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-SDPOptimization

作　　者：付中涛 饶书航 潘嘉滨 李淼 黄涛 陈绪兵[1] FU Zhongtao;RAO Shuhang;PAN Jianbin;LI Miao;HUANG Tao;CHEN Xubing(School of Mechanical and Electrical Engineering,Wuhan Institute of Technology,Wuhan 430205;School of Mechanical Engineering and Automation,Shanghai University,Shanghai 200444;The Institute of Technological Sciences,Wuhan University,Wuhan 430072;State Key Laboratory of Digital Manufacturing Equipment and Technology,Huazhong University of Science and Technology,Wuhan 430074)

机构地区：[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

出　　处：《机械工程学报》2023年第17期109-115,共7页Journal of Mechanical Engineering

基　　金：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);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。

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。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-XB problem 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.

关 键 词：同步标定 KRONECKER积 LMI-SDP优化 手眼方程 

分 类 号：TG156[金属学及工艺—热处理]