凸松弛全局优化机器人手眼标定

doi:10.11772/j.issn.1001-9081.2017.05.1451

计算机应用 ›› 2017, Vol. 37 ›› Issue (5): 1451-1455.DOI: 10.11772/j.issn.1001-9081.2017.05.1451

• 计算机视觉与虚拟现实 • 上一篇下一篇

凸松弛全局优化机器人手眼标定

李巍¹, 吕乃光^1,2, 董明利², 娄小平²

1. 北京邮电大学信息光子学与光通信研究院, 北京 100876;
2. 光电测试技术北京市重点实验室(北京信息科技大学), 北京 100192

收稿日期:2016-09-30 修回日期:2016-12-22 出版日期:2017-05-10 发布日期:2017-05-16
通讯作者: 李巍
作者简介:李巍(1988-),男,河北承德人,博士研究生,主要研究方向:视觉测量、机器视觉;吕乃光(1944-),男,安徽临泉人,教授,博士生导师,主要研究方向:信息光学、光电子学、光电测试;董明利(1965-),女,辽宁鞍山人,教授,博士生导师,博士,主要研究方向:视觉测量、精密测量与仪器;娄小平(1970-),女,河南临颍人,教授,主要研究方向:视觉测量、精密光电测试。
基金资助:
国家863计划项目（2015AA042308）；国家重大科学仪器设备开发专项（2013YQ22089304）；光电测试技术北京市重点实验室开放课题（GDKF2016005）。

Robot hand-eye calibration by convex relaxation global optimization

LI Wei¹, LYU Naiguang^1,2, DONG Mingli², LOU Xiaoping²

1. Institute of Optical Communication & Optoelectronics, Beijing University of Posts & Telecommunications, Beijing 100876, China;
2. Beijing Key Laboratory of Optoelectronics Measurement Technology(Beijing Information Science & Technology University), Beijing 100192, China

Received:2016-09-30 Revised:2016-12-22 Online:2017-05-10 Published:2017-05-16
Supported by:
This work is partially supported by the National High Technology Research and Development Program (863 Program) of China (2015AA042308), the National Science Instrument Program (2013YQ22089304), the Open Project of Beijing Key Laboratory of Optoelectronics Measurement Technology (GDKF2016005).

摘要/Abstract

摘要： 针对机器人运动学正解及相机的外参数标定存在偏差时，基于非线性最优化的手眼标定算法无法确保目标函数收敛到全局极小值的问题，提出基于四元数理论的凸松弛全局最优化手眼标定算法。考虑到机械手末端相对运动旋转轴之间的夹角对标定方程求解精度的影响，首先利用随机抽样一致性（RANSAC）算法对标定数据中旋转轴之间的夹角进行预筛选，再利用四元数参数化旋转矩阵，建立多项式几何误差目标函数和约束，采用基于线性矩阵不等式（LMI）凸松弛全局优化算法求解全局最优手眼变换矩阵。实测结果表明，该算法可以求得全局最优解，手眼变换矩阵几何误差平均值不大于1.4 mm，标准差小于0.16 mm，结果稍优于四元数非线性最优化算法。

关键词: 机器人, 手眼标定, 四元数, 全局优化, 随机抽样一致性, 线性矩阵不等式

Abstract: Hand-eye calibration based on nonlinear optimization algorithm can not guarantee the convergence of the objective function to the global minimum, when there are errors in both robot forward kinematics and camera external parameters calibration. To solve this tricky problem, a new hand-eye calibration algorithm based on quaternion theory by convex relaxation global optimization was proposed. The critical factor of the angle between different interstation rotation axes by a manipulator was considered, an optimal set of relative movements from calibration data was selected by Random Sample Consensus (RANSAC) approach. Then, rotation matrix was parameterized by a quaternion, polynomial geometric error objective function and constraints were established based on Linear Matrix Inequality (LMI) convex relaxation global optimization algorithm, and the hand-eye transformation matrix could be solved for global optimum. Experimental validation on real data was provided. Compared with the classical quaternion nonlinear optimization algorithm, the proposed algorithm can get global optimal solution, the geometric mean error of hand-eye transformation matrix is no more than 1.4 mm, and the standard deviation is less than 0.16 mm.

Key words: robot, hand-eye calibration, quaternion, global optimization, Random Sample Consensus (RANSAC), Linear Matrix Inequality (LMI)

中图分类号:

TP242.2

李巍, 吕乃光, 董明利, 娄小平. 凸松弛全局优化机器人手眼标定[J]. 计算机应用, 2017, 37(5): 1451-1455.

LI Wei, LYU Naiguang, DONG Mingli, LOU Xiaoping. Robot hand-eye calibration by convex relaxation global optimization[J]. Journal of Computer Applications, 2017, 37(5): 1451-1455.

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凸松弛全局优化机器人手眼标定

Robot hand-eye calibration by convex relaxation global optimization

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