Robust Calibration Algorithm Based on Lie Algebra Robot Base Coordinate System

Base coordinate calibration is a key issue for a robot to complete a task in the same coordinate system, especially in industrial operations. In order to solve the orthogonality problem when calibrating the rotation part, the traditional calibration algorithm usually performs quadratic orthogonalization or uses a parameterized rotation matrix, and then obtains the translation part according to the rotation matrix, which greatly affects the accuracy and robustness of the calibration results. To solve this problem, a Lie algebra calibration algorithm based on Random Sample Consensus (RANSAC) is proposed in this paper. Specifically, the pose relationship between the end effector of the robot and the external measuring equipment is obtained through the closed-chain structure of the robot, and the error model is constructed through four sets of non-coplanar configurations, and the Lie algebra corresponding to the transformation matrix is estimated by Gauss-Newton. Furthermore, facing the influence of noise in the actual environment, it is proposed to use RANSAC to eliminate the influence of unreliable data on the calibration results. The proposed calibration method not only significantly reduces the impact of measurement noise on the calibration results but also solves the error propagation problem in step-by-step calibration by avoiding the orthogonalization issue of the rotation matrix. This ensures the consistency of the calibration results. Finally, the superiority of the proposed algorithm in accuracy and robustness is verified by numerical simulation experiments, and the algorithm also provides an effective reference for other pose calibration problems.

I. Introduction

High precision operation plays a vital role in the practical application of industrial robots, such as in 3C high precision assembly [1] [2], medical robot operation [3] [4], aerospace operations and other scenarios [5] [6]. As the most commonly used perception tool for industrial robots, the camera plays an important role in the intelligentization of the robot. Generally speaking, the robot uses the camera as a reference when operating [7]. However, due to the spatial relationship between the camera and the robot, this uncertain spatial relationship inevitably has errors, which affect the accuracy of robot operation guided by the camera. Calibrating the relationship between the robot base coordinate system (RBCS) and the camera world coordinate system (WCS) becomes an important step to improve the high precision operation of the robot [8].