﻿ 基于领航跟随的2型AUV编队航行仿真对比
 舰船科学技术  2024, Vol. 46 Issue (11): 98-102    DOI: 10.3404/j.issn.1672-7649.2024.11.018 PDF

Simulation of two types of AUVs formation based on leader follower formation control
ZHENG Peng, ZHANG Hua, ZHANG Chao, XU Lingling, GU Yuanyuan
National Key Laboratory of Hydrodynamics, China Ship Scientific Research Center, Wuxi 214082, China
Abstract: The leader-follower formation control method is concise and practical, but its control effectiveness on different AUV platforms lacks comparison. This article uses a 500 kg level "HX500" AUV and a 5000 kg level "NPS" AUV to conduct AUV formation navigation simulation, and compares and analyzes the formation distance deviation and formation angle deviation of two types of AUVs based on leader-follower formation control method. The results indicate that the navigation ability of the "HX500" AUV and the "NPS" AUV on path following is similar, and the normal distance from the path after stable navigation is less than 1 m. The formation control method performs well in formation control of two types of AUVs. After stable navigation, the distance deviation between the follower and the leader is maintained at 7～8 m, and the angle deviation is maintained at 3°～5°. However, due to the constraints of the relative position of the formation at the switching point, there are certain requirements for the acceleration and deceleration performance of the inner and outer AUVs of the formation. At the corner of the path, NPS AUVs with larger weight and size have a distance deviation of about 50% greater than the "HX500" AUVs.
Key words: AUV formation control     formation distance deviation     formation angle deviation
0 引　言

1 坐标系定义及模型建立 1.1 AUV模型建立

AUV的运动学方程可表示为：

 $\dot{\mathit{\eta }}=\mathit{J}\left(\mathit{\eta }\right)\mathit{v} 。$ (1)

 \begin{aligned} {\boldsymbol{R}}_{b}^{n}\left(\mathrm{\varTheta }\right)=&{\mathit{R}}_{z,\psi }{\mathit{R}}_{y,\theta }{\mathit{R}}_{x,\varphi } = \\ &\left[\begin{array}{ccc}\cos\psi \cos\theta & -\sin\psi \cos\varphi +\cos\psi \sin\theta \sin\varphi \\ \sin\psi \cos\theta & \cos\psi \cos\varphi +\sin\psi \sin\theta \sin\varphi \\ -\sin\theta & \cos\theta \sin\varphi \end{array}\right. \\& \left.\begin{array}{ccc} \sin\psi \sin\varphi +\cos\psi \sin\theta \cos\varphi \\ -\cos\psi \sin\varphi +\sin\psi \sin\theta \cos\varphi \\ \cos\theta \cos\varphi \end{array}\right],\end{aligned}
 \begin{aligned} &{\mathit{T}}_{\mathrm{\varTheta }}\left(\mathrm{\varTheta }\right)=\left[\begin{array}{ccc}1& \sin\varphi \tan\theta & \cos\varphi \tan\theta \\ 0& \cos\varphi & -\sin\varphi \\ 0& \sin\varphi /\cos\theta & \cos\varphi /\cos\theta \end{array}\right], \\ &\theta \ne \pm 9{0}^{{\mathrm{o}}}，{\mathit{T}}_{\mathrm{\varTheta }}^{-1}\left(\mathrm{\varTheta }\right) = \left[ \begin{array}{ccc}1& 0& -\sin\theta \\ 0& \cos\varphi & \cos\theta \sin\varphi \\ 0& -\sin\varphi & \cos\theta \cos\varphi \end{array} \right],\theta \ne \pm 9{0}^{{\mathrm{o}}} 。\end{aligned}

 $\boldsymbol{M}\dot{v}+\boldsymbol{C}\left(v\right)v+\boldsymbol{D}\left(v\right)v+\mathit{g}\left(\eta \right)=\mathit{\tau } 。$ (2)

