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error modeling and Sensitivity Analysis of a Parallel Robot with SCARA(Selective Compliance Assembly Robot Arm) Motions

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Chinese Journal of Mechanical Engineering 2014年第4期27卷 693-702页

作者： CHEN Yuzhen XIE Fugui LIU Xinjun ZHOU Yanhua Department of Mechanical Engineering Tsinghua University Beijing Key Lab of Precision/Ultra-precision Manufacturing Equipments and Control Tsinghua University Institute of Aircraft Engineering Naval Aeronautical and Astronautical University

Parallel robots with SCARA（selective compliance assembly robot arm） motions are utilized widely in the field of high speed pick-and-place manipulation. error modeling for these robots generally simplifies the parallelogram structures included by the robots as a link. As the established error model fails to reflect the error feature of the parallelogram structures, the effect of accuracy design and kinematic calibration based on the error model come to be undermined. An error modeling methodology is proposed to establish an error model of parallel robots with parallelogram structures. The error model can embody the geometric errors of all joints, including the joints of parallelogram structures. Thus it can contain more exhaustively the factors that reduce the accuracy of the robot. Based on the error model and some sensitivity indices defined in the sense of statistics, sensitivity analysis is carried out. Accordingly, some atlases are depicted to express each geometric error’s influence on the moving platform’s pose errors. From these atlases, the geometric errors that have greater impact on the accuracy of the moving platform are identified, and some sensitive areas where the pose errors of the moving platform are extremely sensitive to the geometric errors are also figured out. By taking into account the error factors which are generally neglected in all existing modeling methods, the proposed modeling method can thoroughly disclose the process of error transmission and enhance the efficacy of accuracy design and calibration.

关键词： parallel robot selective compliance assembly robot arm（SCARA） motions error modeling sensitivity analysis parallelogram structure

Thermal error modeling based on BiLSTM deep learning for CNC machine tool

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Advances in Manufacturing 2021年第2期9卷 235-249页

作者： Pu-Ling Liu Zheng-Chun Du Hui-Min Li Ming Deng Xiao-Bing Feng Jian-Guo Yang School of Mechanical Engineering Shanghai Jiao Tong UniversityShanghai 200240People’s Republic of China

The machining accuracy of computer numerical control machine tools has always been a focus of the manufacturing industry.Among all errors,thermal error affects the machining accuracy considerably.Because of the significant impact of Industry 4.0 on machine tools,existing thermal error modeling methods have encountered unprecedented challenges in terms of model complexity and capability of dealing with a large number of time series data.A thermal error modeling method is proposed based on bidirectional long short-term memory(BiLSTM)deep learning,which has good learning ability and a strong capability to handle a large group of dynamic data.A four-layer model framework that includes BiLSTM,a feedforward neural network,and the max pooling is constructed.An elaborately designed algorithm is proposed for better and faster model training.The window length of the input sequence is selected based on the phase space reconstruction of the time series.The model prediction accuracy and model robustness were verified experimentally by three validation tests in which thermal errors predicted by the proposed model were compensated for real workpiece cutting.The average depth variation of the workpiece was reduced from approximately 50μm to less than 2μm after compensation.The reduction in maximum depth variation was more than 85%.The proposed model was proved to be feasible and effective for improving machining accuracy significantly.

关键词： Thermal error error modeling Bidirectional long short-term memory(BiLSTM) Phase space reconstruction Computer numerical control(CNC)machine tool

Thermal error regression modeling of the real-time deformation coefficient of the moving shaft of a gantry milling machine

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Advances in Manufacturing 2020年第1期8卷 119-132页

作者： Wen-Hua Ye Yun-Xia Guo Heng-Fei Zhou Rui-Jun Liang Wei-Fang Chen College of Mechanical and Electrical Engineering Nanjing University of Aeronautics and AstronauticsNanjing 210016People’s Republic of China Department of Mechanical Engineering Henan Institute of TechnologyXinxiang 453003HenanPeople's Republic of China

