Position Error Model Research Articles

Dynamic positioning error analysis and modeling of CNC machine tool guideway system

The dynamic characteristics of the XY worktable are thoroughly analyzed in this study to accurately compensate the measurement errors of on-machine measurement systems caused by the dynamic and static characteristics under multiple factors. The dynamic positioning error model of the XY worktable motion components is established, and the theoretical model of the dynamic positioning error of the XY worktable is derived. The actual parameters of the experimental platform for the correlation error of CNC machine tools are substituted into the model for theoretical calculation and analysis. Results show that the motion speed of the worktable, the weight of the measured workpiece, the installation position of the workpiece, and the friction force are the main factors causing the dynamic positioning error. Dynamic positioning error analysis and verification experiments were conducted to verify the validity of the proposed theoretical model. Experimental results show that a regular change occurs between the dynamic positioning error and the movement speed of the XY worktable, and the actual measurement results are basically consistent with the theoretical calculation results. The research results can lay a good foundation for establishing the measurement error prediction and compensation model of on-machine measurement systems of CNC machine tools and improving its measurement accuracy.

Impact analysis of platform positioning and orientation error on warship weapon target strike

In order to evaluate the weapon strike effect in the joint of ship formation, this paper discusses the influence of platform positioning and orientation error on weapon strike effect. Based on the mathematical model, the damage expectation of platform positioning and orientation error, the long-range strike accuracy of shipboard missile and the target indicating accuracy of cross-platform are analyzed quantitatively. The model includes weapon strike likelihood, the navigation positioning error model and error transfer model of ship platform. The simulation was be perform in MATLAB environment. The larger the positioning and orientation error is, the more cross platform target sign error will increase. And the acquisition probability and weapon strike effect of missile long-range attack will reduce.

Research of Calibration Method for Industrial Robot Based on Error Model of Position

Based on the current situation of high precision and comparatively low APA (absolute positioning accuracy) in industrial robots, a calibration method to enhance the APA of industrial robots is proposed. In view of the "hidden" characteristics of the RBCS (robot base coordinate system) and the FCS (flange coordinate system) in the measurement process, a comparatively general measurement and calibration method of the RBCS and the FCS is proposed, and the source of the robot terminal position error is classified into three aspects: positioning error of industrial RBCS, kinematics parameter error of manipulator, and positioning error of industrial robot end FCS. The robot position error model is established, and the relation equation of the robot end position error and the industrial robot model parameter error is deduced. By solving the equation, the parameter error identification and the supplementary results are obtained, and the method of compensating the error by using the robot joint angle is realized. The Leica laser tracker is used to verify the calibration method on ABB IRB120 industrial robot. The experimental results show that the calibration method can effectively enhance the APA of the robot.

Precise reliability analysis base on static pose error of 6 degree of freedom serial robot

Taking the JLRB20 industrial robot as the object, the improved D-H modelling method is used to establish the positioning error model of the robot, the reliability of the static pose error of the robot is analysed, and the reliability evaluation index of the static pose error of the robot is established. By analysing the precise reliability base on static pose error of the robot, it is determined that the joint rotation angle has the greatest influence on the accuracy of the static attitude error of the robot end, which provides a basis for improving the reliability of the static pose error of the robot.

A Novel Alignment Method for SINS with Large Misalignment Angles Based on EKF2 and AFIS.

In order to achieve the fine alignment of strapdown inertial navigation (SINS) under large misalignment angles, a novel filtering alignment method is proposed based on the second-order extended Kalman filter (EKF2) and adaptive fuzzy inference system (AFIS). Firstly, the quaternion is employed to represent the attitude errors of SINS. A second-order nonlinear state equation is made based on the nonlinear velocity error model and attitude error model, and the linear measurement equation is based on the velocity outputs from SINS. Then, the filtering scheme is designed based on EKF2 and AFIS. The error estimation and fine alignment can be achieved by using the proposed filtering scheme. The results of Monte Carlo Simulation show that the errors of pitch, roll and yaw misalignment angles quickly decrease to about 14″, 15″ and 7.62′ respectively in 350 s under the condition of any misalignment angles with pitch error from −40° to 40°, roll error from −40° to 40°, and yaw error from −50° to 50°. Even when the initial misalignment angles are all very large such as (80°, 120°, 170°), the proposed nonlinear alignment method still can converge normally by utilizing the adaptive fuzzy inference system (AFIS) to adjust the covariance matrix Pk/k−1. Finally, the turntable experiment was performed, and the effectiveness and superiority of the proposed method were further verified by compared with other nonlinear methods.

