A High-Precision Hand–Eye Coordination Localization Method under Convex Relaxation Optimization

Abstract

Traditional switching operations require on-site work, and the high voltage generated by arc discharges can pose a risk of injury to the operator. Therefore, a combination of visual servo and robot control is used to localize the switching operation and construct hand–eye calibration equations. The solution to the hand–eye calibration equations is coupled with the rotation matrix and translation vectors, and it depends on the initial value determination. This article presents a convex relaxation global optimization hand–eye calibration algorithm based on dual quaternions. Firstly, the problem model is simplified using the mathematical tools of dual quaternions, and then the linear matrix inequality convex optimization method is used to obtain a rotation matrix with higher accuracy. Afterwards, the calibration equations of the translation vectors are rewritten, and a new objective function is established to solve the coupling influence between them, maintaining positioning precision at approximately 2.9 mm. Considering the impact of noise on the calibration process, Gaussian noise is added to the solutions of the rotation matrix and translation vector to make the data more closely resemble the real scene in order to evaluate the performance of different hand–eye calibration algorithms. Eventually, an experiment comparing different hand–eye calibration methods proves that the proposed algorithm is better than other hand–eye calibration algorithms in terms of calibration accuracy, robustness to noise, and stability, satisfying the accuracy requirements of switching operations.

Keywords

• switching operation
• visual servo
• convex relaxation
• hand–eye coordination