柔性空间机械臂区间参数不确定性分析

Uncertainty Analysis with Interval Parameters for Flexible Space Manipulator

研究了柔性空间机械臂动力学分析中由于区间参数的存在而引起的动力学响应不确定性问题.采用能够描述大位移、大变形耦合特性的绝对节点坐标方法来建模柔性机械臂臂杆,建立了含区间参数的多体系统动力学方程,为指标-3的微分代数方程.运用基于Chebyshev多项式的Chebyshev区间扩张函数,将含区间参数的微分代数方程转化为Chebyshev多项式插值点处的确定参数的动力学方程,研究得到了一维区间参数和多维区间参数影响下机械臂系统的动力学响应区间边界,形成了预测机械臂末端轨迹区间的新方法.通过与Taylor方法的对比研究,结果表明,该方法能够有效减少系统仿真工作量,减小动力学响应预测值误差,快速稳定地得到机械臂系统动力学响应区间.

Interval uncertainty method of dynamic analysis for the flexible space manipulator was studied in this paper.Absolute nodal coordinate formulation（ANCF）,which can describe coupling characteristics of large displacement and large deformation precisely,was utilized to model flexible links of space manipulator.Multibody system dynamic model with uncertainties governed by index-3 differential algebraic equations（DAEs）was established based on ANCF and solved by generalized-α algorithm.Chebyshev inclusion functions deduced from truncated Chebyshev series were applied to convert dynamic equations with uncertainties into equations at interpolation points of Chebyshev series.Interval dynamic response of the manipulator system was achieved by single uncertainty and multiple uncertainties respectively,which results in a new prediction method of the manipulator endpoint.Compared with the results of Taylor＇s method,numerical simulations have demonstrated that the proposed method can effectively reduce the emulation workload of the system and errors of the dynamic response prediction value,and quickly obtain the interval dynamic response in a rapid and steady way.