A Fast Weakly-Coupled Double-Layer ESKF Attitude Estimation Algorithm and Application

Aimed at the problem of small unmanned aerial vehicle (UAV) attitude solution accuracy and real-time performance in short-range navigation flight, in this paper, we propose a fast weakly-coupled double-layer error-state Kalman filter (DL-ESKF) attitude estimation algorithm. Considering the application of short-range navigation, we designed an improved attitude error model for low-cost gyroscope/accelerometer/magnetometer devices. In addition, we reasonably simplified certain factors that affect the attitude solution to reduce the filtering calculation burden. For the data coupling phenomenon caused by the different sampling frequencies of the attitude sensor data in the filtering process, we designed a new attitude algorithm combined with the ESKF and hierarchical filter. The first layer of filters used an accelerometer and the second layer used a magnetometer to correct the attitude error. We also built an offline and real-time test platform to verify the performance of the proposed algorithm in a simulation and flight test environment compared with the classic attitude algorithms. The experimental results demonstrated that the proposed algorithm not only improved the attitude solution accuracy and stability but also reduced the filter running time.

MEKF With Navigation Frame Attitude Error Parameterization for INS/GPS

The multiplicative extended Kalman filter (MEKF) is an attractive method for inertial navigation system and Global Positioning System (INS/GPS) integration due to its flexibility and computational efficiency. Traditionally, in MEKF, the attitude error that is used as the local filtering state is always expressed in the body frame. With such definition, the resulting attitude error model contains inevitable disturbance, which may degrade the filtering performance. Motived by the aforementioned fact, this work revisits the MEKF for INS/GPS with the utilization of navigation frame attitude error model in the filter. The presentation of MEKF in this paper is in a self-contained manner, which is tutorial in nature and clearly defines all involved attitude and attitude errors for frame transformation. Since there is no noise/disturbance contaminated factor in the model, the proposed model possesses advantages in terms of both robustness and accuracy. The subtle differences that arise between the used navigation frame attitude error model and traditional body frame attitude error model in MEKF are discussed and evaluated based on simulation and field test results.

Positioning Error Analysis and Control of a Piezo-Driven 6-DOF Micro-Positioner.

This paper presents a positioning error model and a control compensation scheme for a six-degree-of-freedom (6-DOF) micro-positioner based on a compliant mechanism and piezoelectric actuators (PZT). The positioning error model is established by means of the kinematic model of the compliant mechanism and complete differential coefficient theory, which includes the relationships between three typical errors (hysteresis, machining and measuring errors) and the total positioning error. The quantitative analysis of three errors is demonstrated through several experimental studies. Afterwards, an inverse Presiach model-based feedforward compensation of the hysteresis nonlinearity is employed by the control scheme, combined with a proportional-integral-derivative (PID) feedback controller for the compensation of machining and measuring errors. Moreover, a back propagation neural network PID (BP-PID) controller and a cerebellar model articulation controller neural network PID (CMAC-PID) controller are also adopted and compared to obtain optimal control. Taking the translational motion along the X axis as an example, the positioning errors are sharply reduced by the inverse hysteresis model with the maximum error of 12.76% and a root-mean-square error of 4.09%. In combination with the CMAC-PID controller, the errors are decreased to 0.63% and 0.23%, respectively. Hence, simulated and experimental results reveal that the proposed approach can improve the positioning accuracy of 6-DOF for the micro-positioner.

