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基于观测器的人在环多机械臂系统预设性能二分一致性

刘沛明 郭祥贵

刘沛明, 郭祥贵. 基于观测器的人在环多机械臂系统预设性能二分一致性. 自动化学报, xxxx, xx(x): x−xx doi: 10.16383/j.aas.c230622
引用本文: 刘沛明, 郭祥贵. 基于观测器的人在环多机械臂系统预设性能二分一致性. 自动化学报, xxxx, xx(x): x−xx doi: 10.16383/j.aas.c230622
Liu Pei-Ming, Guo Xiang-Gui. Observer-based prescribed performance bipartite consensus for human-in-the-loop multi-manipulator systems. Acta Automatica Sinica, xxxx, xx(x): x−xx doi: 10.16383/j.aas.c230622
Citation: Liu Pei-Ming, Guo Xiang-Gui. Observer-based prescribed performance bipartite consensus for human-in-the-loop multi-manipulator systems. Acta Automatica Sinica, xxxx, xx(x): x−xx doi: 10.16383/j.aas.c230622

基于观测器的人在环多机械臂系统预设性能二分一致性

doi: 10.16383/j.aas.c230622
基金项目: 雄安新区科技创新专项 (2023XAGG0062), 国家自然科学基金 (62173028, 62233015), 广东省基础与应用基础研究基金 (2024A1515011493), 北京自然科学基金 (4232060, IS23065)资助
详细信息
    作者简介:

    刘沛明:北京科技大学自动化学院博士研究生. 主要研究方向为多智能体系统, 容错控制. E-mail: liupeiming1783@126.com

    郭祥贵:北京科技大学自动化学院教授. 2012年获得东北大学控制科学与工程博士学位. 主要研究方向为多智能体系统, 模糊系统, 车辆队列控制和容错控制. 本文通信作者. E-mail: guoxianggui@163.com

Observer-based Prescribed Performance Bipartite Consensus for Human-in-the-loop Multi-manipulator Systems

Funds: Supported by Science, Technology & Innovation Project of Xiongan New Area (2023XAGG0062), National Natural Science Foundation of China (62173028, 62233015), Guangdong Basic and Applied Basic Research Foundation (2024A1515011493), and Beijing Natural Science Foundation (4232060, IS23065)
More Information
    Author Bio:

    LIU Pei-Ming Ph.D. candidate at the School of Automation and Electrical Engineering, University of Science and Technology Beijing. His research interest covers multi-agent systems and fault-tolerant control

    GUO Xiang-Gui Professor at the School of Automation and Electrical Engineering, University of Science and Technology Beijing. He received his Ph.D. degree in control science and engineering from Northeastern University in 2012. His research interest covers multi-agent systems, fuzzy systems, vehicular platoon control, and fault-tolerant control. Corresponding author of this paper

  • 摘要: 研究通讯拓扑为符号有向图的人在环多机械臂系统的预设性能二分一致性跟踪控制问题. 为在预设时间内收敛到预设精度, 提出一种基于观测器的预设性能控制策略. 首先, 设计预设时间和精度的观测器以估计领导者的输出信息, 通过合作/竞争信息交互实现观测器输出的二分一致性. 该观测器不需要领导机械臂的输入信息及输出信息的各阶导数, 并通过无芝诺行为的事件触发机制降低不同机械臂间的通讯负担. 其次, 通过反步法及误差转化方法将有约束的机械臂输出跟踪问题转化为无约束的误差系统稳定性问题, 进而基于观测器输出设计机械臂的输出调节控制器. 值得一提的是, 设计的控制策略不需要系统初始状态的先验知识且避免了预设时刻控制增益无穷大的现象, 增强了系统的可靠性. 最后, 仿真结果表明所提控制策略的可行性及优越性.
  • 图  1  手势及机械臂示意图

