A new positional accuracy reliability analysis method of industrial robots is proposed based on the statistical moment similarity of positional error. The first-two order statistical moments of positional error at some positions are accurately obtained through the differential kinematics method to reduce the computational cost of the proposed method. In practical engineering, the statistical moments of positional error can also be obtained from the limited experimental data. Then, the statistical moment similarity of positional error is quantified by the semivariance function. Besides, the first-two order moments of positional error at any position can be calculated according to the statistical moment similarity. Thus, the positional accuracy reliability analysis of any position can be realized by the first-two order moments according to the saddlepoint approximation method. Besides, an optimal position with the lowest failure probability of positional error can be searched based on the statistical moment similarity. The effectiveness of the proposed method is manifest through calculating the positional accuracy reliability and the optimal position with the lowest failure probability of a 6-degree-of-freedom (6-DoF) industrial robot in a cubic space.

中文翻译：

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基于统计矩相似度度量的工业机器人位置误差可靠性分析

提出一种基于位置误差统计矩相似性的工业机器人位置精度可靠性分析方法。通过微分运动学方法准确获得某些位置位置误差的前二阶统计矩，以降低该方法的计算成本。在实际工程中，也可以从有限的实验数据中获得位置误差的统计矩。然后，通过半方差函数量化位置误差的统计矩相似度。此外，还可以根据统计矩相似度计算任意位置的位置误差的前二阶矩。这样，根据鞍点近似法，通过前二阶矩就可以实现任意位置的位置精度可靠性分析。此外，还可以根据统计矩相似度来搜索位置误差失效概率最低的最佳位置。通过计算六自由度（6-DoF）工业机器人在立方空间中的位置精度可靠性和故障概率最低的最佳位置，证明了该方法的有效性。