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.