本文研究面向海洋勘测任务的多水下机器人系统编队跟踪控制分析和设计问题。首先，以有向图为工具，建立水下机器人之间的信息交互模型，并利用局部相邻个体的信息构建了基于一致性的协议。然后，提出多水下机器人系统实现编队跟踪控制的充分条件。通过分析证明，若期望的编队满足给定条件，则多水下机器人系统可实现预定义的编队队形。此外，通过将编队控制协议增益矩阵计算转化为代数黎卡提方程求解问题，给出了一种确定编队控制协议矩阵的新方法。最后，通过数值模拟验证了所提方法的有效性。
Formation control analysis and design problems for multiple Autonomous Underwater Vehicle (multi-AUV) systems for ocean survey are investigated in this paper. First, using directed graph as a tool, the information model between AUVs is established, and a consensus based protocol is constructed using local neighboring information. Then, sufficient conditions for multi-AUV systems to achieve time-varying formation tracking are presented. It is obtained that the predefined time-varying formation can be achieved by multi-AUV systems if the given time-varying formation meets the conditions. Moreover, by transforming the calculation of formation control protocol gain matrix into the solution of algebraic Riccati equation, a new method for determining formation control protocol matrix is given. Finally, numerical simulations are provided to demonstrate the effectiveness of the theoretical results.
2024,46(1): 102-108 收稿日期：2022-11-04
DOI：10.3404/j.issn.1672-7649.2024.01.017
分类号：TP242
基金项目：国家自然科学基金青年基金资助项目（52101379）；广东省自然科学基金面上项目（2021A1515012134）
作者简介：闫勋(1994-),男,博士研究生,研究方向为多海洋无人航行器协同控制
参考文献：
[1] CAMPBELL K J, KINNEAR S, THAME A. AUV technology for seabed characterization and geohazards assessment[J]. The Leading Edge, 2015, 34(2): 170-178.
[2] PAULL L, SETO M, LI H. Design and implementation of an AUV for petroleum pipeline inspection[C]// 2015 7th International Conference on Information Technology and Electrical Engineering (ICITEE). Piscataway: IEEE, 2014: 6592-6599.
[3] TIPSUWAN Y, HOONSUWAN P. Design and implementation of an AUV for petroleum pipeline inspection[C]// 2015 7th International Conference on Information Technology and Electrical Engineering (ICITEE). Piscataway: IEEE, 2015: 382-387.
[4] PETILLOT Y R, REED S R, BELL J M. Real time AUV pipeline detection and tracking using side scan sonar and multi-beam echo-sounder[C]// OCEANS’02 MTS/IEEE. Piscataway: IEEE, 2002: 17-222.
[5] OHTA Y, YOSHIDA H, ISHIBASHI S, et al. Seabed resource exploration performed by AUV Yumeiruka[C]// OCEANS 2016 MTS/IEEE Monterey. Piscataway: IEEE, 2016: 1-4.
[6] XUE L, LIU Y, GU Z Q, et al. Joint design of clustering and in-cluster data route for heterogeneous wireless sensor networks[J]. International Journal of Automation and Computing, 2017, 14(6): 637-649.
[7] REN W. Consensus strategies for cooperative control of vehicle formations[J]. IET Control Theory & Applications, 2007, 1(2): 505-512.
[8] LU X, AYSTIN F, CHEN S. Formation control for second-order multiagent systems with time-varying delays under directed topology[J]. Communications in Nonlinear Science and Numerical Simulation, 2012, 17(3): 1382-1391.
[9] DONG X, HU G. Time-varying formation tracking for linear multiagent systems with multiple leaders[J]. IEEE Transactions on Automatic Control, 2017, 62(7): 3658-3664.
[10] HAN L, DONG X, LI Q, et al. Formation control for time-delayed second-order multi-agent systems with switching topology[C]// 2018 IEEE CSAA Guidance, Navigation and Control Conference (CGNCC). Piscataway: IEEE, 2018: 1-6.
[11] CAO J F, LING Z H, YUAN Y F, et al. Distributed formation control for a multi-agent system with dynamic and static obstacle avoidances[J]. Chinese Physics B, 2014, 23(7): 070509.
[12] DONG X, HUA Y, ZHOU Y, et al. Theory and experiment on formation-containment control of multiple multirotor unmanned aerial vehicle systems[J]. IEEE Transactions on Automation Science and Engineering, 2018, 16(1): 229-240.
[13] XIONG T, PU Z, YI L, et al. Consensus based formation control for multi-uav systems with time-varying delays and jointly connected topologies[C]// 2018 IEEE 14th International Conference on Automation Science and Engineering (CASE). Piscataway: IEEE, 2018: 292-297.
[14] LIN X, TIAN W, ZHANG W. The leaderless multi-AUV system fault-tolerant consensus strategy under heterogeneous communication topology[J]. Ocean Engineering, 2021, 237.
[15] YAN Z P, LIU Y B, C B. Leader-following coordination of multiple UUVs formation under two independent topologies and time-varying delays[J]. Journal of Central South University, 2017, 24(2): 382-393.
[16] HU Z, MA C, ZHANG L, et al. Formation control of impulsive networked autonomous underwater vehicles under fixed and switching topologies[J]. Neurocomputing, 2015, 147: 291-298.
[17] GODSIL C, ROYLE G F. Algebraic graph theory[M]. Berlin: Springer, 2004.
[18] FAX J A, MURRAY R M. Information flow and cooperative control of vehicle formations[J]. IEEE Transactions on Automatic Control, 2004, 49(9): 1465-1476.
[19] HORN R A, JOHNSON C R. Topics in matrix analysis[M]. Cambridge, UK: Cambridge University Press, 1991.
[20] ZAHREDDINE Z, ELSHEHAWEY E F. On the stability of a system of differential equations with complex coefficients[J]. Indian Journal Pure Application Mathematics, 1988, 19(10): 963-972.
[21] ZHANG H, LEWIS F L, Das A. Optimal design for synchronization of cooperative systems: state feedback, observer and output feedback[J]. IEEE Transactions on Automatic Control, 56(8): 1948-1952.
[22] CHEN CT. Linear system theory and design[M]. New York: Holt, Rinchart and Winston, 1984.
