A statistical weighted method for kinematic sensitivity analysis of parallel robots

Abstract

Many efforts have been devoted to propose effective methods and indices of kinematic sensitivity, but all of them have considered equal proportion of errors in the actuated joint coordinates and generally entail several drawbacks. Therefore, all of previous studies conducted in the literature ignored the difference in sensitivity of manipulator to the active joints uncertainties. Solving this issue requires a deep understanding of mathematical modeling of kinematic sensitivity and its interpretations. In this paper, a synergy between kinematic concepts and statistics approaches is employed in order to propose a more reasonable index for the kinematic performance measurement of the robotic mechanical systems, with a more emphasis on parallel mechanisms.To this end, from kinematic stand point, the kinematic sensitivity is adopted as kinematic index performance. In turn, the so-called Sobol’s method is used as the statistics framework of this paper. To do so, first, weighted kinematic sensitivity is introduced and its mathematical formulation is presented. Then, the application of the proposed method is illustrated by implementing the proposed method on two case studies, namely 3-RPR and 6-DOF Gough–Stewart parallel robots. Weighted kinematic sensitivity is calculated over the robot workspace, and consequently, weighted kinematic sensitivity and conventional methods and indices are compared. From the obtained results, it can be inferred that conventional methods predict sensitivity more conservative and the proposed method is more realistic and closer to the reality.