Abstract Time-dependent positional reliability, mathematically defined as the probability of the positional error falling inside a specified safe boundary over a time interval, is of importance for robotic manipulators. This work proposes an enhanced moment-based approach integrating the Lie-group theory, series expansion simulation, sparse grid Gauss-Hermite integration technique and chi-square approximation to attacking this problem. The novelties of this work lie in two points. On the one hand, different from previous methods that compute the first to fourth order moments directly using the original limit-state function, the proposed method takes advantage of the Lie group theory, PCE and EOLE to transform the original limit-state error function into a simple surrogate one for moment calculation, which helps to get rid of repeatedly calling the original error function and therefore results in a great enhancement in efficiency. On the other hand, the proposed method first introduces the non-central chi-square approximation to rebuild the extreme value distribution of the positional error, by which the accuracy of time-dependent positional reliability analysis is highly enhanced. Finally, a 6-DOF robotic manipulator is showcased to demonstrate the effectiveness and advantages of the proposed approach.

中文翻译：

---

一种基于力矩的增强型机器人机械臂时间相关位置可靠性分析方法

摘要 时间相关的位置可靠性，在数学上定义为位置误差在时间间隔内落在指定安全边界内的概率，对机器人操纵器很重要。这项工作提出了一种增强的基于矩的方法，它结合了李群理论、级数展开模拟、稀疏网格 Gauss-Hermite 积分技术和卡方近似来解决这个问题。这项工作的新颖之处在于两点。一方面，不同于以往直接使用原始极限状态函数计算一阶到四阶矩的方法，该方法利用李群理论、PCE和EOLE将原始极限状态误差函数转化为一个用于矩计算的简单代理，这样可以避免重复调用原来的错误函数，从而大大提高了效率。另一方面，所提出的方法首先引入非中心卡方近似来重建位置误差的极值分布，从而大大提高了瞬态位置可靠性分析的准确性。最后，展示了一个 6 自由度机器人机械手，以证明所提出方法的有效性和优势。