    Fig.  1  Schematic diagram of gesture and manipulator

    图  2  控制结构示意图

    Fig.  2  Schematic diagram of the control structure

    图  3  不同机械臂间的通讯拓扑

    Fig.  3  Communication topology among different manipulators

    图  4  不同机械臂的角度轨迹

    Fig.  4  Angle trajectories of different manipulators

    图  7  观测器和机械臂性能

    Fig.  7  Performance of observers and manipulators

    图  5  不同机械臂的触发时刻

    Fig.  5  Trigger instants of different manipulators

    图  6  基于控制器(T2.2)的仿真结果

    Fig.  6  Simulation results based on the controller (T2.2)

    图  8  不同控制方法的跟踪误差

    Fig.  8  Tracking errors of different control methods

    图  9  不同控制方法的比较

    Fig.  9  Comparison of different control methods

    表  1  手势与领导机械臂动作的对应关系

    Table  1  The corresponding relationship between the gesture and the action of the leader manipulator

    手势动作$u_0$
    逆时针挥动逆时针转动$u_0=\Im_g\;{\rm{tanh}}(v_g)$
    顺时针挥动顺时针转动$u_0=-\Im_g\;{\rm{tanh}}(v_g)$
    $\Im_g>0$和$v_g>0$分别为放大系数及经过预处理的手势挥动速度
    下载: 导出CSV

    表  2  预设性能反步控制器

    Table  2  Prescribed performance backstepping controller

    虚拟控制器
    $\alpha_{i}=-\dfrac{\kappa_{i,\;2}+\varphi_{i,\;1}}{\kappa_{i,\;1}}+v_i$ (T2.1)
    $\kappa_{i,\;1}=\left\{\begin{aligned} &\dfrac{1}{h(\xi_i)}-\dfrac{4\delta_i q}{l_{2i}h^2(\xi_i)}(\dfrac{\xi_i}{l_{2i}}-1)^{2q-1}\tilde{y}_{i}^2>0,\; \\ &\qquad \qquad 0<\xi_i< l_{2i}\\ &1,\;\qquad \;\;\xi_i\ge l_{2i} \end{aligned}\right.$
    $\kappa_{i,\;2}=\left\{\begin{aligned} &\dfrac{4\delta_{i}q}{l_{2i}h^2(\xi_i)}(\dfrac{\xi_i}{l_{2i}}-1)^{2q-1}\beta\dot{\beta}\tilde{y}_{i},&&0<\xi_{i}< l_{2i} \\&0,&& \xi_i\ge l_{2i} \end{aligned}\right.$
    其中, $v_i$为所设计观测器(7)的输入信号, $l_{2i}$为安全系数.
    控制器
    $u_{i}=-\dfrac{1}{2}\varphi_{i,\;2}-\kappa_{i,\;1}\varphi_{i,\;1}-\hat{\Phi}_{i}^{\rm T}\Gamma(Z_{i})+\dot{\alpha}^c_{i}$ (T2.2)
    $\dot{\hat{\Phi}}_{i}=-r_{i,\;1}\hat{\Phi}_{i}+r_{i,\;2}\varphi_{i,\;2}\Gamma(Z_{i})$ (T2.3)
    其中, $r_{i,\;1}$和$r_{i,\;2}$为正常数, $Z_{i}=[x_{i,\;1},\;x_{i,\;2}]^{\rm T}$.
    下载: 导出CSV

    表  3  控制器参数

    Table  3  Parameters of the controllers

    参数参数参数
    $c_1$20$c_2$15$o_1$$[0.8,\; 0.5]^{\rm T}$
    $l_{1i}$2.1$l_{2i}$1.5$o_2$$[2.8,\; 2.5]^{\rm T}$
    $r_{i,\;1}$0.001$r_{i,\;2}$0.500$o_3$$[1.1,\; 1.5]^{\rm T}$
    $b_i$5$c_3$0.001$\pi_1$$1.5$
    $\psi_j$3$\nu_i$0.001$\pi_2$$3.0$
    $\delta_i$140$M_1$3$\pi_3$$2.0$
    下载: 导出CSV
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  • 收稿日期:  2023-10-09
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