Optimal AUV Trajectories for Bearings-Only Tracking
WANG Yanyan1,2, LIU Kaizhou1, FENG Xisheng1
1. State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016, China;
2. University of Chinese Academy of Sciences, Beijing 100049, China
为了进一步提高自主水下机器人（AUV）纯方位目标跟踪能力，从AUV轨迹优化方面进行了研究．采用基于距离的分段轨迹优化方法：在跟踪目标的初始阶段以定位的位置误差GDOP（geometrical dilution of precision）作为优化对象，以期在定位跟踪的各个时刻能得到最优的定位精度；针对目标运动要素（位置、速度、航向等）估计趋于收敛的情况，提出了一种基于短期预测的轨迹优化方法，AUV根据物理条件限制预测双方短期状态，计算能够反映跟踪态势特征的收益函数，根据收益函数对自身某状态进行评估，估算出自身各个预测状态的综合收益后，选出综合收益最大的那个状态作为短期目标，执行能到达该状态的行为．目标运动要素估计中使用扩展卡尔曼滤波（EKF）．最后，将该轨迹优化方法与基于GDOP的轨迹优化进行仿真对比，结果表明该方法能够实现AUV与目标较快汇合．
In order to enhance the AUV (autonomous underwater vehicle) capability in bearings-only target tracking, the AUV trajectory optimization needs to be studied. A piecewise trajectory optimization method based on distance is proposed. In the initial phase of target tracking, GDOP (geometrical dilution of precision) matrix of positioning errors is taken as the objective function in optimization, in order to achieve optimal positioning precision at each time. Then, an AUV trajectory optimization method based on short-term prediction is proposed for the cases that the estimation of target navigation parameters (position, velocity and heading) converges. AUV predicts its own and the target's possible future states according to physical limits, and calculates its every state income according to the characteristics of the tracking trend. Based on the income, one of its own states is evaluated, and the consolidated income of every prediction state is estimated. At last, a proper state with the maximum consolidated income is chosen as its shot-term target, and the action leading to the target is executed. The extended Kalman filter algorithm is used to estimate the navigation parameters of the target. Finally, the proposed method and the GDOP based trajectory optimization method are compared through simulation, and the result shows that the AUV using the proposed method can capture the target as soon as possible.
[1] 董志荣.纯方位系统本载体最优机动控制问题[J].潜艇学术研究, 1998(2):7-17.Dong Z R. Optimal observer motion control problemsin bearing-only system[J]. Academic Research Submarine, 1998(2): 7-17.[2] Hammel S E, Liu P T. Optimal observer motion for localization with bearing measurements[J] Computers & Mathematics with Applications, 1989, 18(1-3): 171-180.[3] Helferty J P, Mudgett D R, Dzielski J E. Trajectory optimization for minimum range error in bearings-only source localization[C]//OCEANS'93. Piscataway, USA: IEEE, 1993: 229-234.[4] 夏佩伦.潜艇对机动目标跟踪和攻击若干问题的探讨[J].火力与指挥控制, 2010, 35(2):6-10.Xia P L. Some issues concerning maneuvering target tracking and attacking with submarine[J]. Fire Control & Command Control, 2010, 35(2): 6-10.[5] Helferty J P, Mudgett D R. Optimal observer trajectories for bearings-only tracking by minimizing the trace of the Cramer-Rao lower bound[C]//32nd Conference on Decision and Control. Piscataway, USA: IEEE, 1993: 936-939.[6] Passerieux J M, van Cappel D. Optimal observer maneuver for bearings-only tracking[J]. IEEE Transactions on Aerospace and Electronic Systems, 1998, 34(3): 777-788. [7] 邓新蒲, 周一宇, 卢启中.测角无源定位与跟踪的观测器自适应运动分析[J].电子学报, 2001, 29(3):311-314.Deng X P, Zhou Y Y, Lu Q Z. Adaptive observer maneuver analysis for bearings-only tracking[J]. Acta Electronica Sinica, 2001, 29(3): 311-314.[8] 许志刚.纯方位系统定位与跟踪的观测器最优机动轨迹[J].连云港化工高等专科学校学报, 2002, 15(1):1-4.Xu Z G. Optimal observer maneuver for bearings-only localization and tracking[J]. Journal of Lianyungang College of Chemical Technology, 2002, 15(1): 1-4.[9] 石章松.纯方位目标跟踪中的观测器机动优化研究[J].计算机仿真, 2010, 27(1):334-337.Shi Z S. A study of observer maneuvering optimal trajectory in bearing-only target tracking[J]. Computer Simulation, 2010, 27(1): 334-337.[10] 戴中华, 邓新蒲.基于方位角变化率最大的轨迹优化几何方法[J].航天电子对抗, 2007, 23(4):47-49.Dai Z H, Deng X P. A geometrical method for optimization of trajectory based on maximizing azimuth changing rate[J]. Aerospace Electronic Warfare, 2007, 23(4): 47-49.[11] 邓新蒲, 周一宇.单观测器无源定位误差下界的仿真分析[J].电子与信息学报, 2002, 24(1):54-59.Deng X P, Zhou Y Y. Simulating analysis on estimation error lower bound for single passive observer[J]. Journal of Electronics and Information Technology, 2002, 24(1): 54-59.[12] 陈华雷, 刘开周.估计从UUV 航行参数的混合坐标系下的EKF算法[J].机器人, 2009, 31(s1):6-9.Chen H L, Liu K Z. Slave UUV motion analysis using mixed coordinates EKF[J]. Robot, 2009, 31(s1): 6-9.[13] 张福仁, 赵正业, 董志荣.潜艇纯方位接敌跟踪航路优化方法探讨[J].火力与指挥控制, 2001, 26(1):5860.Zhang F R, Zhao Z Y, Dong Z R. Study on optimal bearings-only tracking of submarine[J]. Fire Control & Command Control 2001, 26(1): 5860.[14] 赵骁飞.单站纯方位无源探测定位的若干技术[D].上海:上海交通大学, 2007.Zhao X F Research of some technologies on bearing-only system[D]. Shanghai: Shanghai Jiao Tong University, 207.[15] 冯子龙, 刘健, 刘开周.AUV自主导航航位推算算法的研究[J].机器人, 2005, 27(2):168-172.Feng Z L, Liu J, Liu K Z. Dead reckoning method for autonomous navigation of autonomous underwater vehicles[J]. Robot, 2005, 27(2): 168-172.
