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Fast error calibration of Flexible Measuring Arm based on an adaptive Genetic Algorithm
Measurement and Control ( IF 2 ) Pub Date : 2021-07-13 , DOI: 10.1177/00202940211030961
Xinhua Zhao 1, 2, 3 , Jiahao Wang 3 , Lei Zhao 1, 2, 3 , Bin Li 1, 2, 3 , Haibo Zhou 1, 2, 3
Affiliation  

With the development of measurement technology, the Flexible Measuring Arm (FMA) is widely used in quality test of automobile processing and industrial production. FMA is a kind of nonlinear system with many parameters. Low cost and efficient calibration method have become the focuses of attention. This article presents a fast calibration method for FMA based on an adaptive Genetic Algorithm (GA) just with several standard balls and a ball plate. It can greatly reduce the calibration cost than common external calibration method which needs high precision instruments and sensors. Firstly, the kinematic model of FMA is established by RPY theory. Secondly, the common GA is optimized and improved, and an adaptive mechanism is added to the algorithms which can realize the automatic adjustment of crossover and mutation operators. A Normalized Genetic Algorithm (NGA) with adaptive mechanism is proposed to complete the optimization calculation. It can improve the numbers of optimal individuals and the convergence speed. So, the search efficiency will be enhanced greatly. Finally, the Least square method (LSM), the General Genetic Algorithm (GGA), and the proposed NGA are respectively used to finish the calibration work. The compensation accuracy and the search efficiency with the above three different algorithms have been systematically analyzed. Experiment indicates that the performance of NGA is much better than LSM and GGA. The data also has proved that the LSM is suitable to complete optimization calculation for linear system. Its convergence stability is much poorer than NGA and GGA because of the ill-condition Jacobin matrix. GGA is easy to fall into local optimization because of the fixed operators. The proposed NGA obviously owns fast convergence speed, high accuracy and better stability than GGA. The position error is reduced from 3.17 to 0.5 mm after compensation with the proposed NGA. Its convergence rate is almost two time of GGA which applies constant genetic factors. The effectiveness and feasibility of proposed method are verified by experiment.



中文翻译:

基于自适应遗传算法的柔性测量臂误差快速标定

随着测量技术的发展,柔性测量臂(FMA)广泛应用于汽车加工和工业生产的质量检测。FMA 是一种具有多参数的非线性系统。低成本、高效的校准方法成为关注的焦点。本文介绍了一种基于自适应遗传算法 (GA) 的 FMA 快速校准方法,仅使用几个标准球和一个球板。与需要高精度仪器和传感器的普通外部校准方法相比,它可以大大降低校准成本。首先,利用RPY理论建立了FMA的运动学模型。其次,对通用遗传算法进行优化改进,在算法中加入自适应机制,实现交叉和变异算子的自动调整。提出了一种具有自适应机制的归一化遗传算法(NGA)来完成优化计算。它可以提高最优个体的数量和收敛速度。因此,搜索效率将大大提高。最后分别使用最小二乘法(LSM)、通用遗传算法(GGA)和提出的NGA完成标定工作。系统分析了上述三种不同算法的补偿精度和搜索效率。实验表明,NGA 的性能远优于 LSM 和 GGA。数据也证明了LSM适合完成线性系统的优化计算。由于存在病态雅各宾矩阵,其收敛稳定性比NGA和GGA差很多。GGA由于操作符固定,容易陷入局部优化。所提出的 NGA 显然比 GGA 具有收敛速度快、精度高和更好的稳定性。使用建议的 NGA 进行补偿后,位置误差从 3.17 毫米减少到 0.5 毫米。它的收敛速度几乎是应用恒定遗传因素的 GGA 的两倍。通过实验验证了所提方法的有效性和可行性。

更新日期:2021-07-14
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