Towards Accurate Solution of Robot Hand-eye Relationship Based on the LMI-SDP Optimization

doi:10.3901/JME.2023.17.109

Abstract

Abstract: Accurate solution of the robot hand-eye relationship (X) is extremely important for visually-guided robotic operation, and is usually symbolized by the AX=XB equation. The existing methodologies always calibrate the X matrices using the separation of the rotational and translational components, causing the calibration error accumulation. Meanwhile, the minimum singular value of the regression matrix in the derived linear equation affects the accuracy of the calibration results. To this end, a novel and generic calibration methodology is proposed for solving the AX=XBproblem using the LMI-SDP (linear matrix inequality and semi-definite programming) optimization to simultaneously calibrate the optimal solution. In this approach, the linear form of the calibration equation is retrieved by means of the Kronecker product, and formulated as a convex optimization problem involving the unknown variable matrix X combined with the QR decomposition form of the regression matrix, in which the simultaneous solution is obtained via the LMI-SDP toolbox. Through simulation analysis and calibration experiments with different noise levels and data pairs, the proposed method is compared to the iterative method and the Dual Quaternion-based approach. The results show that the proposed method outperforms traditional methods in terms of accuracy and effectiveness, and owns the signification for the generalization and application of robot hand-eye system.

Key words: simultaneous coordinate calibration, kronecker product, lmi-sdp optimization, eye-hand equation

CLC Number:

TG156

FU Zhongtao, RAO Shuhang, PAN Jianbin, LI Miao, HUANG Tao, CHEN Xubing. Towards Accurate Solution of Robot Hand-eye Relationship Based on the LMI-SDP Optimization[J]. Journal of Mechanical Engineering, 2023, 59(17): 109-115.

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