This paper describes a novel modeling method for determining the thermal deformation coefficient of the moving shaft of a machine tool.Firstly,the relation between the thermal deformation coefficient and the thermal expansion coefficient is expounded,revealing that the coefficient of thermal deformation is an important factor affecting the precision of moving shaft feed systems.Then,thermal errors and current boundary and machining conditions are measured using sensors to obtain the first set of parameters for a thermal prediction model.The dynamic characteristics of the positioning and straightness thermal errors of the moving axis of a machine tool are analyzed under different feed speeds and mounting modes of the moving shaft and bearing.Finally,the theoretical model is derived from experimental data,and the axial and radial thermal deformation coefficients at different time and positions are obtained.The expressions for the axial and radial thermal deformation of the moving shaft are modified according to theoretical considerations,and the thermal positioning and straightness error models are established and experimentally verified.This modeling method can be easily extended to other machine tools to determine thermal deformation coefficients that are robust and self-correcting.

关键词： Moving shaft Ball screw Thermal expansion Thermal deformation coefficient error modeling

error modeling and analysis of inclinometer based on digital accelerometer

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Journal of Measurement Science and Instrumentation 2013年第4期4卷 321-324页

作者：白渚铨张晓明刘俊 Key Laboratory of Instrumentation Science & Dynamic Measurement(North University of China) Ministry of Education Department of Electronic Science and Technology North University of China

Measuring accuracy of inclinometer based on accelerometer is mainly influenced by the adopted accelerometer sensor.To improve the measuring accuracy of the inclinometer,the structure of the measuring system is given and measuring principle is analyzed,and the error model is established in this paper.Furthermore,the model is verified by simulation and experiment,which not only gives the smallest errors of the measured pitch and roll,but also lays foundation for sensor selection,error analysis and error compensation.The results show that the error model is of practical value.

关键词： inclinometer accelerometer error modeling error analysis

A Comparative Study on Kinematic Calibration for a 3-DOF Parallel Manipulator Using the Complete-Minimal,Inverse-Kinematic and Geometric-Constraint error Models

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Chinese Journal of Mechanical Engineering 2023年第5期36卷 206-230页

作者： Haiyu Wu Lingyu Kong Qinchuan Li Hao Wang Genliang Chen State Key Laboratory of Mechanical System and Vibration Shanghai Jiao Tong UniversityShanghai 200240China Intelligent Robot Research Center Zhejiang LabHangzhou 311100China School of Mechanical Engineering Zhejiang Sci-Tech UniversityHangzhou 310018China

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.

关键词： Kinematic calibration Parallel manipulator error modeling Product of exponential(POE)

A Long Short-Term Memory-based INS error modeling algorithm for GNSS/INS Integrated Navigation in Urban Environments

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A Long Short-Term Memory-based INS Error Modeling algorithm ...

error modeling and Integrity Risk Analysis in SPP

第十三届中国卫星导航年会

作者： Lei Jiang Rui Sun Nanjing University of Aeronautics and Astronautics

Without the assistance of GNSS, errors in low-cost INS will spread rapidly resulting in a steady decline in accuracy. Yet, GNSS signals are easily blocked by various obstacles in urban environments. To solve the problem above, this paper proposes an INS error modeling algorithm for GNSS/INS integrated navigation in urban environments based on Long Short-Term Memory（LSTM）. The dynamic nonlinear mapping and long-term memory ability of LSTM allows us to make full use of the relationship between past and current navigation information to realize accurate prediction. When sufficient GNSS satellites are observable, the LSTM model is trained with the specific force, angular velocity, position, velocity from the last epoch of INS, combined with the position and velocity from the current epoch of integrated system, so that it can fully learn the rules to compensate for the INS navigation error. Then, when insufficient satellites are observable, the trained LSTM model outputs the corresponding position and velocity to correct the error of INS. The proposed algorithm is verified using the RTK/INS loosely-coupled model, observing GPS and BDS satellites at the same time. When the GNSS are unobservable for 30 seconds, compared with the pure INS solution, the accuracy of RTK/INS based on LSTM is improved by 69.83%, 78.90% and 80.74% in three different experimental scenarios. This demonstrates a significantly better navigational ability during periods of GNSS outages.

