A Moment Approach to Positioning Accuracy Reliability Analysis for Industrial Robots

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.

[1]  R. Rackwitz,et al.  Structural reliability under combined random load sequences , 1978 .

[2]  A. Kiureghian,et al.  Multivariate distribution models with prescribed marginals and covariances , 1986 .

[3]  Feng Gao,et al.  A New Study on the Relative Kinematic Accuracy Reliability of a Novel Exoskeleton with Series-Parallel Topology , 2015 .

[4]  Sitakanta Mohanty,et al.  Sensitivity analysis of a complex, proposed geologic waste disposal system using the Fourier Amplitude Sensitivity Test method , 2001, Reliab. Eng. Syst. Saf..

[5]  Kevin Barraclough,et al.  I and i , 2001, BMJ : British Medical Journal.

[6]  A. C. Bittencourt,et al.  Static Friction in a Robot Joint—Modeling and Identification of Load and Temperature Effects , 2012 .

[7]  Ilya M. Sobol,et al.  Sensitivity Estimates for Nonlinear Mathematical Models , 1993 .

[8]  Tomasz Trzepieciński,et al.  The repeatability positioning analysis of the industrial robot arm , 2014 .

[9]  B. Christianson.  Cheap Newton steps for optimal control problems: automatic differentiation and Pantoja's algorithm , 1999 .

[10]  Xiukai Yuan,et al.  Nataf transformation based point estimate method , 2008 .

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

[12]  Jun Xia,et al.  An efficient global sensitivity analysis approach for distributed hydrological model , 2012, Journal of Geographical Sciences.

[13]  Zhonglai Wang,et al.  Reliability sensitivity analysis for structural systems in interval probability form , 2011 .

[14]  Selçuk Erkaya,et al.  Effects of Joint Clearance on Motion Accuracy of Robotic Manipulators , 2017 .

[15]  D G Altman,et al.  Indirect comparison in evaluating relative efficacy illustrated by antimicrobial prophylaxis in colorectal surgery. , 2000, Controlled clinical trials.

[16]  Sergei S. Kucherenko,et al.  Derivative based global sensitivity measures and their link with global sensitivity indices , 2009, Math. Comput. Simul..

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

[18]  Zhao-Hui Lu,et al.  Structural Reliability Analysis Including Correlated Random Variables Based on Third-Moment Transformation , 2017 .

[19]  Xiaoping Du.  Time-Dependent Mechanism Reliability Analysis With Envelope Functions and First-Order Approximation , 2014 .

[20]  David W. Coit,et al.  System Reliability Modeling Considering Correlated Probabilistic Competing Failures , 2018, IEEE Transactions on Reliability.

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

[22]  K E Willard,et al.  Probabilistic Analysis of Decision Trees Using Monte Carlo Simulation , 1986, Medical decision making : an international journal of the Society for Medical Decision Making.

[23]  Teik C. Lim,et al.  Dynamics of a hypoid gear pair considering the effects of time-varying mesh parameters and backlash nonlinearity , 2007 .

[24]  Jiafan Zhang,et al.  Sensitivity-analysis based method in single-robot cells cost-effective design and optimization , 2016 .

[25]  Dan Zhang,et al.  Analysis of the Kinematic Accuracy Reliability of a 3-DOF Parallel Robot Manipulator , 2015 .

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

[27]  Jie Liu,et al.  Time-Variant Reliability Analysis through Response Surface Method , 2017 .

[28]  A. Kiureghian,et al.  STRUCTURAL RELIABILITY UNDER INCOMPLETE PROBABILITY INFORMATION , 1986 .

[29]  Wang-Ji Yan,et al.  Statistic structural damage detection based on the closed-form of element modal strain energy sensitivity , 2012 .

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

[31]  M. Bendsøe,et al.  Generating optimal topologies in structural design using a homogenization method , 1988 .

[32]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[33]  Rui Kang,et al.  Benefits and Challenges of System Prognostics , 2012, IEEE Transactions on Reliability.

[34]  Xu Han,et al.  Kinematic response of industrial robot with uncertain-but-bounded parameters using interval analysis method , 2019, Journal of Mechanical Science and Technology.

[35]  Bo Yu,et al.  An importance learning method for non-probabilistic reliability analysis and optimization , 2018, Structural and Multidisciplinary Optimization.

[36]  Xu Han,et al.  A Single-Loop Approach for Time-Variant Reliability-Based Design Optimization , 2017, IEEE Transactions on Reliability.

[37]  Tang Jinyuan,et al.  Nonlinear dynamic characteristics of geared rotor bearing systems with dynamic backlash and friction , 2011 .

[38]  Neil Genzlinger.  A. and Q , 2006 .

[39]  Kuei-Yuan Chan,et al.  Identifying joint clearance via robot manipulation , 2018 .

[40]  Dequan Zhang,et al.  A time-variant reliability analysis method based on stochastic process discretization , 2014 .

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

[42]  Xu Han,et al.  Probability assessments of identified parameters for stochastic structures using point estimation method , 2016, Reliab. Eng. Syst. Saf..

[43]  Hongguang Wang,et al.  Dynamic deformation analysis of a spot welding robot under high speed and heavy load working condition , 2013, 2013 IEEE International Conference on Robotics and Biomimetics (ROBIO).

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

[45]  Jean Pierre Merlet.  Interval analysis and reliability in robotics , 2009 .

[46]  Zeng Meng,et al.  Convergence control of single loop approach for reliability-based design optimization , 2018 .

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

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

[49]  Qing Xiao.  Evaluating correlation coefficient for Nataf transformation , 2014 .

[50]  Yeou-Koung Tung,et al.  Investigation of polynomial normal transform , 2003 .

[51]  Jing Yang,et al.  Convergence and uncertainty analyses in Monte-Carlo based sensitivity analysis , 2011, Environ. Model. Softw..

[52]  Dian-Qing Li,et al.  Performance of translation approach for modeling correlated non-normal variables , 2012 .

[53]  Li Han,et al.  Stratified Deformation Space and Path Planning for a Planar Closed Chain with Revolute Joints , 2006, WAFR.

[54]  Constantinos C. Pantelides,et al.  Monte Carlo evaluation of derivative-based global sensitivity measures , 2009, Reliab. Eng. Syst. Saf..

[55]  Kody Varahramyan,et al.  Statistical optimization and manufacturing sensitivity analysis of 0.18 mm SOI MOSFETs , 1999 .