Multivariate orthogonal polynomial-based positioning error modeling and active compensation of dual-driven feed system

The nonsynchronous error of the dual-driven feed system seriously affects the positioning and machining accuracy of CNC machine tools. Improving the positioning error is an extremely important task as it determines the geometric accuracy of the manufactured parts. In this paper, a Multivariate Orthogonal Polynomial Regression model has been developed to predict the positioning error in terms of motion parameters such as position and speed of the X1 and X2 axes of the dual-driven worktable. Orthogonal Experimental Design has been engaged in conducting experiments. The positioning errors are measured by a dual-frequency laser interferometer. In addition, a real-time error compensation system is developed based on the proposed active compensation control strategy in the dual-driven feed system controlled by Beckhoff motion control card. Experimental results show that the proposed positioning error model and error compensation strategy can be utilized as an effective manner to improve the accuracy of dual-driven CNC machine tools.

Fast Online Coordinate Correction of a Multi-Sensor for Object Identification in Autonomous Vehicles.

Multi-sensor perception systems may have mismatched coordinates between each sensor even if the sensor coordinates are converted to a common coordinate. This discrepancy can be due to the sensor noise, deformation of the sensor mount, and other factors. These mismatched coordinates can seriously affect the estimation of a distant object’s position and this error can result in problems with object identification. To overcome these problems, numerous coordinate correction methods have been studied to minimize coordinate mismatching, such as off-line sensor error modeling and real-time error estimation methods. The first approach, off-line sensor error modeling, cannot cope with the occurrence of a mismatched coordinate in real-time. The second approach, using real-time error estimation methods, has high computational complexity due to the singular value decomposition. Therefore, we present a fast online coordinate correction method based on a reduced sensor position error model with dominant parameters and estimate the parameters by using rapid math operations. By applying the fast coordinate correction method, we can reduce the computational effort within the necessary tolerance of the estimation error. By experiments, the computational effort was improved by up to 99.7% compared to the previous study, and regarding the object’s radar the identification problems were improved by 94.8%. We conclude that the proposed method provides sufficient correcting performance for autonomous driving applications when the multi-sensor coordinates are mismatched.

Model-Based Compensation and Pareto-Optimal Trajectory Modification Method for Robotic Applications

This study addresses the problem in accuracies of robot positioning and trajectory with compliance and geometric errors in robotic applications. A rigid–flexible coupling position error model of serial robot is presented to identify geometric and compliance error parameters simultaneously. On the basis of the error compensation model, the predicted position error can be corrected by the proposed hybrid error compensation method. Particular attention is paid to the deviation along the desired trajectory with respect to the corresponding updated trajectory, which is consecutively changing and cannot be corrected directly. A segmentation trajectory control method based on the Pareto-optimal with weighted-sum algorithm is proposed to solve the multi-objective optimisation problem in trajectory modification. The offline program optimiser integrates the proposed model-based compensation and trajectory modification method by MATLAB and VS software development platform. The method is developed to be an effective solution for the problem in absolute accuracies of positioning and trajectory with the experimental results achieved on a Staubli TX60L robot. Additional experiment is conducted with a Staubli RX160L robot to demonstrate the extensive feasibility and practical effectiveness of our approach for other industrial robots.

Improved Position Error Model for Airborne Hyperspectral Imaging Systems

An improved position error model for airborne hyperspectral imaging systems is proposed to quantify the position errors caused by the deficiencies of instruments and the manual installation of integrated systems. The model is based on a thorough analysis of position error sources, which include uncertainties caused by camera position and altitude, interior camera parameters, gyro stabilized mount, position setting error of the global positioning system antenna, and boresight angle error. An improved position error model that describes these error sources is established based on collinear equations. This model is then expanded into the first-order Taylor series. Finally, the error propagation law is applied to estimate the position errors. The performance of the proposed method is evaluated based on real hyperspectral images of Hymap. Results show that the mean square error of the position error is better than 2.1 pixels, which is almost the same as that of ground truth.

