In this paper we define the tensor products of spaces of exponential type vectors of closed unbounded operators in Banach spaces. Using the real method of interpolation （K-functional） we prove the interpolation theo...In this paper we define the tensor products of spaces of exponential type vectors of closed unbounded operators in Banach spaces. Using the real method of interpolation （K-functional） we prove the interpolation theorems that permit to characterize of tensor products of spaces of exponential type vectors, We show an application of abstract results to the theory of regular elliptic operators on bounded domains. For such operators the exponential type vectors are root vectors. Thus we describe the tensor products of root vectors of regular elliptic operators on bounded domains.展开更多
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
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
The inverse kinematics problems of robots are usually decomposed into several Paden–Kahan subproblems based on the product of exponential model. However, the simple combination of subproblems cannot solve all the inv...The inverse kinematics problems of robots are usually decomposed into several Paden–Kahan subproblems based on the product of exponential model. However, the simple combination of subproblems cannot solve all the inverse kinematics problems, and there is no common approach to solve arbitrary three-joint subproblems in an arbitrary postural relationship. The novel algebraic geometric (NAG) methods that obtain the general closed-form inverse kinematics for all types of three-joint subproblems are presented in this paper. The geometric and algebraic constraints are used as the conditions precedent to solve the inverse kinematics of three-joint subproblems. The NAG methods can be applied in the inverse kinematics of three-joint subproblems in an arbitrary postural relationship. The inverse kinematics simulations of all three-joint subproblems are implemented, and simulation results indicating that the inverse solutions are consistent with the given joint angles validate the general closed-form inverse kinematics. Huaque III minimally invasive surgical robot is used as the experimental platform for the simulation, and a master–slave tracking experiment is conducted to verify the NAG methods. The simulation result shows the inverse solutions and six sets given joint angles are consistent. Additionally, the mean and maximum of the master–slave tracking experiment for the closed-form solution are 0.1486 and 0.4777 mm, respectively, while the mean and maximum of the master–slave tracking experiment for the compensation method are 0.3188 and 0.6394 mm, respectively. The experiments results demonstrate that the closed-form solution is superior to the compensation method. The results verify the proposed general closed-form inverse kinematics based on the NAG methods.展开更多
文摘In this paper we define the tensor products of spaces of exponential type vectors of closed unbounded operators in Banach spaces. Using the real method of interpolation （K-functional） we prove the interpolation theorems that permit to characterize of tensor products of spaces of exponential type vectors, We show an application of abstract results to the theory of regular elliptic operators on bounded domains. For such operators the exponential type vectors are root vectors. Thus we describe the tensor products of root vectors of regular elliptic operators on bounded domains.
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.
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the Foundation for Innovative Research Groups of the National Natural Science Foundation of China(Grant No.51521003)the National Natural Science Foundation of China(Grant No.61803341)the Self-planned Task of State Key Laboratory of Robotics and System(Harbin Institute of Technology)(Grant No.SKLRS202009B).No conflicts of interest exist in this paper.
文摘The inverse kinematics problems of robots are usually decomposed into several Paden–Kahan subproblems based on the product of exponential model. However, the simple combination of subproblems cannot solve all the inverse kinematics problems, and there is no common approach to solve arbitrary three-joint subproblems in an arbitrary postural relationship. The novel algebraic geometric (NAG) methods that obtain the general closed-form inverse kinematics for all types of three-joint subproblems are presented in this paper. The geometric and algebraic constraints are used as the conditions precedent to solve the inverse kinematics of three-joint subproblems. The NAG methods can be applied in the inverse kinematics of three-joint subproblems in an arbitrary postural relationship. The inverse kinematics simulations of all three-joint subproblems are implemented, and simulation results indicating that the inverse solutions are consistent with the given joint angles validate the general closed-form inverse kinematics. Huaque III minimally invasive surgical robot is used as the experimental platform for the simulation, and a master–slave tracking experiment is conducted to verify the NAG methods. The simulation result shows the inverse solutions and six sets given joint angles are consistent. Additionally, the mean and maximum of the master–slave tracking experiment for the closed-form solution are 0.1486 and 0.4777 mm, respectively, while the mean and maximum of the master–slave tracking experiment for the compensation method are 0.3188 and 0.6394 mm, respectively. The experiments results demonstrate that the closed-form solution is superior to the compensation method. The results verify the proposed general closed-form inverse kinematics based on the NAG methods.
