绳驱空间机械臂动力学建模与仿真效率分析

针对一种适用于在轨服务精细操作的绳驱空间机械臂进行讨论。建立该机械臂的动力学模型，将机械臂视为链式多刚体系统，认为绳索满足线弹性假设并忽略绳索的质量，利用空间算子代数方法推导了机械臂的动力学方程。分析动力学模型的数值仿真效率，求解出机械臂微振动的振动频率，将最高阶振动频率作为特征系数代入到微分方程数值算法的稳定区域，计算得到仿真步长的临界值；对动力学模型中的绳索模型进行改进，通过增大仿真时间步长临界值来提高动力学模型的数值仿真效率。仿真算例表明，改进后动力学模型的仿真效率最多可提高200多倍，并可以实现实时仿真。

Dynamic Modeling of Rope-Driven Space Manipulator and Analysis of Computational Efficiency

This paper studies the dynamics of a space manipulator. The space manipulator is designed for precise on-orbit servicing missions in a highly constrained environment. First, this paper proposes a dynamic model of the manipulator. The manipulator is modeled as a rigid multibody system and the ropes are assumed to be massless and linear elastic. The equations of motion are derived using space operator algebra. Then, this paper studies the computational efficiency of numerical simulation. The governing equations of vibration are derived by perturbation method and the values of natural frequencies are calculated. The value of the upper bound of time step is calculated based on the stability region of numerical methods of ordinary differential equations. The computational efficiency of the numerical simulation is limited by the value of the upper bound. Two modifications of the dynamic model are introduced to relax the upper bound of the time step. The results of numerical examples show that the computational efficiency is improved by over two hundred times and real-time simulation is realized.