Kinematic Reliability Analysis of a 7-DOF Redundant Robot

The kinematic reliability of robots, defined as the probability that the end-effector falls inside the specified safe boundary, is of great significance in predicting the accuracy achieved in reality. This work selects the 7 degrees-of-freedom (7-DOF) redundant robot as an example to conduct reliability analysis by utilizing the envelope method against time-related issues in this work. Since variables in industrial robots are very small relative to their means, the motion error functions are commonly linearized by the first-order Taylor's formula to simplify calculation, and the failure models in all directions and attitude angles are then established through the probability method over the entire input interval. As a result, the actual accuracy of the robot in each pose component will be displayed, instead of merely considering the position error like other scholars. The principle of the proposed method is to transform a time-dependent problem into a time-independent one with the help of the failure extreme points and endpoints, so as to enhance the operation efficiency under the premise of ensuring accuracy. Finally, the simulation results verify that the relative error of the envelope method is less than 6.0% compared with that of the Monte Carlo simulation method, and the computational efficiency is higher than that of the Monte Carlo method, which demonstrates that the envelope method has better comprehensive performance.