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白争锋, 孔清峰, 赵起. 软体连续机械臂动力学建模与仿真. 力学学报, 2022, 54(1): 184-195. DOI: 10.6052/0459-1879-21-481
引用本文: 白争锋, 孔清峰, 赵起. 软体连续机械臂动力学建模与仿真. 力学学报, 2022, 54(1): 184-195. DOI: 10.6052/0459-1879-21-481
Bai Zhengfeng, Kong Qingfeng, Zhao Qi. Dynamic modeling and simulation of soft continuous manipulator. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(1): 184-195. DOI: 10.6052/0459-1879-21-481
Citation: Bai Zhengfeng, Kong Qingfeng, Zhao Qi. Dynamic modeling and simulation of soft continuous manipulator. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(1): 184-195. DOI: 10.6052/0459-1879-21-481

软体连续机械臂动力学建模与仿真

DYNAMIC MODELING AND SIMULATION OF SOFT CONTINUOUS MANIPULATOR

  • 摘要: 由于软体机械臂的质量是沿臂的长度连续分布, 因此采用拉格朗日方法建立软体机械臂的动力学模型时, 涉及计算复杂的积分运算, 采用离散化的集中质量模型降低了计算的复杂性, 但准确性不足. 为了提高软体机械臂动力学建模与仿真的准确度和计算效率, 本文采用模态方法对软体机械臂进行运动学描述, 并从能量的角度分析软体机械臂动力学特性, 研究发现, 角速度产生的转动动能计算复杂, 影响动力学方程的求解效率. 在给定条件下, 占总动能的百分比不超过3%, 对动力学结果影响很小, 可以忽略. 在此基础上, 提出一种基于质心集中质量描述的软体机械臂动力学模型, 该模型将软体机械臂的连续分布质量模型等效为位于质心的集中质量模型, 利用统计的方法计算出动能等效系数, 通过动能等效系数实现两种模型的动能匹配. 仿真结果表明, 与通常将集中质量放置在任意位置(例如, 软体机械臂的中点或末端)的集中质量模型相比, 该模型兼顾了连续分布质量模型的准确性, 以及集中质量模型的计算高效性, 能够准确、高效地获得软体机械臂的动力学特性, 并且数值计算稳定.

     

    Abstract: Since the mass of the soft manipulator is distributed along the length of arm continuously, when Lagrange method is used to establish the dynamic modeling of the soft manipulator, it involves complex integral calculation. The discrete centralized mass model reduces the complexity, but the accuracy is limited. In this paper, in order to improve the accuracy and efficiency of dynamics modeling and simulation, of the soft manipulator, the modal method is adopted to describe the kinematics of the soft manipulator. Then, considering the dynamic characteristics of the soft manipulator from the energy point of view, it is found that the calculation of rotational kinetic energy generated by the angular velocity is complex, which affect the efficiency of solving the dynamics equation. However, the percentage of rotational kinetic energy in the process of dynamic modeling is less than 3% of the total kinetic energy on a given condition. Consequently, the effect on the dynamics results is small and it can be ignored in the modeling process. Further, a dynamics model of the soft manipulator is proposed based on the concentrated mass description of the center of mass. The continuous distribution mass of the soft manipulator is equivalent to the concentrated mass located in the center of mass. The kinetic energy equivalent coefficient is calculated based on the statistical method. Then, the kinetic energy matching between the two is realized by the kinetic energy equivalent coefficient and the calculation accuracy is improved. The simulation results show that compared with the centralized mass model which usually places the concentrated mass at any position (for example, the midpoint or end of the soft manipulator), the model takes into account the accuracy of the continuous distributed mass model and the calculation efficiency when using the centralized mass model. The model proposed in this work can obtain the dynamics characteristics of the soft manipulator accurately and efficiently, and the numerical calculation is stable.

     

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