﻿ 多自主式水下航行器轨迹精准跟踪控制方法
 舰船科学技术  2023, Vol. 45 Issue (11): 102-105    DOI: 10.3404/j.issn.1672-7619.2023.11.020 PDF

Research on precise trajectory tracking control method for multi autonomous underwater vehicles
GUO Li-ping
Hubei University of Technology Engineering and Technology College, Wuhan 430068, China
Abstract: To address the uncertainty issue in trajectory tracking control of multi-autonomous underwater vehicles, a precise trajectory tracking control method for multi-autonomous underwater vehicles is studied. Build a trajectory accurate tracking control model based on gray prediction, use the gray prediction model to predict the aircraft's heading angle, build a unitary polynomial regression model, fit the residual between the initial heading angle of the aircraft and the predicted heading angle, optimize the gray prediction model, and improve the prediction accuracy of the aircraft's heading angle. Bring the predicted heading angle results into the PID controller, determine the position error, velocity error, and acceleration error by calculating the heading angle control rate, and achieve accurate tracking control of the aircraft trajectory by controlling the above errors. The experimental results show that this method can accurately track trajectories under different motion characteristics of the aircraft and has good control effects.
Key words: multi autonomous     underwater vehicles     track tracking control     grey prediction     heading angle     PID controller
0 引　言

1 水下航行器轨迹跟踪控制 1.1 轨迹精准跟踪控制方法架构

 图 1 灰色预测的轨迹精准跟踪控制模型架构 Fig. 1 Architecture of trajectory precise tracking control model based on grey prediction
1.2 基于灰色预测模型的航向角预测 1.2.1 航向角预测

 $\left\{ \begin{gathered} {w^{\left( 0 \right)}}\left( {k,1} \right),{w^{\left( 0 \right)}}\left( {k,2} \right), \cdots ,{w^{\left( 0 \right)}}\left( {k,n} \right),n \geqslant 3，\\ {g^{\left( 0 \right)}}\left( {k,1} \right),{g^{\left( 0 \right)}}\left( {k,2} \right), \cdots ,{g^{\left( 0 \right)}}\left( {k,n} \right),n \geqslant 3。\\ \end{gathered} \right.$ (1)

 $\left\{ \begin{gathered} {w^{\left( 1 \right)}}\left( {k,i} \right) = \sum\limits_{j = 1}^i {{w^{\left( 0 \right)}}\left( {k,j} \right)} ,i = 1,2, \cdots ,n {\text{,}} \\ {g^{\left( 1 \right)}}\left( {k,i} \right) = \sum\limits_{j = 1}^i {{g^{\left( 0 \right)}}\left( {k,j} \right)} ,i = 1,2, \cdots ,n \text{。} \\ \end{gathered} \right.$ (2)

 ${g^{\left( 1 \right)}}\left( {k,i} \right) + {a_g}\left( k \right){s^{\left( 1 \right)}}\left( {k,i} \right) = {b_g}\left( k \right) 。$ (3)

 $\frac{{{\rm{d}}{g^{\left( 1 \right)}}\left( t \right)}}{{{\rm{d}}t}} + {a_g}{g^{\left( 1 \right)}}\left( t \right) = {b_g} \text{。}$ (4)

 $g_P^{\left( 1 \right)}\left( {k + 1} \right) = \left[ {{g^{\left( 0 \right)}}\left( {k + 1} \right) - \frac{{{b_g}}}{{{a_g}}}} \right]{e^{ - {a_g}k}} + \frac{{{b_g}}}{{{a_g}}} \text{。}$ (5)

 $g_P^{\left( 0 \right)}\left( {k + M} \right) = \left[ {{g^{\left( 0 \right)}}\left( k \right) - \frac{{{b_g}}}{{{a_g}}}} \right]{e^{ - {a_g}M}}\left( {1 - {e^{ - {a_g}}}} \right) \text{。}$ (6)
1.2.2 灰色预测模型优化

 ${\delta ^{\left( 0 \right)}} = \left\{ {{\delta ^{\left( 0 \right)}}\left( 2 \right),{\delta ^{\left( 0 \right)}}\left( 3 \right), \cdots {\delta ^{\left( 0 \right)}}\left( n \right)} \right\} 。$ (7)

 ${\delta ^{\left( 0 \right)}}\left( k \right) = \sum\limits_{p = 0}^m {{c_p}} \cdot {k^p}。$ (8)

