External Kinematic Calibration of Hybrid Kinematics Machine Utilizing Lower-DOF Planar Parallel Kinematics Mechanisms

Abstract

This paper presents the implementation of nonlinear least squares and iterative linear least squares algorithms for external kinematic calibration of a hybrid kinematics machine composed of two 3PRR planar parallel kinematics mechanisms by utilizing a laser tracker. First the hand-eye and robot-world transformations were obtained by a separable closed-form solution and refined by the nonlinear least squares. Subsequently, the geometric parameters of the machine’s mechanisms were estimated using the two algorithms. Due to the rank deficiency, we implemented the nonlinear least squares algorithm through a subset selection approach in which we performed the estimation in two steps. We iterated the closed-form solution of the linear least squares until the solution converges to the actual values. We have shown that the nonlinear least squares algorithm successfully refined the hand-eye and robot-world transformations and outperformed the iterative linear squares algorithm in the estimation of the geometric parameters of the mechanisms.