Efficient Kinematic Calibration for Articulated Robot Based on Unit Dual Quaternion

Abstract

Removing the parameter redundancy in the kinematic error model does improve the robustness of parameter identification. However, this does not help much on saving the calculation time on the error compensation process, which is closely related to the data structure used for representing rigid-body motion. Compared with the homogenous transformation matrix (HTM), the unit dual quaternion (UDQ) can describe the rigid-body motion in term of an array with eight entries, thus it is a conducive data structure for efficient kinematic computation. In this work, the exponential and logarithm mappings of a UDQ are defined explicitly, so that the relationship between finite and instantaneous motions is set up under the exponential coordinate. Thereafter, by defining the adjoint operator of UDQ to transform the twist under different frames, the linearized kinematic error models are built with local product-of-exponentials (POE) formula. This facilitates the upcoming parameter identification and error compensation processes. Specially, the counts of elementary operations are evaluated throughout the compensation processes, which shows the number of arithmetic operations are greatly reduced compared with using POE formula based on HTM. Additionally, the simple data structure in term of 1-D arrays saves the data dispatch time when performing adjoint operations. These make the developed model suitable for calibration of articulated robot with a long sequence of trajectories. Experiments on a 6-degree-of-freedom industrial robot validate the effectiveness of proposed approach.