基于PDE的欠驱动无人船航行编队与队形切换控制

doi:10.19423/j.cnki.31-1561/u.2025.114

船舶 ›› 2026, Vol. 37 ›› Issue (02): 50-58.DOI: 10.19423/j.cnki.31-1561/u.2025.114

基于PDE的欠驱动无人船航行编队与队形切换控制

刘义^1,3, 刘晨^2,*, 吴乃龙², 沈佳诚^1,3, 施攀好^1,3

1.中国船舶及海洋工程设计研究院上海 200011;
2.东华大学信息科学与技术学院上海 201620;
3.上海市船舶工程重点实验室上海 200011

收稿日期:2025-07-26 修回日期:2025-10-15 发布日期:2026-04-28
通讯作者: 刘晨（1994—）男,博士研究生。研究方向：智能船舶。吴乃龙（1987—）男,博士,副教授/博士生导师。研究方向：智能机器人。沈佳诚（1995—）男,硕士,工程师。研究方向：智能船舶。施攀好（1997—）男,本科,工程师。研究方向：机械自动化。
作者简介:刘义（1988—）女,博士,高级工程师。研究方向：智能船舶。
基金资助:
中央高校基本科研业务费专项资金资助（2232025D-48）; 中国船舶及海洋工程设计研究院科研项目（K48000-17）

PDE-Based Formation Control and Shape Switching for Underactuated Unmanned Surface Vehicles

LIU Yi^1,3, LIU Chen^2,*, WU Nailong², SHEN Jiacheng^1,3, SHI Panhao^1,3

1. Marine Design & Research Institute of China, Shanghai 200011, China;;
2. College of Information Science and Technology, Donghua University, Shanghai 201620 , China;
3. Shanghai Key Laboratory of Ship Engineering, Shanghai 200011, China

Received:2025-07-26 Revised:2025-10-15 Published:2026-04-28

摘要/Abstract

摘要： 针对欠驱动无人船的多智能体编队控制问题,该文提出一种基于偏微分方程（partial differential equation,PDE）的分布式控制方法,融合了改进的人工势场法以实现避障功能。首先,建立领航-跟随编队框架,推导跟随船的期望位置与跟踪速度的表达式;其次,基于PDE理论设计编队控制律,以保证多船协同运动的稳定性;最后,改进人工势场法,引入切向力分量与角度自适应系数以优化避障路径。该文基于ArduPilot-SITL、ROS和QGroundControl软件搭建仿真平台,验证了算法在编队保持、队形切换及避障方面的有效性。结果表明,该方法能使编队误差快速收敛,并有效规避静态障碍物,具有良好的鲁棒性和实用性。

关键词: 偏微分方程, 协同编队, 无人船, 避障控制

Abstract: This paper investigates the multi-agent formation control problem for underactuated unmanned surface vehicles (USVs) and proposes a distributed control strategy based on partial differential equations (PDE), integrated with an improved artificial potential field (APF) method for obstacle avoidance. A leader-follower formation framework is first established, where the desired positions and tracking velocities of follower vessels are derived. Subsequently, a PDE-based formation control law is designed to ensure stability in multi-USV cooperative motion. The APF approach is enhanced by introducing tangential force components and angle-adaptive coefficients to optimize obstacle avoidance trajectories. The proposed algorithm is validated through simulations using ArduPilot-SITL, ROS, and QGroundControl, demonstrating its effectiveness in formation maintenance, formation switching, and obstacle avoidance. Experimental results show that the method achieves rapid convergence of formation errors while effectively avoiding static obstacles, exhibiting strong robustness and practical applicability.

Key words: partial differential equations (PDE), multi-agent formation, unmanned surface vehicles (USV), obstacle avoidance control

中图分类号:

TM344.1

刘义, 刘晨, 吴乃龙, 沈佳诚, 施攀好. 基于PDE的欠驱动无人船航行编队与队形切换控制[J]. 船舶, 2026, 37(02): 50-58.

LIU Yi, LIU Chen, WU Nailong, SHEN Jiacheng, SHI Panhao. PDE-Based Formation Control and Shape Switching for Underactuated Unmanned Surface Vehicles[J]. Ship & Boat, 2026, 37(02): 50-58.

