A screw theory based approach to determining the identifiable parameters for calibration of parallel manipulators

Abstract

Establishing complete, continuous and minimal error models is fundamentally significant for the calibration of robotic manipulators. Motivated by practical needs for models suited to coarse plus fine calibration strategies, this paper presents a screw theory based approach to determining the identifiable geometric errors of parallel manipulators at the model level. The paper first addresses two specific issues: (1) developing a simple approach that enables all encoder offsets to be retained in the minimal error model of serial kinematic chains; and (2) exploiting a fully justifiable criterion that allows the detection of the unidentifiable structural errors of parallel manipulators. Merging these two threads leads to a new, more rigorous formula for calculating precisely the number of identifiable geometric errors, including both encoder offsets and identifiable structural errors, of parallel manipulators. It shows that the identifiability of structural errors in parallel manipulators depends highly upon joint geometry and actuator arrangement of the limb involved. The process is used to determine the unidentifiable structural errors of two lower mobility parallel mechanisms to illustrate the effectiveness of the proposed approach.