Error Compensation Scheme Research Articles

Error compensation strategy with high installation tolerance for angle encoders

Radial error (comprising eccentricity error and runout error) and graduation error of circular scales are the primary sources of error for angle encoders. This paper presents a compensation strategy for radial error and graduation error with a high installation tolerance, achieved through the utilization of three measurement heads and one calibration head. Three reading heads, evenly distributed, are employed to compensate for radial error and non-3k order graduation error, while one reading head, positioned in a specific arrangement, serves to identify 3k order errors for compensation purposes. To mitigate the installation tolerance requirements of reading heads, this study employs two methods. Firstly, it investigates the impact of reading head position deviation on compensating radial error and proposes a method for compensating residual radial error. Secondly, it utilizes the Monte Carlo method to assess the effect of reading head position deviation on identifying graduation error when the maximum deviation is ±1°. The simulation and experimental results confirm that the proposed method effectively compensates for radial error and the first 10-order graduation error within a position deviation range of ±1°. Based on the experimental results, this method demonstrates superior compensation accuracy, achieving an error of 0.44″, compared to evenly distributing three reading heads (0.53″) and four reading heads (0.85″). Additionally, when compared to the combination method of evenly distributing three and four reading heads (0.47″), it provides similar compensation accuracy while utilizing fewer reading heads.

Terrain preview detection system based on loosely coupled and tightly coupled fusion with lidar and IMU

The ride comfort of emergency rescue vehicles is considerably affected by the terrain preview accuracy. In this paper, a robust, precise terrain preview detection system that integrates lidar with IMU is presented based on loosely and tightly coupled fusion. To evaluate the terrain measurement error, lidar measurement error and vehicle motion error are considered to achieve centimeter-level mapping and localization accuracy in disparate scenes. To reduce the localization cumulative error, the frontend laser odometer and backend factor graph optimization are innovatively combined, and the cumulative error compensation strategy is designed. Experimental validation is conducted in different scenes to assess the performance of the prototype and to validate the simulation results. The vehicle localization accuracy is greater than 4–8 cm, and the simulated and measured terrain elevation waveforms exhibit strong correlations, which verifies the reliability and validity of the simulation method. The elevation measurement accuracy reaches 87 %.

Robot error compensation strategy based on error sensitivity

Abstract Due to the errors in manufacturing and assembly, there are differences between the actual model and the theoretical model of the robot, which affects the positioning accuracy of the robot end-effector. In order to improve the accuracy of robot end-effector position, a robot error compensation strategy based on error sensitivity is proposed.Firstly, the robot kinematic model is established by Denavit-Hartenberg (D-H) method, and the sensitivity of end-effector position error is analyzed. According to the influence degree of different kinematic parameters on the robot end-effector position accuracy in the whole workspace, different weights are given to different kinematic parameters. {\color{red}Secondly, the kinematic error model is established, and the redundancy of the error parameter matrix is analyzed to obtain an independent error model. Thirdly, based on the error sensitivity analysis, a Weighted Levenberg-Marquard (WLM) algorithm with adaptive penalty factor is proposed, and the kinematic parameters are iteratively identified.} Finally, an error compensation experiment is carried out by using a universal serial six-degree-of-freedom robot. The experimental results show that the maximum error, mean absolute error and root mean square error of the position error on the test set are reduced by 90.75%, 89.86% and 95.64% respectively. The research in this paper provides a theoretical basis for robot end error compensation.

