The uncertain variables of the link dimensions and joint clearances, whose deviation is caused by manufacturing and assembling errors, have a considerable influence on the positioning accuracy of industrial robots. Understanding how these uncertain variables affect the positioning accuracy of industrial robots is very important to select appropriate parameters during design process. In this paper, the positioning accuracy reliability of industrial robots is analyzed considering the influence of uncertain variables. First, the kinematic models of industrial robots are established based on the Denavit–Hartenberg method, in which the link lengths and joint rotation angles are treated as uncertain variables. Second, the Sobol’ method is used to analyze the sensitivity of uncertain variables for the positioning accuracy of industrial robots, by which the sensitive variables are determined to perform the reliability analysis. Finally, in view of the sensitive variables, the first-four order moments and probability density function of the manipulator's positioning point are assessed by the point estimation method (PEM) in three examples. The Monte Carlo simulation method, the maximum entropy problem with fractional order moments (maximum entropy problem with fractional order moments method (ME-FM) method), and the experimental method are also performed as comparative methods. All the results demonstrate that the proposed PEM has a higher accuracy and efficiency to assess the positioning accuracy reliability of industrial robots.

中文翻译：

---

工业机器人定位精度可靠性分析的矩法

由制造和装配误差引起的连杆尺寸和关节间隙的不确定变量对工业机器人的定位精度有相当大的影响。了解这些不确定变量如何影响工业机器人的定位精度，对于在设计过程中选择合适的参数非常重要。本文考虑不确定变量的影响，对工业机器人定位精度可靠性进行了分析。首先，基于Denavit-Hartenberg方法建立工业机器人的运动学模型，其中连杆长度和关节旋转角度被视为不确定变量。其次，利用Sobol'方法分析不确定变量对工业机器人定位精度的敏感性，确定敏感变量以进行可靠性分析。最后，针对敏感变量，利用点估计法（PEM）在三个实例中对机械手定位点的一阶四阶矩和概率密度函数进行了评估。蒙特卡罗模拟方法、分数阶矩的最大熵问题（maximum entropy problem with fractional order moment method (ME-FM) method）和实验方法也作为比较方法进行。所有结果表明，所提出的 PEM 具有更高的精度和效率，用于评估工业机器人的定位精度可靠性。机械手定位点的一阶四阶矩和概率密度函数通过点估计方法（PEM）在三个例子中进行评估。蒙特卡罗模拟方法、分数阶矩的最大熵问题（maximum entropy problem with fractional order moment method (ME-FM) method）和实验方法也作为比较方法进行。所有结果表明，所提出的 PEM 具有更高的精度和效率，用于评估工业机器人的定位精度可靠性。机械手定位点的一阶四阶矩和概率密度函数通过点估计方法（PEM）在三个例子中进行评估。蒙特卡罗模拟方法、分数阶矩的最大熵问题（maximum entropy problem with fractional order moment method (ME-FM) method）和实验方法也作为比较方法进行。所有结果表明，所提出的 PEM 具有更高的精度和效率，用于评估工业机器人的定位精度可靠性。分数阶矩的最大熵问题（maximum entropy problem with fractional order moment method (ME-FM) 方法），以及实验方法也作为比较方法进行。所有结果表明，所提出的 PEM 具有更高的精度和效率，用于评估工业机器人的定位精度可靠性。分数阶矩的最大熵问题（maximum entropy problem with fractional order moment method (ME-FM) 方法），以及实验方法也作为比较方法进行。所有结果表明，所提出的 PEM 具有更高的精度和效率，用于评估工业机器人的定位精度可靠性。