基于事件触发的AUVs固定时间编队控制

王洪斌; 高静; 苏博; 王跃灵

doi:10.16383/j.aas.c190816

基于事件触发的AUVs固定时间编队控制

doi: 10.16383/j.aas.c190816

王洪斌^{1, 2,},
高静^{1, 2,},
苏博^{1, 2,},
王跃灵^{1, 2,}

1.
燕山大学电气工程学院秦皇岛 066004
2.
燕山大学工业计算机控制工程河北省重点实验室秦皇岛 066004

基金项目: 国家自然科学基金(61473248)资助

详细信息

作者简介:
王洪斌：燕山大学教授. 主要研究方向为过程自动化, 机器人控制技术, 变结构控制系统, 鲁棒控制和视觉伺服. E-mail: hb_wang@ysu.edu.cn

高静：燕山大学电气工程学院研究生. 主要研究方向为自主水下航行器编队控制. 本文通信作者.E-mail: jing1883049@163.com

苏博：燕山大学电气工程学院博士研究生. 主要研究方向为水下机器人非线性控制.E-mail: bosu@stumail.ysu.edu.cn

王跃灵：燕山大学工业计算机控制工程河北省重点实验室讲师, 机械工程学院博士研究生. 主要研究方向为智能控制, 迭代学习控制和自适应控制.E-mail: yuelingw@ysu.edu.cn

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出版历程
- 收稿日期: 2019-11-30
- 录用日期: 2020-03-11
- 网络出版日期: 2022-09-06
- 刊出日期: 2022-09-16

Fixed-time Formation of AUVs Based on Event-triggered Control

WANG Hong-Bin^{1, 2
,},
GAO Jing^{1, 2
,},
SU Bo^{1, 2
,},
WANG Yue-Ling^{1, 2
,}

1.
School of Electrical Engineering, Yanshan University, Qinhuangdao 066004
2.
Key laboratory of Industrial Computer Control Engineering of Hebei Province, Yanshan University, Qinhuangdao 066004

Funds: Supported by National Natural Science Foundation of China (61473248)

More Information

Author Bio:
WANG Hong-Bin　Professor at Yanshan University. His research interest covers process automation, robot control technology, variable structure control system, robust control and visual servo

GAO Jing　Master student at the School of Electrical Engineering, Yanshan University. Her main research interest is formation control of autonomous underwater vehicle formation control. Corresponding author of this paper

SU Bo　Ph.D. candidate at the School of Electrical Engineering, Yanshan University. Her main research interest is nonlinear control of underwater vehicles and underactuated system control

WANG Yue-Ling　Lecturer at the Key laboratory of Industrial Computer Control Engineering of Hebei Province, and Ph.D. candidate at the School of Mechanical Engineering, Yanshan University. His research interest covers intelligent control, iterative learning control, and adaptive control

摘要

摘要: 针对多自主水下航行器编队系统受限于有限的通信资源及收敛速度慢等问题, 提出一种基于事件触发的自主水下航行器固定时间领航−跟随编队控制方法. 首先, 将动态面控制算法与反步法结合, 消除“计算膨胀”问题; 其次, 为节约有限通信资源, 将事件触发通讯机制和固定时间理论引入多自主水下航行器编队控制中, 设计编队控制器, 实现编队系统的固定时间稳定, 且系统收敛时间与初始状态无关, 并通过理论证明无Zeno行为; 最后, 对4艘自主水下航行器的编队进行仿真实验, 验证算法的有效性.
- 多自主水下航行器 /
- 事件触发 /
- 领航者−跟随者法 /
- 动态面控制 /
- 固定时间控制
Abstract: In this paper, the limited communication resources and slow convergence speed of multi-autonomous underwater vehicles formation system are considered, a fixed-time leader-follower formation control method of autonomous underwater vehicles with event-triggered mechanism is proposed. Firstly, by combining dynamic surface control with backstepping technique, the algorithm can overcome the “explosion of complexity” problem. Secondly, in order to save communication resources, the formation controller is designed by combining the event-triggered control strategy and the fixed-time theory. Thus, the target of formation is stable in fixed-time and the convergence time of system is independent of the initial state, and the theory is used to prove that there is no Zeno behavior. Finally, in order to verify the validity of algorithm, the formation experiment of four autonomous underwater vehicles is studied by simulation.
- Multi-autonomous underwater vehicles /
- event-triggered /
- leader-follower method /
- dynamic surface control /
- fixed-time control