An online error compensation strategy for hybrid robot based on grating feedback

Purpose This paper aims to enhance the machining accuracy of hybrid robots by treating the moving platform as the first joint of a serial robot for direct position measurement and integrating external grating sensors with motor encoders for real-time error compensation. Design/methodology/approach Initially, a spherical coordinate system is established using one linear and two circular grating sensors. This system enables direct acquisition of the moving platform’s position in the hybrid robot. Subsequently, during the coarse interpolation stage, the motor command for the next interpolation point is dynamically updated using error data from external grating sensors and motor encoders. Finally, fuzzy proportional integral derivative (PID) control is applied to maintain robot stability post-compensation. Findings Experiments were conducted on the TriMule-600 hybrid robot. The results indicate that the following errors of the five grating sensors are reduced by 94%, 93%, 80%, 75% and 88% respectively, after compensation. Using the fourth drive joint as an example, it was verified that fuzzy adaptive PID control performs better than traditional PID control. Practical implications The proposed online error compensation strategy significantly enhances the positional accuracy of the robot end, thereby improving the actual processing quality of the workpiece. Social implications This method presents a technique for achieving online error compensation in hybrid robots, which promotes the advancement of the manufacturing industry. Originality/value This paper proposes a cost-effective and practical method for online error compensation in hybrid robots using grating sensors, which contributes to the advancement of hybrid robot technology.

Geometry accuracy control in abrasive water jet taper hole machining of ultra‐thick carbon fiber‐reinforced polymer (CFRP) laminates

AbstractThe primary factors affecting the geometric accuracy of abrasive water jet (AWJ) machining of ultra‐thick carbon fiber‐reinforced polymer (CFRP) laminates are the cutting front drag and kerf width deviation caused by energy dissipation. Firstly, this study comprehensively analyzes the influence of the coupling relationship between cutting front drag and kerf width deviation on the geometric accuracy of hole machining. Secondly, a gradient distribution theory for jet traverse speed with cutting depth is proposed for taper hole machining characteristics. Finally, a general geometric error model applicable to both straight and taper hole machining of ultra‐thick CFRP laminates using AWJ is established, along with a geometric error compensation method. A series of experiments validate the accuracy of the proposed geometric error model and compensation method. The novelty of this research lies in unifying the geometric error models for straight and taper hole machining of ultra‐thick CFRP laminates by considering the gradient distribution of jet traverse speed. The proposed error compensation method reduces the high degree of freedom required for machine tools. This study provides a general geometric error model and compensation strategy for AWJ hole machining of ultra‐thick CFRP laminates, which has significant engineering value for achieving 3D controllable AWJ machining of complex ultra‐thick CFRP components.Highlights The high geometric precision taper holes machining technique is a necessary prerequisite for achieving precise machining of complex trajectories in ultra‐thick CFRP with abrasive water jet. The influence of the coupling relationship between cutting front drag and kerf taper on the geometric accuracy of hole processing is comprehensively analyzed. A model considering the gradient distribution of traverse speed during taper holes machining was established, and a geometric error model considering this gradient distribution of traverse speed was developed. A taper holes machining geometric error compensation method with high engineering applicability was proposed. Geometric error prediction experiments and error compensation experiments were conducted, and the results proved the accuracy of the geometric error model and error compensation method.

Object azimuth measurement based on optical orbital angular momentum phase spectrum under tilted irradiation condition

In optical remote sensing, a beam carrying orbital angular momentum can be used to identify the azimuth of an object. However, most of the studies reported currently require the beam to be illuminated vertically to the surface of the object, and the general case of tilted irradiation for the beam has not been fully discussed. In this paper, an object azimuth measurement method based on orbital angular momentum phase spectrum under tilted irradiation condition is proposed. We analyze the relationship between the measurement error caused by the beam oblique irradiation and the angle of tilt and propose an error compensation method. In the experiment, the orbital angular momentum phase spectrum of the Laguerre-Gaussian beam is obtained by a four-step phase-shifting method, and the error caused by tilt modulation is measured. After implementing the error compensation scheme, the maximum absolute error in azimuth measurement under tilted irradiation conditions is maintained within 2.15°. Across all tilt angles, the average absolute error remains below 0.73°. The method proposed in this paper has a certain reference value for expanding the practical application of orbital angular momentum beams in the field of remote sensing.

