Proficiency of statistical moment-based methods for analysis of positional accuracy reliability of industrial robots

General presence of uncertainties in geometrical parameters of industrial robots, such as link length, distance between two connecting rods, joint rotation angle and torsional angle, leads to deviations from the specified trajectory of robotic end-effector. It is of practical significance to analyze the positional accuracy reliability for industrial robots in terms of these uncertainties. Among the existing analysis methods, statistical moment-based methods are highly prioritized in evaluating the positional accuracy reliability for industrial robots due to the high accuracy and good computing efficiency. In this study, three different statistical moment-based methods, namely the sparse grid numerical integration (SGNI) method, the point estimation method (PEM) and the univariate dimension reduction method (UDRM), are applied to quantitatively evaluate the positional accuracy reliability of industrial robots. The kinematics model of industrial robots is established through the Denavit-Hartenberg method. The aforementioned three methods are then programmed to calculate the first-four order moments of the established kinematics model. The industrial robots’ positional accuracy reliability is calculated using the SGNI, PEM and UDRM under specified threshold and compared with that from Monte Carlo simulation (MCS) method. Comparison of results shows that the SGNI method performs best in terms of computational accuracy and the PEM exhibits the highest computational efficiency among the three candidate methods.

[1]  Xu Han,et al.  Kinematic Reliability Analysis of Robotic Manipulator , 2020, Journal of Mechanical Design.

[2]  Yan Shi,et al.  Dynamic reliability analysis model for structure with both random and interval uncertainties , 2018, International Journal of Mechanics and Materials in Design.

[3]  Sadiq M. Sait,et al.  A Comparative Study of Metaheuristic Algorithms for Reliability-Based Design Optimization Problems , 2020, Archives of Computational Methods in Engineering.

[4]  Zeng Meng,et al.  New target performance approach for a super parametric convex model of non-probabilistic reliability-based design optimization , 2018, Computer Methods in Applied Mechanics and Engineering.

[5]  Jun Xu,et al.  A new unequal-weighted sampling method for efficient reliability analysis , 2018, Reliab. Eng. Syst. Saf..

[6]  Yan Zeng,et al.  A novel structural reliability analysis method via improved maximum entropy method based on nonlinear mapping and sparse grid numerical integration , 2019, Mechanical Systems and Signal Processing.

[7]  Miomir Vukobratović,et al.  Accuracy of the robot positioning and orientation assessed via its manufacturing tolerances , 1995 .

[8]  S. S. Rao,et al.  Probabilistic approach to manipulator kinematics and dynamics , 2001, Reliab. Eng. Syst. Saf..

[9]  John E. Renaud,et al.  Reliability-Based Design Optimization of Robotic System Dynamic Performance , 2006, 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[10]  Yang Liu,et al.  Reliability analysis of structures using stochastic response surface method and saddlepoint approximation , 2017 .

[11]  Xiaoping Du,et al.  Time-Dependent Reliability Analysis for Function Generator Mechanisms , 2011 .

[12]  M. Pandey,et al.  Structural reliability analysis based on the concepts of entropy, fractional moment and dimensional reduction method , 2013 .

[13]  Zeng Meng,et al.  An active learning method combining Kriging and accelerated chaotic single loop approach (AK-ACSLA) for reliability-based design optimization , 2019 .

[14]  Antonio Visioli,et al.  On the Inclusion of Temperature in the Friction Model of Industrial Robots , 2017 .

[15]  S. Rahman,et al.  A univariate dimension-reduction method for multi-dimensional integration in stochastic mechanics , 2004 .

[16]  B. Y. Ni,et al.  Uncertainty propagation analysis by an extended sparse grid technique , 2019 .

[17]  M. Pandey,et al.  System reliability analysis of the robotic manipulator with random joint clearances , 2012 .

[18]  Gang Li,et al.  Maximum Entropy Method-Based Reliability Analysis With Correlated Input Variables via Hybrid Dimension-Reduction Method , 2019, Journal of Mechanical Design.

[19]  Jun Xu,et al.  A novel fractional moments-based maximum entropy method for high-dimensional reliability analysis , 2019, Applied Mathematical Modelling.

[20]  Zeping Wu,et al.  Hybrid metamodel of radial basis function and polynomial chaos expansions with orthogonal constraints for global sensitivity analysis , 2020 .

[21]  Dixiong Yang,et al.  A new directional stability transformation method of chaos control for first order reliability analysis , 2017 .

[22]  Ying Xiong,et al.  A new sparse grid based method for uncertainty propagation , 2010 .

[23]  Xu Han,et al.  A Moment Approach to Positioning Accuracy Reliability Analysis for Industrial Robots , 2020, IEEE Transactions on Reliability.

[24]  Jianguang Fang,et al.  Hybrid Learning Algorithm of Radial Basis Function Networks for Reliability Analysis , 2021, IEEE Transactions on Reliability.

