Time-Dependent System Kinematic Reliability Analysis for Robotic Manipulators

Abstract

Time-dependent system kinematic reliability of robotic manipulators, referring to the probability of the end-effector’s pose error falling into the specified safe boundary over the whole motion input, is of significant importance for its work performance. However, investigations regarding this issue are quite limited. Therefore, this work conducts time-dependent system kinematic reliability analysis defined with respect to the pose error for robotic manipulators based on the first-passage method. Central to the proposed method is to calculate the outcrossing rate. Given that the errors in robotic manipulators are very small, the closed-form solution to the covariance of the joint distribution of the pose error and its derivative is first derived by means of the Lie group theory. Then, by decomposing the outcrossing event of the pose error, calculating the outcrossing rate is transformed into a problem of determining the first-order moment of a truncated multivariate Gaussian. Then, based on the independent assumption that the outcrossing events occur independently, the analytical formula of the outcrossing rate is deduced for the stochastic kinematic process of robotic manipulators via taking advantage of the moment generating function of the multivariate Gaussian, accordingly leading to achievement of the time-dependent system kinematic reliability. Finally, a 6-DOF robotic manipulator is used to demonstrate the effectiveness of the proposed method by comparison with the Monte Carlo simulation and finite-difference based outcrossing rate method.

Structural dynamic reliability analysis: review and prospects

“…Yan et al (2017) discussed the application of FORM combined with outcrossing rate in ship structure reliability evaluation. Zhao et al (2021) improved the solution method for outcrossing rate and avoided using a numerical scheme to calculate the outcrossing rate. Qian et al (2020) provided a modified outcrossing rate method for time-dependent reliability analysis by avoiding assumptions in Rice's formula to improve computational accuracy.…”

“…(2017) discussed the application of FORM combined with outcrossing rate in ship structure reliability evaluation. Zhao et al. (2021) improved the solution method for outcrossing rate and avoided using a numerical scheme to calculate the outcrossing rate.…”

Moment-independent sensitivity analysis of a fold mechanism based on an active learning kriging method

“…However, form manufacturing processes to usage processes, the uncertainties are ubiquitous and various, which seriously affect the safety performance of folding rudder. In order to reduce errors 1 and prevent failures, this paper evaluates the safety of the folding rudder by the reliability theory 2 and assesses the influence of uncertainty factors with sensitivity analysis. 3 Reliability is one of the basic attributes of motion system.…”

Kinematic Reliability Analysis of a 7-DOF Redundant Robot

“…With the improvement of relevant theories over time, some algorithms are appropriately used for robot timedependent reliability analysis after reasonable modification. Zhao et al [24] introduced the first-passage method into the analysis of the 6-DOF robot's pose error, showing that the method's accuracy is fairly good when accounting for low relationships between discrete points, but the calculation area is limited to situations with a very low failure rate. Pendey and Zhang [25] effectively computed the fluctuation range around the intended motion, and the probability density function of the extreme value distribution points is derived in terms of the principle of maximum entropy.…”