Unified framework for geometric error compensation and shape-adaptive scanning in five-axis metrology systems

In response to the escalating demand for precise shape metrology of complex optical surfaces, this study unveils a unified geometric error compensation and trajectory planning framework tailored for high-accuracy five-axis scanning metrology systems, which remains a notably underexplored field compared to error compensation in machine tools. Founded on a unified geometric model, the proposed framework seamlessly integrates a versatile shape-adaptive trajectory planning strategy, a thorough global error sensitivity analysis approach, and an exhaustive geometric error compensation scheme. Leveraging inverse kinematics, an innovative shape-adaptive scanning trajectory generation strategy is mathematically formulated, thereby facilitating adaptable measurement trajectory generation for diverse surface geometries. Employing forward kinematics, an exhaustive geometric error model is established to extensively address the 53 distinct geometric errors in the metrology system. This proposed error model fundamentally augments conventional geometric error models in machine tool by managing not only the geometric errors from the motion system, but also those from the probe and workpiece. To streamline the error compensation procedure, a novel global error sensitivity analysis approach is introduced, identifying both system-oriented and process-oriented sensitive geometric errors for targeted compensation. Experimental validation using a standard ball, which achieved an exceptional 89.35% reduction in the root mean square of the measurement errors, further confirms the feasibility and effectiveness of the proposed framework. By offering an universal trajectory planning, sensitivity analysis and error compensation trinity for five-axis scanning metrology systems, this study sets the stage for precision advancements and design optimization across diverse configurations of metrology systems.

Geometric Error-Based Multi-Source Error Identification and Compensation Strategy for Five-Axis Side Milling

Based on a multi-source error model, this paper discusses the principle of error element identification and uses the mirror bias method to compensate the geometric errors of a process system. Firstly, a nine-line measurement method to determine the geometric error of the linear feed axes of machine tools is introduced, and the geometric error identification model based on the “nine-line method” is established. Then, using a ballbar mounted in the axial, tangential, and radial directions of the machine, the geometric error elements of the rotation axis are identified by three simple measurements in each direction. Subsequently, for the more common flat vise clamping workpiece in actual production, the workpiece position error is identified by using the traditional process of dimensional chain, and the workpiece attitude error is identified by fitting the angle between the positioning plane and the horizontal plane by the least squares method. Finally, based on the tool position points and tool axis vectors obtained from the multi-source error model, the error compensation value is solved using inverse machine tool kinematics to offset the machining error by mirroring the error value of the same size, and based on the “S-shaped specimen” to compensate the processing experiments, after compensation, the processing error is reduced by 30~45%, verifying the effectiveness of the compensation method.

Novel Winding Arrangements for Measuring High-Amplitude Current With Interference Error Compensation Scheme

Novel Winding Arrangements for Measuring High-Amplitude Current With Interference Error Compensation Scheme

Temperature error compensation method of fiber optic gyroscope based on deep learning

This work provides an error compensation strategy based on deep learning to address the temperature error of a fiber optic gyroscope (FOG). The Attention structure was used to improve the Long Short-Term Memory Network (LSTM), and the improved network was utilized to establish the prediction and compensation model of FOG error. From the two perspectives of the learning ability of the neural network and the improvement of FOG performance, this paper selects three indicators: prediction accuracy, mean square error, and FOG bias stability to comprehensively evaluate the performance of the compensation model. Through comparison, the compensation effect is significantly enhanced.