参考文献

[1] 彭周华,吴文涛,王丹,等.多无人艇集群协同控制研究进展与未来趋势[J].中国舰船研究,2021,16(1):51-64.
[2] 张伟,廖煜雷,姜峰,等.无人水面USV技术发展回顾与趋势分析[J].无人系统技术,2019,2(6):1-9.
[3] WU N,WANG M,GE T,et al.Experiments on high-performance maneuvers control for a work-class 3000-m remote operated vehicle[J]. Proceedings of the Institution of Mechanical Engineers,Part I:Journal of Systems and Control Engineering,2019,233(5):558-569.
[4] LI J,FAN Y,LIU J.Distributed fixed-time formation tracking control for multiple underactuated USVs with lumped uncertainties and input saturation[J]. ISA Transactions,2024,154:186-198.
[5] FAN Y,QIU B,LIU L,et al.Global fixed-time trajectory tracking control of underactuated USV based on fixed-time extended state observer[J]. ISA Transactions,2023,132:267-277.
[6] FENG G,HAO P,GUO H,et al.Event-triggered simultaneous tracking control and stabilization of underactuated USVs[J]. Ocean Engineering,2024,302:117680.
[7] WU T,XUE K,WANG P.Leader-follower formation control of USV using APF-based adaptive fuzzy logic nonsingular terminal sliding mode control method[J]. Journal of Mechanical Science and Technology,2022,36(4):2007-2018.
[8] SKJETNE R,MOI S,FOSSEN T I.Nonlinear formation control of marine craft[C]//Proceedings of the 41st IEEE Conference on Decision and Control,2002. IEEE,2002,2:1699-1704.
[9] ARRICHIELLO F,CHIAVERINI S,FOSSEN T I.Formation control of underactuated surface vessels using the null-space-based behavioral control[C]// 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems. Beijing:IEEE,2006:5942-5947.
[10] HUANG C,ZHANG X,ZHANG G.Improved decentralized finite-time formation control of underactuated USVs via a novel disturbance observer[J]. Ocean Engineering,2019,174:117-124.
[11] SARLETTE A,SEPULCHRE R.A PDE viewpoint on basic properties of coordination algorithms with symmetries[C]//Proceedings of the 48th IEEE Conference on Decision and Control (CDC) Held Jointly with 28th Chinese Control Conference. Shanghai:IEEE,2009:5139-5144.
[12] QI J,PAN F,QI J.A PDE approach to formation tracking control for multi-agent systems[C]//Proceedings of the 34th Chinese Control Conference. Hangzhou:IEEE,2015:7136-7141.
[13] CHEN H,QI J,DONG Y,et al.Multi-Robot formation control and implementation[C]//Proceedings of the 40th Chinese Control Conference. Shanghai:IEEE,2021:879-884.
[14] AZZABI A,NOURI K.An advanced potential field method proposed for mobile robot path planning[J]. Transactions of the Institute of Measurement & Control,2019,41(11):3132-3144.
[15] FEDELE G,D’ALFONSO L,CHIARAVALLOTI F,et al. Obstacles avoidance based on switching potential functions[J]. Journal of Intelligent & Robotic Systems,2018,90(2):387-405.
[16] DONG Z,ZHANG Z,QI S,et al.Autonomous cooperative formation control of underactuated USVs based on improved MPC in complex ocean environment[J]. Ocean Engineering,2023,270:113633.
[17] YU H,NING L.Coordinated obstacle avoidance of multi-AUV based on improved artificial potential field method and consistency protocol[J]. Journal of Marine Science and Engineering,2023,11(6):1157.

编辑推荐

Metrics

联系电话：（021）63161688-105006
传真：（021）63151255
E-mail：chuanbo@maric.com.cn

基于PDE的欠驱动无人船航行编队与队形切换控制

PDE-Based Formation Control and Shape Switching for Underactuated Unmanned Surface Vehicles

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 6

编辑推荐

Metrics

[1]	李宗余, 许志远. 基于双向APF-RRT*算法的无人船航行路径规划研究[J]. 船舶, 2026, 37(02): 43-49.
[2]	靳渊, 楼建坤, 王鸿东, 王志鸿, 张咏舟. 无人船舶局部路径规划算法综述[J]. 船舶, 2025, 36(03): 10-22.
[3]	甘章泽, 刘志强, 黄子业, 向青青, 蒋晨曦. 基于明轮的全向移动式无人船舶设计[J]. 船舶, 2024, 35(04): 21-28.
[4]	高炳, 王林, 张少明, 陈锦濠. 应用粒子群优化算法改进无人船航行路径规划研究[J]. 船舶, 2022, 33(06): 47-54.
[5]	胡以怀, 芮晓松, 方云虎, 张陈. 某化学品船无人化设备配置及运行经济性[J]. 船舶, 2020, 31(06): 65-69.
[6]	高炳;严健雄;王磊;张少明;. 智能船舶主要技术分析与小型无人船研发[J]. 船舶, 2019, 30(02): 21-26.