针对工业机器人在高度制造领域精度不高的问题,本文提出了一种基于POE模型的工业机器人运动学参数二次辨识方法。阐述了基于指数积(Product of exponential, POE)模型的运动学误差模型构建方法,并建立基于POE误差模型的适应度函数;为实...针对工业机器人在高度制造领域精度不高的问题,本文提出了一种基于POE模型的工业机器人运动学参数二次辨识方法。阐述了基于指数积(Product of exponential, POE)模型的运动学误差模型构建方法,并建立基于POE误差模型的适应度函数;为实现高精度的参数辨识,提出了一种二次辨识方法,先利用改进灰狼优化算法(Improved grey wolf optimizer, IGWO)实现运动学参数误差的粗辨识,初步将Staubli TX60型机器人的平均位置误差和平均姿态误差分别从(0.648 mm, 0.212°)降低为(0.457 mm, 0.166°);为进一步提高机器人的精度性能,再通过LM(Levenberg-Marquard)算法进行参数误差的精辨识,最终将Staubli TX60型机器人平均位置误差和平均姿态误差进一步降低为(0.237 mm, 0.063°),机器人平均位置误差和平均姿态误差分别降低63.4%和70.2%。为了验证上述二次辨识方法的稳定性,随机选取5组辨识数据集和验证数据集进行POE误差模型的参数误差辨识,结果表明提出的二次辨识方法能够稳定、精确地辨识工业机器人运动学参数误差。展开更多
Maximum product spacing for stress–strength model based on progressive Type-II hybrid censored samples with different cases has been obtained.This paper deals with estimation of the stress strength reliability model ...Maximum product spacing for stress–strength model based on progressive Type-II hybrid censored samples with different cases has been obtained.This paper deals with estimation of the stress strength reliability model R=P(Y<X)when the stress and strength are two independent exponentiated Gumbel distribution random variables with different shape parameters but having the same scale parameter.The stress–strength reliability model is estimated under progressive Type-II hybrid censoring samples.Two progressive Type-II hybrid censoring schemes were used,Case I:A sample size of stress is the equal sample size of strength,and same time of hybrid censoring,the product of spacing function under progressive Type-II hybrid censoring schemes.Case II:The sample size of stress is a different sample size of strength,in which the life-testing experiment with a progressive censoring scheme is terminated at a random time T 2 e0;1T.The maximum likelihood estimation and maximum product spacing estimation methods under progressive Type-II hybrid censored samples for the stress strength model have been discussed.A comparison study with classical methods as the maximum likelihood estimation method is discussed.Furthermore,to compare the performance of various cases,Markov chain Monte Carlo simulation is conducted by using iterative procedures as Newton Raphson or conjugate-gradient procedures.Finally,two real datasets are analyzed for illustrative purposes,first data for the breaking strengths of jute fiber,and the second data for the waiting times before the service of the customers of two banks.展开更多
Kinematic calibration is a reliable way to improve the accuracy of parallel manipulators, while the error model dramatically afects the accuracy, reliability, and stability of identifcation results. In this paper, a c...Kinematic calibration is a reliable way to improve the accuracy of parallel manipulators, while the error model dramatically afects the accuracy, reliability, and stability of identifcation results. In this paper, a comparison study on kinematic calibration for a 3-DOF parallel manipulator with three error models is presented to investigate the relative merits of diferent error modeling methods. The study takes into consideration the inverse-kinematic error model, which ignores all passive joint errors, the geometric-constraint error model, which is derived by special geometric constraints of the studied RPR-equivalent parallel manipulator, and the complete-minimal error model, which meets the complete, minimal, and continuous criteria. This comparison focuses on aspects such as modeling complexity, identifcation accuracy, the impact of noise uncertainty, and parameter identifability. To facilitate a more intuitive comparison, simulations are conducted to draw conclusions in certain aspects, including accuracy, the infuence of the S joint, identifcation with noises, and sensitivity indices. The simulations indicate that the complete-minimal error model exhibits the lowest residual values, and all error models demonstrate stability considering noises. Hereafter, an experiment is conducted on a prototype using a laser tracker, providing further insights into the diferences among the three error models. The results show that the residual errors of this machine tool are signifcantly improved according to the identifed parameters, and the complete-minimal error model can approach the measurements by nearly 90% compared to the inverse-kinematic error model. The fndings pertaining to the model process, complexity, and limitations are also instructive for other parallel manipulators.展开更多