关键词： Urban positioning Integrated navigation error modeling LSTM GNSS outage

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Error Modeling and Integrity Risk Analysis in SPP

An error Equivalent Model of Revolute Joints with Clearances for Antenna Pointing Mechanisms

第十一届中国卫星导航年会

作者： Yuan Song Qingsong Li Yi Dong Wanli Jian Dingjie Wang Jie Wu National University of Defense Technology

With the popularity and development of GNSS, the concept of integrity is proposed in order to ensure the safety of navigation and positioning. In some related fields such as civil aviation and lifesav

关键词： SPP Integrity Monitoring Integrity Risk Analysis error modeling FDE

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Chinese Journal of Mechanical Engineering 2018年第2期31卷 97-105页

作者： Quan Liu Sheng-Nan Lu Xi-Lun Ding School of Mechanical Engineering and Automation Beihang University

Joint clearances in antenna pointing mechanisms lead to uncertainty in function deviation. Current studies mainly focus on radial clearance of revolute joints, while axial clearance has rarely been taken into consideration. In fact, own?ing to errors from machining and assembly, thermal deformation and so forth, practically, axial clearance is inevitable in the joint. In this study, an error equivalent model(EEM) of revolute joints is proposed with considering both radial and axial clearances. Compared to the planar model of revolute joints only considering radial clearance, the journal motion inside the bearing is more abundant and matches the reality better in the EEM. The model is also extended for analyzing the error distribution of a spatial dual?axis("X–Y" type) antenna pointing mechanism of Spot?beam antennas which especially demand a high pointing accuracy. Three case studies are performed which illustrates the internal relation between radial clearance and axial clearance. It is found that when the axial clearance is big enough, the physical journal can freely realize both translational motion and rotational motion. While if the axial clearance is limited, the motion of the physical journal will be restricted. Analysis results indicate that the consideration of both radial and axial clearances in the revolute joint describes the journal motion inside the bearing more precise. To further validate the proposed model, a model of the EEM is designed and fabricated. Some suggestions on the design of revolute joints are also provided.

关键词： error modeling Joint clearances Antenna pointing mechanism Radial clearance Axial clearance

error analysis and optimization of a 3-degree of freedom translational Parallel Kinematic Machine

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Frontiers of Mechanical Engineering 2014年第2期9卷 120-129页

作者： S. SHANKAR GANESH A. B. KOTESWARA RAO Department of Mechanical Engineering G.V.E College of Engineering Visakhapatnam 530048 India

In this paper, error modeling and analysis of a typical 3-degree of freedom translational Parallel Kine- matic Machine is presented. This mechanism provides translational motion along the Cartesian X-, Y- and Z- axes. It consists of three limbs each having an arm and forearm with prismatic-revolute-revolute-revolute joints. The moving or tool platform maintains same orientation in the entire workspace due to its joint arrangement. From inverse kinematics, the joint angles for a given position of tool platform necessary for the error modeling and analysis are obtained. error modeling is done based on the differentiation of the inverse kinematic equations. Variation of pose errors along X, Y and Z directions for a set of dimensions of the parallel kinematic machine is presented. A non-dimensional performance index, namely, global error transformation index is used to study the influence of dimensions and its corresponding global maximum pose error is reported. An attempt is made to find the optimal dimensions of the Parallel Kinematic Machine using Genetic Algorithms in MATLAB. The methodology presented and the results obtained are useful for predicting the performance capability of the Parallel Kinematic Machine under study.

关键词： translational Parallel Kinematic Machine error modeling global error transformation index