A Self-Correctional Hand-Eye Calibration Regime Using Extensive Pose-Image Pairs with Quantifiable Gaussian Errors from Homogeneous Matrices Decomposition

Normally, the eye-to-hand calibration algorithm usually requires 10-20 pairs of coupled robot and object poses in the camera frame to solve the overdetermined linear system of AX=XB. One significant contribution of this research is in quantifying the uncertainties in the results of calibration. The fixed poses represented as homogeneous matrices can be separated into the rotation vectors and the translation vectors, and the rotation vectors are further decoupled into the magnitudes of rotation and the normal vectors representing the direction of rotation. The Gaussian distributions of the magnitudes of rotation, the direction cosines from the average normal direction, and L2 norms of the translation are computed. The spreads of the distributions will not only serve as the close-loop convergence parameters for self-correcting the calibration result, but also as the indicator for the overall quality of the calibration. In addition, given the same set of 100 pose pairs, under the self-correctional approach, we study and compare the rate of convergence, the accuracy of the final calibration results, and the speed of calibration among the algorithms for overdetermined AX=XB developed by Tsai, Park, Horaud, Andreff, and Danillidis.

I. Introduction

Using RGBD camera to provide depth and color information is used to provide the sensing capabilities of the work targets and the environment. As an active research area, computer vision and vision-based artificial intelligence are used widely to segment and identify objects of interest [1] and acquire objects’ poses in three-dimensional space [2], [3]. Object detection has now been widely used in many real-world applications, such as autonomous driving, robot vision, video surveillance, etc. For robot’s end effectors to act on identified objects, it is required to transform the objects’ poses from the camera coordinate to the robot’s base coordinate. In the visually guided drilling [4] and grinding [5] applications, accurate hand-eye calibration is needed to precisely position the drill and the grinder. In Li and other’s study on visually guided grinding application [5], a criterion sphere is used to calculate the calibration parameters, thus eliminating the complicated process of tracking correspondences. In addition, a unified objective function is used to model joint parameters and pose parameters. Other areas where the hand-eye calibration can play a major factor include robotic surgery [6], robotic welding [7], machine vision metrology [8], robotic grasping [9], and robotic obstacle avoidance [10].