2009, 39(5):1116-1125. Click to display the text [20] Shin H S, Thak M J, Kim H J.Nonlinear model predictive control for multiple UAV formation using passive sensing[J].International Journal of Aeronautical and Space Science, 2011, 12(1):16-23. Click to display the text [21] Raol J R.Multi-sensor data fusion with MATLAB?[M].London:CRC Press, 2009:157-159.

#### 文章信息

ZHU Qian, ZHOU Rui, DONG Zhuoning, LI Hao

Coordinated standoff target tracking using two UAVs with only bearing measurement

Journal of Beijing University of Aeronautics and Astronsutics, 2015, 41(11): 2116-2123.
http://dx.doi.org/10.13700/j.bh.1001-5965.2014.0716