“海翔500”AUV为中国船舶科学研究中心研发的重490 kg、长3.7 m的中小型AUV。“NPS”AUV为美国海军研究生院研发的重 5450 kg、长5.3 m的中大型AUV。2型AUV均采用尾部双推进器、扁平体结构，在操纵特性上类似，以该2型平台开展领航跟随编队控制方法在不同重量AUV下编队队形控制效果比较研究较为合理。“海翔500”AUV和“NPS”AUV的数学模型详见文献[1011]，其外形如图1所示。

 图 1 “海翔500”AUV与“NPS”AUV样机对比 Fig. 1 Comparison of "HX500" AUV and "NPS" AUV prototypes
1.2 领航跟随编队控制算法

 $\mathit{P}=\left[{P}_{1},{P}_{2},\cdots {P}_{i},{P}_{i+1},{P}_{i+2},\cdots {P}_{n}\right],i=\mathrm{1,2},...,n-2。$

 ${p}_{f}^{d}={p}_{a}+{R}^{bo}\left({\phi }_{a}\right)\left[\begin{array}{c}\rho {\cos}\left(\theta \right)\\ \rho {\sin}\left(\theta \right)\end{array}\right]。$

 $\left|{\widehat{p}}_{f}^{d}-{p}_{f}^{d}\right|={\rho }_{k}\sqrt{2-2\rm{cos}{\alpha }_{i+1}}。$

2 数值仿真 2.1 路径跟随仿真比较

 \begin{aligned} &{P}_{1}=\left(\mathrm{0,0}\right),{P}_{2}=\left(\mathrm{1450,0}\right),{P}_{3}=\left(\mathrm{1450,1300}\right),\quad\quad\ \ \\ &{P}_{4}=\left(\mathrm{500,1300}\right),{P}_{5}=\left(\mathrm{500,500}\right), \end{aligned}
 \begin{aligned}&{P}_{6}=\left(\mathrm{0,500}\right),{P}_{7}=\left(-\mathrm{500,1800}\right),{P}_{8}=\left(\mathrm{1000,1800}\right),\\ &{P}_{9}=\left(\mathrm{2000,1800}\right),{P}_{10}=\left(\mathrm{2500,180}\right) 。\end{aligned}

 图 2 2型AUV在路径跟随任务中的航行轨迹对比 Fig. 2 Comparison of trajectories of 2 AUVs in path following tasks

 图 3 2型AUV在路径跟随任务中的航向及法向偏差距离对比 Fig. 3 Comparison of heading and normal deviation distance of 2 AUVs in path following tasks

2.2 基于领航跟随控制的“海翔500”AUV编队仿真

 图 4 基于领航者跟随者控制的“HX500”AUV编队轨迹 Fig. 4 The formation trajectory of "HX500" AUVs based on leader follower control

 图 5 “HX500”AUV编队中跟随者与领航者距离偏差、角度偏差时间历程 Fig. 5 Time history of distance deviation and angle deviation between follower and leader in the"HX500"AUVs formation

2.3 基于领航跟随控制的NPS AUV编队仿真

 图 6 基于领航者跟随者控制的“NPS”AUV编队轨迹 Fig. 6 The formation trajectory of “NPS” AUVs based on leader follower control

 图 7 NPS AUV编队中跟随者与领航者距离偏差、角度偏差时间历程 Fig. 7 Time history of distance deviation and angle deviation between follower and leader in the NPS AUVs formation

2.4 不同AUV编队的队形保持效果对比

 图 8 “HX500”与NPS AUV编队中1号跟随者与领航者的距离偏差、角度偏差时间历程对比 Fig. 8 Comparison of the time history of distance deviation and angle deviation between follower-1 and leader in the "HX500" AUV formation and NPS AUV formation

 图 9 “HX500”与NPS AUV编队中2号跟随者与领航者的距离偏差、角度偏差时间历程对比 Fig. 9 Comparison of the time history of distance deviation and angle deviation between follower-2 and leader in the "HX500" AUV formation and NPS AUV formation
3 结　语