DVL-Aided SINS In-Motion Alignment Filter Based on a Novel Nonlinear Attitude Error Model

A novel nonlinear attitude error model based on square root cubature information filter (SR-CIF) is proposed aiming to speed up the convergence rate of DVL-aided strapdown inertial navigation system (SINS) in-motion initial alignment for autonomous underwater vehicle (AUV) when both large initial heading error and large initial level attitude errors exist The new nonlinear attitude error model and measurement model are applicable for initial alignment after a short-time coarse alignment with large attitude errors exist. The SR-CIF embeds the whole iterative process into the data structure framework of the information filtering, replacing the covariance matrix in the square root cubature Kalman filter (SR-CKF) with an information matrix which simplifies the filter initialization. The square root technology ensures the symmetry and positive definiteness of the information matrix with enhanced stability of the filter. The simulation and experimental results indicate that the proposed DVL-aided alignment filter is effective with large initial attitude errors. The rate of convergence and estimation accuracy of the SR-CIF is higher than that of the conventional SR-CKF with large attitude misalignments.

Research on Measurement Error Model of GNSS/INS Integration Based on Consistency Analysis

Kalman filter is widely taken as an optimal fusion algorithm in GNSS/INS integration, and GNSS positioning error is often simply modeled as white noise in a loosely-coupled system. But many research results have shown that GNSS positioning error has the characteristic of temporal correlation. Correct error model of Kalman filter can ensure that the level of estimated accuracy is equal to that of actual accuracy. Inaccurate model will influence the consistency between estimated accuracy and actual integrated accuracy. Moreover, quality control method based on variance-covariance with inconsistency is not reliable and not utilized to detect gross errors. So, this paper mainly researches on GNSS positioning and velocity error model and its impact on quality control in GNSS/INS integration. In this paper, state-augmentation method is applied to solve the problems of GNSS colored noise to ensure the navigation accuracy consistency, and the rationality of the improved model is verified by the effect of quality control. Simulation and field test results show that state-augmentation method can improve the consistency between actual error and estimation standard deviation, and satisfy the requirement of quality control based on variance-covariance to improve the integration reliability.

An Efficient Calibration Algorithm for Large Aperture Array Position Errors in a GEO SAR

Geosynchronous orbit synthetic aperture radar (GEO SAR) plays an important role in wide-area surveillance and the continuous coverage of areas containing targets of interest. However, the relative position errors of large aperture arrays will distort the antenna pattern, which significantly degrades the target detection performance in a GEO SAR system. To address this issue, most of the conventional calibration methods are focused on the independent errors, without consideration of the parametric error model, which may increase the position estimation errors. To solve this problem, an efficient calibration algorithm for position errors in a GEO SAR is proposed in this letter. For the large antenna arrays, the parametric error model is first established. Then, the calibration method is performed to estimate the parameters of the position error model. Based on this, the accurate position errors can be obtained by the least-squares algorithm. Compared with the conventional methods, the target detection performance of a GEO SAR system can be significantly improved after the precise array position error compensation by the proposed algorithm. Moreover, the proposed algorithm transforms the estimation from 3-D positions to the finite parameters of the error model, which can considerably decrease the computational complexity and obtain a more accurate estimation of the position errors simultaneously. Several simulated results are presented to validate the proposed algorithm for the position error correction in a GEO SAR system.

Modeling and Control of Negative-Buoyancy Tri-Tilt-Rotor Autonomous Underwater Vehicles Based on Immersion and Invariance Methodology

Spot hover and high speed capabilities of underwater vehicles are essential for ocean exploring, however, few vehicles have these two features. Moreover, the motion of underwater vehicles is prone to be affected by the unknown hydrodynamics. This paper presents a novel negative-buoyancy autonomous underwater vehicle equipped with tri-tilt-rotor to obtain these two features. A detailed mathematical model is derived, which is then decoupled to altitude and attitude subsystems. For controlling the underwater vehicle, an attitude error model is designed for the attitude subsystem, and an adaptive nonlinear controller is proposed for the attitude error model based on immersion and invariance methodology. To demonstrate the effectiveness of the proposed controller, a three degrees of freedom (DOF) testbed is developed, and the performance of the controller is validated through a real-time experiment.

