Kinematic calibration of a 6-DOF hybrid robot by considering multicollinearity in the identification Jacobian

This paper presents a systematic approach for the kinematic calibration of a 6-DOF hybrid polishing robot. It concentrates particularly on dealing with ill-conditioning that arises from multicollinearity in the identification Jacobian as a consequence of limited pose measurements. A linearized error model is formulated, using screw theory, by considering all possible source errors at the joint/link level. Calibration is based upon pose error measurements captured using a laser tracker when the polishing head undergoes pure translation within the task workspace. A two-step procedure for error parameter estimation and pose error compensation is then proposed: (1) coarse estimation and compensation of the encoder offsets using linear least squares; and (2) fine estimation of the whole set of identifiable error parameters using a Liu estimation and subsequent modification of the NC trajectory dataset of the polishing head. Both simulations and experiments on a prototype machine show that the overall standard deviation of the error parameters identified by Liu estimator is much less than that estimated by linear least squares, confirming its greater robustness in the presence of measurement uncertainty. The proposed approach results in satisfactory pose accuracy of the polishing head throughout the entire task workspace