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带有双球面摆和变绳长效应的桥式起重机轨迹规划

李刚 马昕 李轾 李贻斌

李刚, 马昕, 李轾, 李贻斌. 带有双球面摆和变绳长效应的桥式起重机轨迹规划. 自动化学报, xxxx, xx(x): x−xx doi: 10.16383/j.aas.c220988
引用本文: 李刚, 马昕, 李轾, 李贻斌. 带有双球面摆和变绳长效应的桥式起重机轨迹规划. 自动化学报, xxxx, xx(x): x−xx doi: 10.16383/j.aas.c220988
Li Gang, Ma Xin, Li Zhi, Li Yi-Bin. Trajectory planning for overhead crane with double spherical pendulum and varying cable length effect. Acta Automatica Sinica, xxxx, xx(x): x−xx doi: 10.16383/j.aas.c220988
Citation: Li Gang, Ma Xin, Li Zhi, Li Yi-Bin. Trajectory planning for overhead crane with double spherical pendulum and varying cable length effect. Acta Automatica Sinica, xxxx, xx(x): x−xx doi: 10.16383/j.aas.c220988

带有双球面摆和变绳长效应的桥式起重机轨迹规划

doi: 10.16383/j.aas.c220988
基金项目: 山东省重点研发计划项目(2021CXGC010701), 国家自然科学基金—山东省政府联合基金项目(U1706228) 资助
详细信息
    作者简介:

    李刚:山东大学控制科学与工程学院机器人研究中心博士研究生. 主要研究方向为欠驱动起重机系统的轨迹规划与非线性控制. E-mail: ligangsdu@mail.sdu.edu.cn

    马昕:山东大学控制科学与工程学院机器人研究中心教授. 主要研究方向为移动机器人, 机器视觉和欠驱动系统控制. 本文通信作者. E-mail: maxin@sdu.edu.cn

    李轾:山东大学控制科学与工程学院机器人研究中心博士后. 主要研究方向为四旋翼无人机系统, 船用起重机系统的非线性控制. E-mail: lizhisucro@sdu.edu.cn

    李贻斌:山东大学控制科学与工程学院机器人研究中心教授. 主要研究方向为智能机器人技术, 智能控制系统. E-mail: liyb@sdu.edu.cn

Trajectory Planning for Overhead Crane With Double Spherical Pendulum and Varying Cable Length Effect

Funds: Supported by Key Research and Development Project of Shandong Province (2021CXGC010701) and the Joint Fund of National Natural Science Foundation of China and Shandong Province (U1706228)
More Information
    Author Bio:

    LI Gang Ph. D. candidate at the Center for Robotics, School of Control Science and Engineering, Shandong University. His research interest covers planning trajectory and nonlinear control of underactuated crane system

    MA Xin Professor at the Center for Robotics, School of Control Science and Engineering, Shandong University. Her research interest covers mobile robots, machine vision and control of underactuated system. Corresponding author of this paper

    LI Zhi Postdoctoral researcher at the Center for Robotics, School of Control Science and Engineering, Shandong University. His research interest covers unmanned aerial vehicle system and nonlinear control of offshore crane system

    LI Yi-Bin Professor at the Center for Robotics, School of Control Science and Engineering, Shandong University. His research interest covers intelligent robot technology and intelligent control system

  • 摘要: 带有双球面摆和变绳长效应的桥式起重机具有多输入多输出以及欠驱动的动力学特性, 目前仍缺乏有效的控制策略. 在台车移动、桥架移动、负载升降同步作业过程中, 吊钩和负载两级球面摆动特性更为复杂, 各状态量之间的非线性耦合关系更强, 桥式起重机的防摆控制更具挑战性. 不仅如此, 现有方法无法保证桥式起重机系统全状态量的暂态控制性能. 为解决上述问题, 提出了一种基于多项式的优化轨迹规划方法. 首先, 在未进行近似简化的前提下, 使用拉格朗日方法建立了带有双球面摆和变绳长效应的7自由度桥式起重机的精确动力学模型. 在此基础上, 构造了一组包含各状态量的辅助信号, 将施加在台车、桥架、绳长以及吊钩、负载摆动上的约束转化为对辅助信号的约束, 从而将桥式起重机的轨迹规划问题转化为与辅助信号相关的时间优化问题, 并使用二分法求解. 该轨迹规划方法不仅缩短了吊运时间, 而且确保了全状态量满足约束条件. 最后, 仿真结果证明了动力学模型的准确性和轨迹规划方法的有效性.
  • 图  1  7自由度桥式起重机系统

    Fig.  1  Seven degree-of-freedom overhead crane system

    图  2  控制系统框图

    Fig.  2  Block diagram of the proposed control system

    图  3  双球面摆动力学响应

    Fig.  3  Double spherical pendulum dynamic response

    图  4  驱动状态量的仿真结果

    Fig.  4  Simulation results of actuated states

    图  5  非驱动状态量的仿真结果

    Fig.  5  Simulation results of unactuated states

    图  6  吊钩和负载轨迹

    Fig.  6  Trajectories of the hook and payload

    图  7  不同索具绳长度$ l_2$的仿真结果

    Fig.  7  Simulation results of different rigging cable lengths $ l_2$

    图  8  不同负载质量$ m_2$的仿真结果

    Fig.  8  Simulation results of different payload masses $ m_2$

    表  1  本文与桥式起重机相关工作的比较

    Table  1  Comparison between our work and the relevant works about overhead crane

    自由度参考文献台车移动桥架移动变绳长吊钩摇摆负载摇摆
    2[78]$\checkmark$$\times$$\times$$\times$$\checkmark$
    3[911]$\checkmark$$\times$$\times$$\checkmark$$\checkmark$
    3[1214]$\checkmark$$\times$$\checkmark$$\times$$\checkmark$
    4[1517]$\checkmark$$\times$$\checkmark$$\checkmark$$\checkmark$
    4[1819]$\checkmark$$\checkmark$$\times$$\times$$\checkmark$
    5[2021] $\checkmark$$\checkmark$$\checkmark$$\times$$\checkmark$
    6[2224]$\checkmark$$\checkmark$$\times$$\checkmark$$\checkmark$
    7本文$\checkmark$$\checkmark$$\checkmark$$\checkmark$$\checkmark$
    下载: 导出CSV

    表  2  系统参数

    Table  2  System parameters

    参数物理意义单位
    $M_1$台车质量kg
    $M_2$台车和桥架质量之和kg
    $m_1,m_2$吊钩、负载质量kg
    $x,y$台车、桥架位移m
    $l_1,l_2$吊绳、索具绳长度m
    $\theta_1,\theta_2,\theta_3,\theta_4$吊钩、负载三维空间摆角 deg
    $F_x,F_y,F_z$台车、桥架、吊绳驱动力N
    $g$重力加速度m/s2
    下载: 导出CSV

    表  3  量化指标对比结果

    Table  3  Comparison results of quantitative indices

    控制方法$t_s$/s${\theta _{1\max }}$/deg${\theta _{1{\rm{res}}}}$/deg${\theta _{3\max }}$/deg${\theta _{3{\rm{res}}}}$/deg
    EI$>15.00$2.690.793.631.46
    光滑器$>15.00$2.290.232.460.35
    EAB$>15.00$3.140.225.391.21
    CTP4.823.030.013.240.02
    本文方法4.911.9201.970
    下载: 导出CSV
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  • 收稿日期:  2022-12-21
  • 录用日期:  2023-04-13
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