Thermal error compensation for a fluid-cooling ball-screw feed system

Thermal deformation resulted from the heat generated by the motor and the frictional behavior between the moving pairs significantly reduces the positioning accuracy of feed systems and thus influences the machining quality of parts. The internal cooling ball screw takes advantage of the cooling liquid to strengthen the convection heat transfer actively and suppress the temperature rise. Owing to the intermittent starting and stopping operation modes of the cooling machine, the heat flux arising from various heat sources cannot be completely removed by the coolant; consequently, thermal errors still exist. In this study, K-means++ clustering and correlation analyses were used to select thermal key points. A difference equation model of the thermal error was established to describe the transient change relationship between the temperatures of the thermal key points and the ball-screw shaft elongation, which was separated from the thermal characteristic experimental data according to the linear superposition principle of geometric and thermal errors to constitute the positioning error. The model parameters were identified using the least-squares method, and a thermal error compensation strategy based on the origin offset method was implemented. Experiments comparing the thermal error compensation of the three models under different working conditions were conducted to confirm that the thermal error difference equation model can be applied to reduce the thermal error of the feed system effectively and maintain excellent robustness.

Research on thermal error compensation strategy of CNC machine tools based on full working area modeling

Abstract Traditional manufacturing equipment is developing in the direction of precision, intelligence and integration, and the precision requirements of CNC machine tools are getting higher and higher. Compensating and controlling the thermal error of the machine tool is an important part of improving machining accuracy. This paper uses a cuckoo search algorithm to optimize the BP neural network to get the CSBP neural network model and inputs the temperature value of the CNC machine tool into the CSBP model to get the thermal error prediction results. Combined with the thermal error values of each measurement point on the CNC machine table, the B-spline function is used to fit the thermal error prediction model for the entire working area. Finally, the thermal error compensation system of the CNC machine tool has been established. Simulation and empirical studies show that the fitting and prediction accuracy of the model in this paper are better, and the maximum error value of the prediction is reduced by 20.27% compared to the LSTM model. After the application of the thermal compensation system in this paper, the thermal error of the CNC machine tool is greatly reduced, and most of the offset caused by the thermal deformation of the machine tool is eliminated through compensation. In this paper, the design of a thermal error compensation system based on full work area modeling can effectively reduce the thermal error of CNC machine tools, which can be applied to the actual machining process of machine tools to improve the machining accuracy of CNC machine tools.

Accurate road user localization in aerial images captured by unmanned aerial vehicles

Unmanned aerial vehicles (UAVs) have become increasingly popular for traffic data collection. However, the depth relief of road users and the perspective distortion of the onboard camera induce nonnegligible measurement errors while exploiting UAVs to localize road users. To address this issue, this paper presents a method for accurate road user location estimation in aerial images. First, a deep-learning-based method was employed to detect road users in aerial images using oriented bounding boxes. Then, the localization error induced by the depth relief and perspective distortion was examined and modeled, based on which an error compensation scheme was developed to offset the localization error for each road user so that higher localization accuracy is attainable. Field experiments were conducted to evaluate the proposed method's performance. The results demonstrated a promising accuracy in estimating the location of road users, signifying the method's potential to improve the credibility of UAVs in traffic applications.

Analysis of unified power quality conditioner errors

This article is devoted to error analysis of the unified power quality regulator. In the context of the growing importance of reliable and high-quality power supply, power quality regulators are becoming key devices to ensure the stability of networks and meet the needs of domestic consumers. The paper proposes a comprehensive approach to error analysis of the unified power quality conditioner, the main purpose of which is to compensate for the impact of rapidly changing loads on power quality. At the same time, indicators of general harmonic distortion of the quality of electricity are analyzed, and factors such as the magnitude and duration of loads are also taken into account. A large part of the article is devoted to the study of the sources of errors in unified power quality conditioner. A comparison of the parallel-serial and series-parallel topologies of unified power quality conditioner is performed. The influence of the unified power quality conditioner control algorithm on the formation of errors of each topology is analyzed. Using Matlab/Simulink computer simulation tools, the article proposes a framework for error quantification, which allows accurate estimation of errors at various stages of unified power quality conditioner operation. This framework covers the Fourier series transformation of voltage and power for comprehensive estimation of error magnitudes. To confirm the effectiveness of the proposed error analysis and compensation strategies, the article presents graphs of simulation results in the time and frequency domains. Active and reactive power generation errors and voltage setpoint errors are described. These findings emphasize the ability of unified power quality conditioner to improve the quality of electricity, despite measurement errors. The main results include the analysis of deviations of voltage quality indicators, the establishment of a connection between compensation errors and deficiencies in the functioning of the system, as well as the development of recommendations for improving the efficiency of compensation devices.