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图 1 领航−跟随多AUVs编队示意图

Fig. 1 The diagram of leader-follower formation of AUVs

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图 2 编队跟踪控制示意图

Fig. 2 The diagram of formation control

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图 3 工况 1 下的轨迹

Fig. 3 The trajectory under working Condition 1

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图 12 跟随 AUV 1 的事件触发时刻

Fig. 12 The triggered interval of AUV 1

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图 4 工况 1 下的位置

Fig. 4 The position under working Condition 1

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图 5 工况 1 下的位置跟踪误差

Fig. 5 The position tracking error under working Condition 1

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图 6 工况 1 下的速度

Fig. 6 The velocity under working Condition 1

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图 7 工况 1 下速度跟踪误差

Fig. 7 The velocity tracking error under working Condition 1

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图 8 工况 1 下的虚拟控制律

Fig. 8 The virtual control law under working Condition 1

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图 9 工况 1 下的控制输入

Fig. 9 The control input under working Condition 1

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图 10 工况 1 下的事件触发时刻仿真图

Fig. 10 The triggered interval under working Condition 1

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图 11 跟随AUV 1的控制输入${\tau _f}(t)$

Fig. 11 The control input ${\tau _f}(t)$ of AUV 1

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图 13 工况2下的轨迹

Fig. 13 The trajectory under working condition 2

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图 17 工况 2 下的事件触发时刻仿真图

Fig. 17 The triggered interval under working condition 2

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图 14 工况 2 下的位置跟踪误差

Fig. 14 The position tracking error under working condition 2

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图 15 工况 2 下速度跟踪误差

Fig. 15 The velocity tracking error under working condition 2

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图 16 工况 2 下的控制输入

Fig. 16 The control input under working condition 2

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图 18 跟随 AUV 1 的位置跟踪误差

Fig. 18 The position tracking error of AUV 1

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图 19 跟随 AUV 1 的速度跟踪误差${z_2}(t)$

Fig. 19 The velocity tracking error of AUV 1

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表 1 跟随 AUVs 的任意初始状态

Table 1 The arbitrary initial state of AUVs

工况	状态	AUV 1	AUV 2	AUV 3
1	${p_f}\left( 0 \right)$	${\left[ {1,0,0} \right]^{\rm{T}}}$	${\left[ {1,1.5,2} \right]^{\rm{T}}}$	${\left[ {2,0,1} \right]^{\rm{T}}}$
1	${\upsilon _f}\left( 0 \right)$	${\left[ { - 1,3,2} \right]^{\rm{T}}}$	${\left[ {3,2,4} \right]^{\rm{T}}}$	${\left[ {3, - 1, - 4} \right]^{\rm{T}}}$
2	${p_f}\left( 0 \right)$	${\left[ {7, - 3,2} \right]^{\rm{T}}}$	${\left[ { - 10,8,2} \right]^{\rm{T}}}$	${\left[ {12, - 8,2} \right]^{\rm{T}}}$
2	${\upsilon _f}\left( 0 \right)$	${\left[ {6,0,8} \right]^{\rm{T}}}$	${\left[ {4, - 3,1} \right]^{\rm{T}}}$	${\left[ { - 1,4, - 3} \right]^{\rm{T}}}$

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表 2 跟随者AUVs的事件触发次数和触发率

Table 2 Event-triggered and triggered ratios for follower AUVs

工况	采样次数		触发次数		触发率 (%)
工况	1	2	1	2	1	2
AUV 1	—	—	37	99	3.7	9.9
AUV 2	1000	1000	56	125	5.6	12.5
AUV 3	—	—	58	135	5.8	13.5

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表 3 本文算法和PID算法的比较结果

Table 3 Comparison results in the algorithm of proposed in paper and PID

均方差	PID算法	本文算法	平均值	PID算法	本文算法
${D_{{z_{1x}}}}$	2.9667	1.6717	${E_{{z_{1x}}}}$	−1.0323	−0.6265
${D_{{z_{1y}}}}$	1.4782	0.6209	${E_{{z_{1y}}}}$	0.4794	0.3294
${D_{{z_{1z}}}}$	1.3127	0.4251	${E_{{z_{2z}}}}$	−0.3611	−0.4203
${D_{{z_{2u}}}}$	2.1902	0.9823	${E_{{z_{2u}}}}$	0.3229	0.0098
${D_{{z_{2v}}}}$	1.6632	1.0471	${E_{{z_{2v}}}}$	0.0898	0.0871
${D_{{z_{2w}}}}$	3.4603	2.3432	${E_{{z_{2w}}}}$	−0.0569	−0.7105

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