Thermal positioning error modeling of machine tools using a bat algorithm-based back propagation neural network

Thermal error of a machine tool is one of the main reasons affecting the machining accuracy. Heat production and heat transfer of a machine tool are too complicated to predict the generated thermal error accurately. According to the nonlinear and time-varying characteristics of thermal error, the back propagation (BP) neural network is perfectly suitable for thermal error modeling, which has been extensively used to map the nonlinear relationship. However, traditional BP neural network usually has poor prediction performance under different operating conditions. Therefore, a new swarm intelligent optimization algorithm, bat algorithm (BA), is introduced to optimize BP neural network and improve its performance. The focus of this paper is the application of the combined algorithm (bat algorithm-based back propagation neural network) to solve the problem of thermal error modeling. Thermal positioning error experiments were conducted on a three-axis experiment bench. The experimental results show that thermal positioning error model built by BA-BP neural network is more stable and has high prediction accuracy and strong robustness, which can provide a candidate method for thermal error modeling.

Prediction and compensation of geometric error for translational axes in multi-axis machine tools

This paper proposes an integrated geometric error prediction and compensation method to eliminate the positioning inaccuracy of tool ball for a double ball bar (DBB) caused by the translational axes’ geometric errors in a multi-axis machine tool (MAMT). Firstly, based on homogeneous transform matrix (HTM) and multi-body system (MBS) theory, the positioning error model only considering the translational axes of a MAMT is established. Then, an integrated error parameter identification method (IEPIM) by using a laser interferometer is proposed. Meanwhile, the identification discrete results of geometric error parameters for the translational axes are obtained by identification experiments. According to the discrete values, the optimal polynomials of 18 position-dependent geometric errors (PDGEs) are founded. As a basis, an iterative compensation method is constructed to modify the NC codes generated with the ordinary compensation method in self-developed compensation software. Finally, simulation verification is conducted with these two compensation methods. Simulation results show the positioning errors for test path of tool ball calculated with the iterative compensation method that are limited within 0.001 mm, and its average accuracy and accuracy stability are improved by 79.5 and 52.2%, respectively. In order to further verify the feasibility of the presented method, a measuring experiment is carried out in XY plane of a five-axis machine tool by using DBB. The experiment results show that the maximum circularity error with the iterative compensation method is reduced about 40.4% than that with the ordinary compensation method. It is therefore reasonable to conclude that the proposed method in this paper can avoid the influence of the translational axes’ geometric errors on rotary ones during a DBB test.

Fast heading-rotation-based high-accuracy misalignment angle estimation method for INS and GNSS

Abstract When an inertial navigation system (INS) is used to evaluate the performance of an attitude determination system (GADS) based on the global navigation satellite system, the misalignment angles between them should be estimated correctly. The traditional misalignment angle estimation method treats the average attitude differences between GADS and INS as misalignment angles. Hence, the east and north components (levels) of the attitude errors caused by the accelerometer errors are mistakenly treated as misalignment angles. In this study, the level attitude error model is built considering the accelerometer errors. Furthermore, a fast and highly accurate misalignment angle estimation method based on heading-rotation is proposed to estimate the level attitude errors and misalignment angles simultaneously. This proposed method is examined through a turntable test. Experiment results demonstrate the capability of the proposed method in estimating the misalignment angles between high-accuracy GADS and INS.

Two Error Models for Calibrating SCARA Robots based on the MDH Model

This paper describes the process of using two error models for calibrating Selective Compliance Assembly Robot Arm (SCARA) robots based on the modified Denavit-Hartenberg(MDH) model, with the aim of improving the robot's accuracy. One of the error models is the position error model, which uses robot position errors with respect to an accurate robot base frame built before the measurement commenced. The other model is the distance error model, which uses only the robot moving distance to calculate errors. Because calibration requires the end-effector to be accurately measured, a laser tracker was used to measure the robot position and distance errors. After calibrating the robot and, the end-effector locations were measured again compensating the error models' parameters obtained from the calibration. The finding is that the robot's accuracy improved greatly after compensating the calibrated parameters.