1）500 kg的“海翔500”AUV与 5000 kg的“NPS”AUV在路径跟随上的航行能力接近，且基于领航跟随的编队控制方法对500 kg与5000 kg级别的AUV编队均具有较好的控制效果，稳定航行段跟随者与领航者的距离偏差保持在10 m以内，角度偏差保持在5°以内。

2）基于领航跟随的编队控制方法在切换点处，由于队形相对位置的约束，对平台的加减速性能有一定要求，重量尺寸更大的NPS AUV在直角拐弯处跟随者与领航者的距离偏差较“海翔500”AUV增大50%左右。

 [1] EDWARDS D B, BEAN T, ODELL D, et al. A leader-follower lgorithm for multiple AUV formations[C]// Autonomous Underwater Vehicles, Sebasco, Maine, The United State, 2004. IEEE, 2004: 501−509. [2] CALADO P, SOUSA J. Leader-follower control of underwater vehicles over acoustic communications[C]//OCEANS, Santander, Spain, 2011. IEEE, 2011: 501−506P. [3] 姜成林, 徐会希. 面向复杂地形海洋勘探的Multi-AUV编队协同控制策略[J]. 舰船科学技术, 2021, 43(3): 93-100. JIANG Chenglin, XU Huixi. Multi-autonomous underwater vehicles formation control and strategy for complex terrain oceanographic exploration[J]. Ship Science and Technology, 2021, 43(3): 93-100. DOI:10.3404/j.issn.1672-7649.2021.02.020 [4] 袁健, 唐功友. 采用一致性算法与虚拟结构的多自主水下航行器编队控制[J]. 智能系统学报, 2011, 6(3): 248-253. YUAN Jian, TANG Gongyou. Formation control of autonomous underwater vehicles with consensus algorithms and virtual structure[J]. CAAI Transactions on Intelligent Systems, 2011, 6(3): 248-253. DOI:10.3969/j.issn.1673-4785.2011.03.009 [5] 潘无为, 姜大鹏, 庞永杰, 等. 人工势场和虚拟结构相结合的多水下机器人编队控制[J]. 兵工学报. 2017(2): 326−334. PAN Wuwei, JIANG Dapeng, PANG Yongjie. et al. A multi-AUV formation algorithm combining artificial potential field and virtual structure[J]. ACTA Armamentarii, 2017(2): 326−334. [6] 王银涛, 严卫生. 多自主水下航行器系统一致性编队跟踪控制[J]. 控制理论与应用. 2013, 30(3): 379−384. WANG Yintao,YAN Weisheng. Consensus formation tracking control of multiple autonomous underwater vehicle systems[J]. Control Theory & Applications, 2013, 30(3): 379−384. [7] 何斌. 多AUV编队控制与协同搜索技术研究[D]. 哈尔滨: 哈尔滨工程大学, 2017. [8] GHABCHELLO R. Coordinated path following of multiple autonomous vehicles[D]. Lisbon: Ph. D Thesis of Technical University of Lisbon, 2007: 23−64. [9] 边信黔, 牟春晖, 严浙平. 多UUV沿多条给定路径运动的协调编队控制[J]. 哈尔滨工业大学学报. 2013, 45(1): 106−111. BIAN Xinqian, MU ChunLui, YAN Zheping. Coordinated control for multi-UUV formation motion on a set of given paths[J]. Journal of Harbin Institute of Technology, 2013, 45(1): 106−111. [10] ZHANG C, ZHANG H, ZHANG Y, et al. Parameter identification of hybrid-driven underwater glider based on differential evolution algorithm[C]// International Conference on Artificial Intelligence and Electromechanical Automation. IEEE, 2021. [11] HEALEY A J, LIENARD D. Multivariable sliding mode control for autonomous diving and steering of unmanned underwater vehicles[J]. IEEE Journal of Oceanic Engineering, 1993, 18(3): 327-339. DOI:10.1109/JOE.1993.236372