 ${\hat \delta ^{\left( 0 \right)}}\left( k \right) = \sum\limits_{p = 0}^m {{c_p}} \cdot {k^p} \text{。}$ (9)

1.3 基于PID算法的轨迹跟踪控制方法

 $L' = {\dot V_d} + {h_v}\dot \gamma + {h_p}\gamma \text{,}$ (10)

$\gamma$ 可通过下式确定：

 $\gamma = {P_d} - P \text{。}$ (11)

$\dot \gamma$ 可通过下式确定：

 $\dot \gamma = {V_d} - V \text{。}$ (12)

 $\ddot \gamma = {\dot V_d} - \dot V \text{。}$ (13)

 $\ddot \gamma + {h_v}\dot \gamma + {h_p}\gamma = 0\text{。}$ (14)

2 仿真测试

2.1 轨迹跟踪测试

 图 2 直线轨迹跟踪结果 Fig. 2 Linear trajectory tracking results

 图 3 曲线轨迹跟踪结果 Fig. 3 Curve trajectory tracking results
2.2 控制器控制效果

 图 4 本文方法速度控制结果 Fig. 4 Speed control results of the method in this article
3 结　语

 [1] 黄哲敏, 程舟济, 夏英凯, 等. X舵自主式水下航行器抗横滚控制研究与操纵性试验[J]. 中国舰船研究, 2021, 16(S1): 19-30. HUANG Zhemin, CHENG Zhouji, XIA Yingkai, et al. Anti-roll control and maneuverability test of X-rudder autonomous underwater vehicle[J]. Chinese Journal of Ship Research, 2021, 16(S1): 19-30. DOI:10.19693/j.issn.1673-3185.02395 [2] 孙雪洁, 李纪伟. 基于MOOS-IvP的自主式水下航行器的机载软件系统容错设计[J]. 船舶工程, 2021, 43(6): 90-95. SUN Xuejie, LI Jiwei. Fault tolerant design of airborne software system for autonomous underwater vehicles based on MOOS-IvP[J]. Ship Engineering, 2021, 43(6): 90-95. DOI:10.13788/j.cnki.cbgc.2021.06.17 [3] 李韶华, 杨泽坤, 王雪玮. 基于T-S模糊变权重MPC的智能车轨迹跟踪控制[J]. 机械工程学报, 2023, 59(4): 199-212. LI Chaohua, YANG Zekun, WANG Xuewei. Intelligent vehicle trajectory tracking control based on T-S fuzzy variable weight MPC[J]. Chinese Journal of Mechanical Engineering, 2023, 59(4): 199-212. DOI:10.3901/JME.2023.04.199 [4] 滕建平, 梁霄, 陶浩, 等. 无人水下航行器全局路径规划及有限时间跟踪控制[J]. 上海海事大学学报, 2022, 43(1): 1-7. TENG Jianping, LIANG Xiao, TAO Hao, et al. Global path planning and finite-time tracking control of unmanned underwater vehicles[J]. Journal of Shanghai Maritime University, 2022, 43(1): 1-7. DOI:10.13340/j.jsmu.2022.01.001 [5] 赵婧旭, 赵晨, 周锋. 基于主从式水下自主航行器移动组网的合作目标定位方法[J]. 电子与信息学报, 2022, 44(6): 1919-1926. ZHAO Jingxu, ZHAO Chen, ZHOU Feng. cooperative target location method based on master-slave autonomous underwater vehicles mobile network[J]. Journal of Electronics & Information Technology, 2022, 44(6): 1919-1926. DOI:10.11999/JEIT211359 [6] 李文魁, 周铸, 宦爱奇, 等. 自主水下航行器自适应S面三维轨迹跟踪的仿真验证[J]. 中国舰船研究, 2022, 17(4): 38-46+91. LI Wenkui, ZHOU Zhu, HUAN Aiqi, et al. Simulation and verification of an adaptive S-plane three-dimensional trajectory tracking control for autonomous underwater vehicles[J]. Chinese Journal of Ship Research, 2022, 17(4): 38-46+91. [7] 曹晓明, 魏勇, 衡辉, 等. 海流扰动下无人水下航行器的动态面反演轨迹跟踪控制[J]. 系统工程与电子技术, 2021, 43(6): 1664-1672. CAO Xiaoming, WEI Yong, HENG Hui, et al. Dynamic surface backstepping trajectory tracking control of unmanned underwater vehicles with ocean current disturbances[J]. Systems Engineering and Electronics, 2021, 43(6): 1664-1672. DOI:10.12305/j.issn.1001-506X.2021.06.25