Kinematic trajectory accuracy reliability analysis for industrial robots considering intercorrelations among multi-point positioning errors

The kinematic trajectory accuracy reliability is an essential index to evaluate the service performance of industrial robots. This study proposes a new kinematic trajectory accuracy reliability analysis method for industrial robots by integrating the sparse grid technique, the saddlepoint approximation method and copula functions. The novelty of this study lies in comprehending the intercorrelations among single point three-coordinate directional positioning errors and multiple points positioning errors on the kinematic trajectory. To start with, the statistical moments of the positioning errors at an arbitrary point on the trajectory of industrial robots are calculated by the extended sparse grid (SPGR) technique. The single-point positioning accuracy reliability is then evaluated by the saddlepoint approximation (SPA) method. The joint failure probability of positioning accuracy between any two points and the matrix of correlation coefficients of positioning errors among multiple points are subsequently calculated by copula functions. Two methods, namely the boundary theory and the multivariate normal distribution theory, are employed in the current study to calculate the failure probability of kinematic trajectory accuracy. Three examples are implemented to demonstrate the proficiency of the currently proposed methods.