After having laid down the Axiom of Algebra, bringing the creation of the square root of -1 by Euler to the entire circle and thus authorizing a simple notation of the nth roots of unity, the author uses it to organiz...After having laid down the Axiom of Algebra, bringing the creation of the square root of -1 by Euler to the entire circle and thus authorizing a simple notation of the nth roots of unity, the author uses it to organize homogeneous divisions of the limited development of the exponential function, that is opening the way to the use of a whole bunch of new primary functions in Differential Calculus. He then shows how new supercomplex products in dimension 3 make it possible to calculate fractals whose connexity depends on the product considered. We recall the geometry of convex polygons and regular polygons.展开更多
以三轴立式加工中心为研究对象,提出一种基于指数积(Product of exponential,POE)旋量理论的几何误差综合建模方法。首先根据误差和旋量的几何定义建立3个旋量来表示各个轴的6项基本几何误差元素,综合3个旋量建立各个轴的误差POE模型;...以三轴立式加工中心为研究对象,提出一种基于指数积(Product of exponential,POE)旋量理论的几何误差综合建模方法。首先根据误差和旋量的几何定义建立3个旋量来表示各个轴的6项基本几何误差元素,综合3个旋量建立各个轴的误差POE模型;其次在POE建模时考虑垂直度误差,根据垂直度误差的几何属性提出获得垂直度误差POE模型的两种方法;此外根据机床拓扑结构确定旋量和相应指数矩阵的相乘次序,建立综合几何误差POE模型。最后在某三轴立式加工中心上进行建模实验,结果表明本文方法足够有效和精确,根据综合误差模型得到数控机床的误差场。展开更多
Serial robots are used to handle workpieces with large dimensions, and calibrating kinematic parameters is one of the most efficient ways to upgrade their accuracy. Many models are set up to investigate how many kinem...Serial robots are used to handle workpieces with large dimensions, and calibrating kinematic parameters is one of the most efficient ways to upgrade their accuracy. Many models are set up to investigate how many kinematic parameters can be identified to meet the minimal principle, but the base frame and the kinematic parameter are indistinctly calibrated in a one-step way. A two-step method of calibrating kinematic parameters is proposed to improve the accuracy of the robot＇s base frame and kinematic parameters. The forward kinematics described with respect to the measuring coordinate frame are established based on the product- of-exponential （POE） formula. In the first step the robot＇s base coordinate frame is calibrated by the unit quaternion form. The errors of both the robot＇s reference configuration and the base coordinate frame＇s pose are equivalently transformed to the zero-position errors of the robot＇s joints. The simplified model of the robot＇s positioning error is established in second-power explicit expressions. Then the identification model is finished by the least square method, requiring measuring position coordinates only. The complete subtasks of calibrating the robot＇ s 39 kinematic parameters are finished in the second step. It＇s proved by a group of calibration experiments that by the proposed two-step calibration method the average absolute accuracy of industrial robots is updated to 0.23 mm. This paper presents that the robot＇s base frame should be calibrated before its kinematic parameters in order to upgrade its absolute positioning accuracy.展开更多
文摘针对工业机器人在高度制造领域精度不高的问题,本文提出了一种基于POE模型的工业机器人运动学参数二次辨识方法。阐述了基于指数积(Product of exponential, POE)模型的运动学误差模型构建方法,并建立基于POE误差模型的适应度函数;为实现高精度的参数辨识,提出了一种二次辨识方法,先利用改进灰狼优化算法(Improved grey wolf optimizer, IGWO)实现运动学参数误差的粗辨识,初步将Staubli TX60型机器人的平均位置误差和平均姿态误差分别从(0.648 mm, 0.212°)降低为(0.457 mm, 0.166°);为进一步提高机器人的精度性能,再通过LM(Levenberg-Marquard)算法进行参数误差的精辨识,最终将Staubli TX60型机器人平均位置误差和平均姿态误差进一步降低为(0.237 mm, 0.063°),机器人平均位置误差和平均姿态误差分别降低63.4%和70.2%。为了验证上述二次辨识方法的稳定性,随机选取5组辨识数据集和验证数据集进行POE误差模型的参数误差辨识,结果表明提出的二次辨识方法能够稳定、精确地辨识工业机器人运动学参数误差。
文摘Maximum product spacing for stress–strength model based on progressive Type-II hybrid censored samples with different cases has been obtained.This paper deals with estimation of the stress strength reliability model R=P(Y<X)when the stress and strength are two independent exponentiated Gumbel distribution random variables with different shape parameters but having the same scale parameter.The stress–strength reliability model is estimated under progressive Type-II hybrid censoring samples.Two progressive Type-II hybrid censoring schemes were used,Case I:A sample size of stress is the equal sample size of strength,and same time of hybrid censoring,the product of spacing function under progressive Type-II hybrid censoring schemes.Case II:The sample size of stress is a different sample size of strength,in which the life-testing experiment with a progressive censoring scheme is terminated at a random time T 2 e0;1T.The maximum likelihood estimation and maximum product spacing estimation methods under progressive Type-II hybrid censored samples for the stress strength model have been discussed.A comparison study with classical methods as the maximum likelihood estimation method is discussed.Furthermore,to compare the performance of various cases,Markov chain Monte Carlo simulation is conducted by using iterative procedures as Newton Raphson or conjugate-gradient procedures.Finally,two real datasets are analyzed for illustrative purposes,first data for the breaking strengths of jute fiber,and the second data for the waiting times before the service of the customers of two banks.