Two-step deep learning framework with error compensation technique for short-term, half-hourly electricity price forecasting

Prediction of electricity price is crucial for national electricity markets supporting sale prices, bidding strategies, electricity dispatch, control and market volatility management. High volatility, non-stationarity and multi-seasonality of electricity prices make it significantly challenging to estimate its future trend, especially over near real-time forecast horizons. An error compensation strategy that integrates Long Short-Term Memory (LSTM) network, Convolution Neural Network (CNN) and the Variational Mode Decomposition (VMD) algorithm is proposed to predict the half-hourly step electricity prices. A prediction model incorporating VMD and CLSTM is first used to obtain an initial prediction. To improve its predictive accuracy, a novel error compensation framework, which is built using the VMD and a Random Forest Regression (RF) algorithm, is also used. The proposed VMD-CLSTM-VMD-ERCRF model is evaluated using electricity prices from Queensland, Australia. The results reveal highly accurate predictive performance for all datasets considered, including the winter, autumn, spring, summer, and yearly predictions. As compared with a predictive model without error compensation (i.e., the VMD-CLSTM model), the proposed VMD-CLSTM-VMD-ERCRF model outperforms the benchmark models. For winter, autumn, spring, summer, and yearly predictions, the average Legates and McCabe Index is seen to increase by 15.97%, 16.31%, 20.23%, 10.24%, and 14.03%, respectively, relative to the benchmark models. According to the tests performed on independent datasets, the proposed VMD-CLSTM-VMD-ERCRF model can be a practical stratagem useful for short-term, half-hourly electricity price forecasting. Therefore the research outcomes demonstrate that the proposed error compensation framework is an effective decision-support tool for improving the predictive accuracy of electricity price. It could be of practical value to energy companies, energy policymakers and national electricity market operators to develop their insight analysis, electricity distribution and market optimization strategies.

Sphericity measurement based on telecentric imaging mechanism with image distortion correction and eccentricity error compensation

Sphericity is an essential geometric parameter for determining the processing manufacturing quality of spherical components. This study presents a sphericity measurement method based on telecentric imaging mechanism with image distortion correction and eccentricity error compensation. A sphericity measurement system is designed, and the projection images of the cross-section on the equatorial plane of the measured sphere are acquired using a line scan camera with bilateral telecentric lenses. An analytical camera model for this sphericity measurement system is established by considering major sources of image distortion. The subpixel edge points of the projection images are extracted and converted to cross-sectional profiles on the equatorial plane according to the camera model. An eccentricity error compensation strategy for contour matching of the obtained cross-sectional profile on the equatorial plane is also developed to obtain the three-dimensional contour point coordinates of the sphere. Sphericity is then calculated according to the least square criterion. The effectiveness of the proposed method is verified by measuring two steel balls with diameter in 20 mm and 30 mm. The sphericity measurement error is reduced by 0.3383 mm and 0.4653 mm respectively after image distortion correction and is reduced by 0.2268 mm and 0.0795 mm respectively after eccentricity error compensation. The proposed method can be extended to form error measurements for opaque components with rotary structure on the outer contour.

A Feedrate Planning Method in CNC System Based on Servo Response Error Model

Reducing servo response error and further making reduction on contour error is crucial for high-precision computer numerical control (CNC) machine tools. For a permanent magnet synchronous motor (PMSM) servo system, there is always a response lag in feedrate tracking, which would introduce response error into the machining trajectory. Therefore, it is necessary to improve the performance of feedrate planning and interpolation for trajectory path. In this paper, a novel contour error compensation strategy is proposed. Compared with the mainstream methods, the proposed method offers a simplified alternative to existing contour error estimation techniques. Through a three-closed-loop control structure of a PMSM servo system, a response error model is founded. Afterwards, an improved S-model feedrate planning method is introduced according to the servo response error compensation. This predicted error is subsequently compensated in each interpolation cycle, resulting in a reduction of contour error. Finally, simulations and experiments are performed to demonstrate that the contour error can be reduced in both the ‘∞’-shaped Non-Uniform Rational B-Spline (NURBS) curve path and the butterfly-shaped NURBS curve path using the proposed method.

