基于LMI-SDP优化的机器人手眼关系精确求解

doi:10.3901/JME.2023.17.109

机械工程学报 ›› 2023, Vol. 59 ›› Issue (17): 109-115.doi: 10.3901/JME.2023.17.109

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基于LMI-SDP优化的机器人手眼关系精确求解

付中涛¹, 饶书航¹, 潘嘉滨^1,2, 李淼³, 黄涛⁴, 陈绪兵¹

1. 武汉工程大学机电工程学院武汉 430205;
2. 上海大学机电工程与自动化学院上海 200444;
3. 武汉大学工业科学研究院武汉 430072;
4. 华中科技大学数字制造装备与技术国家重点实验室武汉 430074

收稿日期:2022-09-13 修回日期:2022-12-14 出版日期:2023-09-05 发布日期:2023-11-16
通讯作者: 陈绪兵(通信作者),男,1974年出生,博士,教授,博士研究生导师。主要研究方向为智能制造,机器人焊接。E-mail:bluegif@gmail.com
作者简介:付中涛,男,1987年出生,博士,副教授,硕士研究生导师。主要研究方向为机器人理论及技术在智能制造与智慧医疗的应用。E-mail:hustfzt@gmail.com;饶书航,男,1998年出生,硕士研究生。主要研究方向为机器人视觉。E-mail:myLucky1998@163.com
基金资助:
国家自然科学基金（51875415，51805380）、湖北省重点研发计划（2022BCA138）、湖北省中央引导地方科技发展专项（2019ZYYD010）和数字制造装备与技术国家重点实验室开放基金（DMETKF2022019）资助项目。

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

FU Zhongtao¹, RAO Shuhang¹, PAN Jianbin^1,2, LI Miao³, HUANG Tao⁴, CHEN Xubing¹

1. School of Mechanical and Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205;
2. School of Mechanical Engineering and Automation, Shanghai University, Shanghai 200444;
3. The Institute of Technological Sciences, Wuhan University, Wuhan 430072;
4. State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074

Received:2022-09-13 Revised:2022-12-14 Online:2023-09-05 Published:2023-11-16

摘要/Abstract

摘要： 机器人手眼关系（X）的精确求解对于视觉导引的机器人操作及其重要，通常用方程AX=XB表示。现有方法通常采用旋转矩阵与平移分量分离方式分步标定X，从而导致标定误差的累积。同时，推导的线性方程中回归矩阵的最小奇异值影响标定结果的精度。为此，提出了一种新颖且通用的AX=XB标定方法，采用LMI-SDP （线性矩阵不等式与半正定规划）优化同步标定出方程AX=XB的最优解。在此方法中，通过Kronecker积获得标定方程的线性形式，结合回归矩阵的QR分解形式转化为关于未知变量X的凸约束优化问题，通过LMI-SDP工具箱得到精确的同步解。通过考虑到不同噪声水平和数据对的仿真分析以及标定试验，对提出的方法与迭代算法、对偶四元数方法进行比较。结果表明，所提出的方法相比传统方法表现出更好的准确性和有效性，对于实现机器人手眼系统的推广与应用具有重要意义。

关键词: 同步标定, Kronecker积, LMI-SDP优化, 手眼方程

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

中图分类号:

TG156

付中涛, 饶书航, 潘嘉滨, 李淼, 黄涛, 陈绪兵. 基于LMI-SDP优化的机器人手眼关系精确求解[J]. 机械工程学报, 2023, 59(17): 109-115.

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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基于LMI-SDP优化的机器人手眼关系精确求解

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

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