第24卷第2期 2016年2月
文章编号
1004-924X(2016)02-0365-07
光学精密工程
Optics and Precision Engineering
柔性测量臂的RPY建模与误差标定
赵磊，赵新华，王收军，葛为民
Vol. 24No. 2
Feb.2016
（1.天津市先进机电系统设计与智能控制重点实验室；2.天津理工大学机械工程学院，天津300384）摘要：为了提高1P3R型柔性测量臂的检测精度，提出了一种自适应误差标定方法来完成它的参数标定和误差补偿。首行实数编码；在遗传算法(GA)中引人自适应控制算子，提高了父代种群的多样性和最优个体变异数量；最后，对比分析了归-化GA、一般GA和最小二乘法等3种算法的误差标定精度及其收效性，验证了所提出方法的有效性和可行性。结果显示；归一化GA仅用328代导优计算，其精度达到5.2μm，收敏速度是一般GA的2.3倍且精度提高了3.1μm；最小二乘法经20次选代计算后停止收敛，精度仅为18.4μm。实验结果表明：归化GA其有收敏速度快、标定精度高
和收敏稳定性好等明显优势，更易于实现该类测量机的高精度检测。关键词：柔性测量臂；RPY理论；归一化遗传算法；误差标定
中图分类号：TH721
文献标识码：A
doi10.3788/OPE.20162402.0365
RPYmodelinganderrorcalibrationofflexiblemeasuringarm
ZHAOLei'ZHAOXin-hua,WANGShou-jun，GEWei-min
(1.Tianjin Key Laboratory of Design and Intelligent Control of Aduanced Mechatronical System; 2.School of Mechanic Engineering,TianjinUniversity of Technology,Tianjin 300384,China)
Correspondingauthor,E-mail:leizhaotjut163.com
Abstract: An adaptive error calibration method was proposed to complete parameter calibration and er ror compensation to realize the high accuracy test for a 1P3R flexible measuring arm. Firstly, a kine-matic model of 1P3R flexible measuring arm was built based on RPY theory and a differential method was used to deduce the error model of system. Then, the real number encoding was performed based on the theory of Markova chain convergence. Adaptive control factors were added to Genetic Algo-rithm(GA) to improve population diversity and the quantity of the best individual. Finally,the cali-bration accuracy and convergence performance of a normalized GA, a general GA and least square method were compared and analyzed and the results were used to verify the feasibility and effective ness of the proposed method. It shows that the accuracy of the normalized GA has been enhanced from 3. 1 μm to 5. 2 μm just after 328 generation searching, and its convergence velocity is 2. 3 times that of the general GA. Moreover, the convergence of least square method is stopped after 2o generations and its calibration accuracy is only 18. 4 μm. Experiments indicate that normalized GA is characterized by some advantages of fast convergence speed, high calibration accuracy and better stability. It is suitable
收稿日期：2015-08-20；修订日期：2015-09-15
基金项目：国家自然科学基金资助项目（No.51275353)；天津市应用基础与前沿技术研究计划重点资助项目（No
14JCZDJC39100）；天津市自然科学基金资助项目（No.13JCYBJC17700），天津市高等学校科技发展计划资助项目(No.20140401)