An enhanced moment-based approach to time-dependent positional reliability analysis for robotic manipulators

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.