基金Supported by National Key Research and Development Program of China(Grant No.2019YFA0709001)National Natural Science Foundation of China(Grant Nos.52022056,51875334,52205031 and 52205034)National Key Research and Development Program of China(Grant No.2017YFE0111300).
文摘Kinematic calibration is a reliable way to improve the accuracy of parallel manipulators, while the error model dramatically afects the accuracy, reliability, and stability of identifcation results. In this paper, a comparison study on kinematic calibration for a 3-DOF parallel manipulator with three error models is presented to investigate the relative merits of diferent error modeling methods. The study takes into consideration the inverse-kinematic error model, which ignores all passive joint errors, the geometric-constraint error model, which is derived by special geometric constraints of the studied RPR-equivalent parallel manipulator, and the complete-minimal error model, which meets the complete, minimal, and continuous criteria. This comparison focuses on aspects such as modeling complexity, identifcation accuracy, the impact of noise uncertainty, and parameter identifability. To facilitate a more intuitive comparison, simulations are conducted to draw conclusions in certain aspects, including accuracy, the infuence of the S joint, identifcation with noises, and sensitivity indices. The simulations indicate that the complete-minimal error model exhibits the lowest residual values, and all error models demonstrate stability considering noises. Hereafter, an experiment is conducted on a prototype using a laser tracker, providing further insights into the diferences among the three error models. The results show that the residual errors of this machine tool are signifcantly improved according to the identifed parameters, and the complete-minimal error model can approach the measurements by nearly 90% compared to the inverse-kinematic error model. The fndings pertaining to the model process, complexity, and limitations are also instructive for other parallel manipulators.
文摘After having laid down the Axiom of Algebra, bringing the creation of the square root of -1 by Euler to the entire circle and thus authorizing a simple notation of the nth roots of unity, the author uses it to organize homogeneous divisions of the limited development of the exponential function, that is opening the way to the use of a whole bunch of new primary functions in Differential Calculus. He then shows how new supercomplex products in dimension 3 make it possible to calculate fractals whose connexity depends on the product considered. We recall the geometry of convex polygons and regular polygons.
文摘以三轴立式加工中心为研究对象,提出一种基于指数积(Product of exponential,POE)旋量理论的几何误差综合建模方法。首先根据误差和旋量的几何定义建立3个旋量来表示各个轴的6项基本几何误差元素,综合3个旋量建立各个轴的误差POE模型;其次在POE建模时考虑垂直度误差,根据垂直度误差的几何属性提出获得垂直度误差POE模型的两种方法;此外根据机床拓扑结构确定旋量和相应指数矩阵的相乘次序,建立综合几何误差POE模型。最后在某三轴立式加工中心上进行建模实验,结果表明本文方法足够有效和精确,根据综合误差模型得到数控机床的误差场。
基金Supported by State Key Lab of Digital Manufacturing Equipment & Technology(Grant No.DMETKF2015013)National Natural Science Foundation of China(Grant No.51305008)
文摘Serial robots are used to handle workpieces with large dimensions, and calibrating kinematic parameters is one of the most efficient ways to upgrade their accuracy. Many models are set up to investigate how many kinematic parameters can be identified to meet the minimal principle, but the base frame and the kinematic parameter are indistinctly calibrated in a one-step way. A two-step method of calibrating kinematic parameters is proposed to improve the accuracy of the robot＇s base frame and kinematic parameters. The forward kinematics described with respect to the measuring coordinate frame are established based on the product- of-exponential （POE） formula. In the first step the robot＇s base coordinate frame is calibrated by the unit quaternion form. The errors of both the robot＇s reference configuration and the base coordinate frame＇s pose are equivalently transformed to the zero-position errors of the robot＇s joints. The simplified model of the robot＇s positioning error is established in second-power explicit expressions. Then the identification model is finished by the least square method, requiring measuring position coordinates only. The complete subtasks of calibrating the robot＇ s 39 kinematic parameters are finished in the second step. It＇s proved by a group of calibration experiments that by the proposed two-step calibration method the average absolute accuracy of industrial robots is updated to 0.23 mm. This paper presents that the robot＇s base frame should be calibrated before its kinematic parameters in order to upgrade its absolute positioning accuracy.