Evaluation of two model predictive control schemes with different error compensation strategies for power management in fuel cell hybrid electric buses

Fuel cell hybrid electric buses (FCHEBs) employing hydrogen fuel cells as the main power source and supercapacitors as the energy buffer could be a feasible electrified transportation technology. This paper evaluates two model predictive control (MPC) schemes with different error compensation strategies for power management in FCHEBs: MPC scheme with Adaptive Compensation (denoted as AC-MPC) and MPC scheme with Gaussian Process Regression Compensation (denoted as GPRC-MPC). AC-MPC introduces adaptive weights based on the supercapacitor state of charge (SOC) and compensates for the errors associated with the linearization of the nonlinear fuel cell/supercapacitor hybrid energy storage system. GPRC-MPC utilizes Gaussian process regression to predict and compensate for the load disturbance error and the residual error. AC-MPC and GPRC-MPC are evaluated using the New York Bus (NYBus) drive cycle and a drive cycle collected along the GBG17 bus route in Sweden. Simulation results demonstrate the effectiveness of AC-MPC and GPRC-MPC in improving the hydrogen system performance by reducing the hydrogen consumption and the maximum fuel cell current change rate compared to the linear MPC scheme without any compensation while ensuring that the supercapacitor SOC is bounded.

Inverse kinematics and multi-objective configuration optimization of the SSRMS manipulator

The Space Station Remote Manipulator System (SSRMS) type redundant manipulator with higher flexibility and foldability is widely used in the space environment. Inverse kinematics and multi-objective configuration optimization are analyzed in this paper. An arm angle parameterized inverse kinematics method using the approximate solution and error compensation scheme is proposed, which has the advantages of not requiring a selection of initial estimates of joint variables, being insensitive to Jacobian matrix singularities, having no pose error, and finding multiple solutions. In addition, Multiple Objective Particle Swarm Optimization (MOPSO) scheme is adopted to optimize the arm angle trajectory in null space, and the optimization index is set as joint torque and manipulability. Unlike traditional trajectory planning methods, we synthesize null space and configuration control to provide a novel perspective for trajectory planning. Finally, the experiments prove that the inverse kinematics algorithm is efficient and reliable, and the effectiveness of the configuration optimization method is verified by the numerical simulation of single objective and multi-objective optimization.

Model Predictive Direct Speed Control of Permanent-Magnet Synchronous Motors with Voltage Error Compensation

Traditional strategies for model predictive direct speed control of permanent-magnet synchronous motors are known to be vulnerable to voltage errors. In this paper, we present a novel approach that compensates for voltage errors arising from inverter nonlinearity and bus voltage uncertainties, while remaining unaffected by parameter errors. Initially, we conducted a detailed analysis to assess the impact of inverter nonlinearity and bus voltage uncertainties. Subsequently, we proposed a voltage error compensation strategy based on bus voltage identification. Using this strategy, the identified voltage error is effectively compensated within candidate voltage vectors. To validate the effectiveness of our proposed method, we conducted comprehensive experiments. The results demonstrate notable improvements compared with traditional model predictive control. Specifically, our method successfully reduces the total harmonic distortion of phase currents from 23.2% and 49.6% to 11.6% and 13.9%, respectively. Additionally, it accurately identifies voltage errors, even in the presence of parameter errors. Overall, our proposed method presents a robust and reliable solution for addressing voltage errors, thereby enhancing the performance and stability of the system.