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振动驱动移动系统平面避障运动分析

张敏 徐鉴

张敏, 徐鉴. 振动驱动移动系统平面避障运动分析[J]. 力学学报, 2017, 49(2): 397-409. doi: 10.6052/0459-1879-16-367
引用本文: 张敏, 徐鉴. 振动驱动移动系统平面避障运动分析[J]. 力学学报, 2017, 49(2): 397-409. doi: 10.6052/0459-1879-16-367
Zhang Min, Xu Jian. ANALYSIS ON PLANAR OBSTACLE AVOIDANCE LOCOMOTION OF VIBRATION-DRIVEN SYSTEM[J]. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(2): 397-409. doi: 10.6052/0459-1879-16-367
Citation: Zhang Min, Xu Jian. ANALYSIS ON PLANAR OBSTACLE AVOIDANCE LOCOMOTION OF VIBRATION-DRIVEN SYSTEM[J]. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(2): 397-409. doi: 10.6052/0459-1879-16-367

振动驱动移动系统平面避障运动分析

doi: 10.6052/0459-1879-16-367
基金项目: 

国家自然科学基金资助项目 11572224

详细信息
    通讯作者:

    2) 徐鉴, 教授, 主要研究方向:非线性动力学.E-mail:xujian@tongji.edu.cn

  • 中图分类号: O313

ANALYSIS ON PLANAR OBSTACLE AVOIDANCE LOCOMOTION OF VIBRATION-DRIVEN SYSTEM

  • 摘要: 近年来,工业机器人的应用领域日益广泛,可移动机器人的发展备受关注,为了在一些复杂环境中准确地完成作业,学者们提出并研究了振动驱动移动系统.本文研究了在各向异性黏性摩擦环境中一类有两个在平行轨道内做正弦运动的内部质量块的振动驱动移动系统的运动规律,提出了使系统完成包括避障等规定作业的驱动设计方法.首先利用第二类拉格朗日方程,建立了系统的动力学方程;然后,利用速度Verlet积分法分析了系统的运动规律,得到了内部驱动参数与系统运动轨迹、运动速度的关系;最后,结合振动驱动移动系统的运动规律,提出了使系统沿预设路径运动和实现避障运动的驱动设计方法.通过曲线离散得到了系统沿预设路径运动的移动轨迹,进而通过改变内部质量块的驱动参数,使系统沿预设路径运动.为了使移动系统在障碍物环境中达到目标位置,提出了结合栅格法,Floyd算法及最小顶点圆法的优化的路径规划计算方法,得到了振动驱动移动系统在障碍物环境中运动的最优路径,并通过改变内部质量块的驱动参数实现了移动系统的避障运动.

     

  • 图  1  振动驱动系统的平面运动模型

    Figure  1.  The planar motion model of vibration-driven system

    图  2  支撑 $c_i \ (i=1,2,3,4)$ 处的黏性摩擦力模型

    Figure  2.  Model of the viscous frictional force at the i-th support

    图  3  振动驱动系统与平面间的相互作用力和力矩

    Figure  3.  The interaction force and moment of force between vibration-driven system and ground

    图  4  系统直线运动轨迹

    Figure  4.  Trajectories of vibration-driven system

    图  5  系统x方向位移 $x_M$ 与时间t的关系

    Figure  5.  Relations between displacement $x_M$ and time t

    图  6  系统x方向速度 $\dot x_M$ 与时间t的关系

    Figure  6.  Relations between velocity $\dot x_M$ and time t

    图  7  $\omega_1=100$ rad/s, n取不同值时系统轨迹

    Figure  7.  Trajectories of vibration-driven system under different n when $\omega_1=100$ rad/s

    图  8  $\omega_1=100$ rad/s, $n < 1$ 时系统的转角 $\varphi$ 与时间t的关系

    Figure  8.  Relations between angular displacement $\varphi$ and time t when $n < 1$ and $\omega_1=100$ rad/s

    图  9  $\omega_1=100$ rad/s, $n < 1$ 时系统路程s与时间t的关系

    Figure  9.  Relations between displacement s and time t when $n < 1$ and $\omega_1=100$ rad/s

    图  10  $\omega_1=100$ rad/s, 系统曲率半径R与驱动频率比n的关系

    Figure  10.  Relations between radius R and n when $\omega_1=100$ rad/s

    图  11  曲线离散流程图

    Figure  11.  Flow chart of curve discrete

    图  12  曲线离散示例

    Figure  12.  Sample of curve discrete

    图  13  误差分析

    Figure  13.  Error analysis

    图  14  转弯半径

    Figure  14.  Turning radius

    图  15  设计预设轨迹所需驱动的示例

    Figure  15.  Sample of drive design for preset trajectory

    图  16  驱动设计流程图

    Figure  16.  Flow chart of drive design

    图  17  栅格地图模型 (红点:起始点,绿点:目标点)

    Figure  17.  Model of grid map (red: initial point, green: target point)

    图  18  优化的运动路径

    Figure  18.  Optimized motion path

    图  19  设计驱动到达目标位置示例

    Figure  19.  Sample of reaching the target position

    图  20  仿真实验截图

    Figure  20.  Screenshots of simulation experiment

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出版历程
  • 收稿日期:  2016-12-07
  • 网络出版日期:  2017-02-22
  • 刊出日期:  2017-03-18

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