[25]  Paulo Flores,et al.  Modeling and simulation of wear in revolute clearance joints in multibody systems , 2009 .

[26]  Xiaoping Du,et al.  Time-dependent reliability analysis for function generation mechanisms with random joint clearances , 2015 .

[27]  Yongshou Liu,et al.  A parametric study on thermo-mechanical vibration of axially functionally graded material pipe conveying fluid , 2019, International Journal of Mechanics and Materials in Design.

[28]  Dequan Zhang,et al.  On reliability analysis method through rotational sparse grid nodes , 2021 .

[29]  Jun Xu,et al.  Adaptive scaled unscented transformation for highly efficient structural reliability analysis by maximum entropy method , 2019, Structural Safety.

[30]  Kyung K. Choi,et al.  Sampling-Based RBDO of Ship Hull Structures Considering Thermo-Elasto-Plastic Residual Deformation , 2015 .

[31]  Masoud Rais-Rohani,et al.  Reliability estimation using univariate dimension reduction and extended generalised lambda distribution , 2010 .

[32]  Polynomials satisfying a binomial theorem , 1970 .

[33]  Jianmin Zhu,et al.  Uncertainty analysis of planar and spatial robots with joint clearances , 2000 .

[34]  Gang Li,et al.  A combined reliability analysis approach with dimension reduction method and maximum entropy method , 2011 .

[35]  Ning-Cong Xiao,et al.  Adaptive kriging-based efficient reliability method for structural systems with multiple failure modes and mixed variables , 2020 .

[36]  Xiaoping Du,et al.  Uncertainty Analysis by Dimension Reduction Integration and Saddlepoint Approximations , 2005, DAC 2005.

[37]  H. Hong.  An efficient point estimate method for probabilistic analysis , 1998 .

[38]  A. Abouelsoud,et al.  The effect of frequency of vibration and humidity on the stick–slip amplitude , 2010 .

[39]  Zeng Meng,et al.  Adaptive stability transformation method of chaos control for first order reliability method , 2017, Engineering with Computers.

[40]  Gang Li,et al.  An improved maximum entropy method via fractional moments with Laplace transform for reliability analysis , 2018, Structural and Multidisciplinary Optimization.

[41]  Jie Liu,et al.  Forward and inverse structural uncertainty propagations under stochastic variables with arbitrary probability distributions , 2018, Computer Methods in Applied Mechanics and Engineering.

[42]  Liang Gao,et al.  A general failure-pursuing sampling framework for surrogate-based reliability analysis , 2019, Reliab. Eng. Syst. Saf..

[43]  Weihua Zhang,et al.  Global sensitivity analysis using a Gaussian Radial Basis Function metamodel , 2016, Reliab. Eng. Syst. Saf..

[44]  Jie Liu,et al.  A computational framework of kinematic accuracy reliability analysis for industrial robots , 2020 .

[45]  John E. Renaud,et al.  Reliability-Based Design Optimization of Robotic System Dynamic Performance , 2007 .

[46]  Huang He,et al.  Computational prediction and experimental validation of revolute joint clearance wear in the low-velocity planar mechanism , 2017 .

[47]  Chao Dang,et al.  A novel hybrid cubature formula with Pearson system for efficient moment-based uncertainty propagation analysis , 2020, Mechanical Systems and Signal Processing.

[48]  Masoud Rais-Rohani,et al.  Reliability Estimation using Dimension Reduction and Extended Generalized Lambda Distribution , 2008 .

[49]  Tzong-Shi Liu,et al.  A reliability approach to evaluating robot accuracy performance , 1994 .

[50]  Zhencai Zhu,et al.  An improved high order moment-based saddlepoint approximation method for reliability analysis , 2020 .

[51]  Jun He,et al.  A Sparse Grid Stochastic Collocation Method for Structural Reliability Analysis , 2014, 8th International Symposium on Reliability Engineering and Risk Management.

[52]  Xianmin Zhang,et al.  Dynamic modeling and comparative analysis of a 3- P RR parallel robot with multiple lubricated joints , 2020 .

[53]  Bingyu Ni,et al.  Uncertain vibration analysis based on the conceptions of differential and integral of interval process , 2020, International Journal of Mechanics and Materials in Design.

[54]  Liang Gao,et al.  Real-time estimation error-guided active learning Kriging method for time-dependent reliability analysis , 2020 .

[55]  J. Denavit,et al.  A kinematic notation for lower pair mechanisms based on matrices , 1955 .

[56]  Jun Xu,et al.  A cubature collocation based sparse polynomial chaos expansion for efficient structural reliability analysis , 2018, Structural Safety.

[57]  Dequan Zhang,et al.  Positioning Accuracy Reliability of Industrial Robots Through Probability and Evidence Theories , 2020 .

[58]  B. Kang,et al.  Stochastic approach to kinematic reliability of open-loop mechanism with dimensional tolerance , 2010 .