Error Compensation Method Research Articles

Kinematic Calibration Method for Large-Sized 7-DoF Hybrid Spray-Painting Robots

Large-sized seven-degrees-of-freedom (7-DoF) hybrid spray-painting robots combine ample working space and high flexibility, making them lucrative for the spray painting of aircraft and rocket surfaces. However, their kinematic calibration is hindered by gravitational deformation, which problem is addressed in this study by introducing a rigid-flexible coupling error modeling method. The latter combines the finite element method (FEM) and stiffness matrix method to assess the spatial gravitational deformation of a hybrid robot, which is then introduced into a geometric error model to establish the rigid-flexible coupling error identification model. Given many redundant parameters in the identification model for 7-DoF robots, these parameters are classified and simplified using the nonlinear least-square regularization method for parameter identification. Combining the inverse solution of 7-DoF spray-painting robots with dynamic characteristics considered, an error compensation method for 7-DoF robots is proposed. The kinematic calibration test results strongly indicate that position errors are significantly reduced with gravity compensation taken into consideration, and error convergence speed increases, demonstrating that the kinematic calibration method is feasible and can effectively improve the accuracy of spray-painting robots. The mean errors in the X- and Y-directions are reduced by 20 and 17%, respectively, compared to the conventional method. The proposed method is instrumental in the accurate kinematic calibration of large-sized 7-DoF hybrid robots.

Database-driven patient-specific registration error compensation method for image-guided laparoscopic surgery

A surgical navigation system helps surgeons understand anatomical structures in the operative field during surgery. Patient-to-image registration, which aligns coordinate systems between the CT volume and a positional tracker, is vital for accurate surgical navigation. Although a point-based rigid registration method using fiducials on the body surface is often utilized for laparoscopic surgery navigation, precise registration is difficult due to such factors as soft tissue deformation. We propose a method that compensates a transformation matrix computed using fiducials on the body surface based on the analysis of positional information in the database. We built our database by measuring the positional information of the fiducials and the guidance targets in both the CT volume and positional tracker coordinate systems through previous surgeries. We computed two transformation matrices: using only the fiducials and using only the guidance targets in all the data in the database. We calculated the differences between the two transformation matrices in each piece of data. The compensation transformation matrix was computed by averaging these difference matrices. In this step, we selected the data from the database based on the similarity of the fiducials and the configuration of the guidance targets. We evaluated our proposed method using 20 pieces of data acquired during laparoscopic gastrectomy for gastric cancer. The locations of blood vessels were used as guidance targets for computing target registration error. The mean target registration errors significantly decreased from 33.0 to 17.1 mm before and after the compensation. This paper described a registration error compensation method using a database for image-guided laparoscopic surgery. Since our proposed method reduced registration error without additional intraoperative measurements during surgery, it increases the accuracy of surgical navigation for laparoscopic surgery.

Rectilinear strain sensing framework for real time compensation of structural distortions in precision machinery

Precision machinery such as machine tools use heavy duty structural elements to provide high accuracy and repeatability. However, external forces and thermal effects can still cause significant errors. Machine builders put significant emphasis on good design for error avoidance and more recently, utilise software-based error compensation methods to further improve performance. For geometric errors which result from build tolerances, and which normally only vary slowly over time, most Numerical Control systems provide functionality for pre-calibrated error compensation. For compensation of thermal errors, temperature sensors are often used to provide data for a model which calculates the effect of the temperature field on the machine structure. Although this method is widely researched, there is often significant residual error due the time-variant non-linear relationship between temperature and the error between the tool and workpiece. This may be exacerbated by introducing multi-material structural elements to reduce weight. Direct measurement and combining temperature with direct measurement can enable more precise modelling but can add significant cost of additional sensors. In this research a direct measurement method is applied using a series of short-range, ultra-low-cost displacement sensors, exploiting a particular arrangement of compact slotted photo-microsensors. These are organised in a novel rectilinear framework to enable detection of the bending of a machine tool structure. The design provides high resolution measurement of strain over arbitrary lengths and cost-effective hardware for permanently embedding on a machine. The system was applied to the ram of a high precision 3-axis machine tool and used to compensate the thermal error caused by running the integrated high-speed spindle. The residual error was reduced from 10 to 4 µm, even reducing the magnitude of the effect of the chiller cycles.

Non-uniform machining allowance planning method of thin-walled parts based on the workpiece deformation constraint

In order to reduce the machining deformation of thin-walled parts during milling, a non-uniform allowance planning method for thin-walled parts based on the workpiece deformation constraint with the idea of adding materials in reverse material removal sequence is proposed in this paper. This method does not require accurate deformation prediction and extensive experiments compared to traditional error compensation methods. It strives to maximize the allowance to enhance the stiffness of the in-process workpiece. First, a cutting force threshold calculation method is proposed according to the finite element method. The cutting force threshold at different positions is calculated by obtaining the local stiffness characteristics at the cutter-contact point under the constraint of allowable deformation. And then, the maximum machining allowance at the cutter-contact point is calculated depending on the cutting force model. Considering that the stiffness of the workpiece is position-dependent and affected by material removal, the stiffness of the workpiece is updated by adding elements in the reverse cutting direction, and the finishing stock is obtained by surface fitting. Experimental results show that compared with the traditional uniform allowance method, the error of the proposed method is reduced by about 83%, which can effectively reduce the deformation and improve the machining accuracy.

Separation and compensation of nonlinear errors in sub-nanometer grating interferometers.

In this paper, to separate and compensate the nonlinear error in the grating interferometer, we analyze the source and generation mechanism of this error, deduce the nonlinear error model of the measured signal and the calculated phase signal, and study the characteristics of the established nonlinear error model. The reason why the frequency multiples of ideal phase signals and higher-order nonlinear errors caused by ghost reflections and angular errors of the laser's z-axis are not integers is explained. Then, a nonlinear error separation and compensation method based on cross-correlation coefficient is proposed. Experiments show that the frequency multiplier relationship between the high-order nonlinear error and the ideal interference signal is close to but not equal to 3-fold. The peak-to-peak value of the compensated nonlinear error is reduced from 17.40 nm to 7.05 nm.

Modeling and control of cable-driven continuum robot used for minimally invasive surgery.

Continuum robot has great advantages in minimally invasive surgery (MIS) due to the slenderness and dexterity. But the friction and backlash result in the low trajectory tracking accuracy. This paper aims to study the transmission process of the driving force and the error compensation method. The statics is performed considering the frictional transmission process, and the variation of friction force with driving force is revealed by the model. The hysteresis effect of the tip trajectory is revealed. Then the relationship between the load history and the robot shape is studied, next, the deflection of the robot subject to the different loading forces can be predicted. The correctness of the mechanical model is verified by numerical simulation and experiments. Furthermore, the control methods according to the cable length and the driving force are compared respectively, and a method of error compensation according to the cable length is worked out considering the mechanical model. The rationality of the compensation method is validated by experiment. The results show that the compensation method based on cable length greatly improves the control accuracy, and the maximum deviation is 1.08 mm. The established model and compensation method create conditions for clinical application of the proposed continuum robot.

Error analysis and compensation method of underground turbine motor voltage sensor

the control system of petroleum drilling engineering has been in a bad and high temperature environment for a long time. In the unknown downhole working environment, the signal detection accuracy of turbine motor determines the drilling quality and cost of rotary steering drilling engineering. In order to design a high-temperature voltage sensor that meets the needs of oil drilling engineering, this paper takes 206B voltage sensor as the experimental object, simulates the downhole environment, carries out high-temperature experiments on this type of sensor, and analyzes the influencing factors of its error. The experimental data show that the downhole turbine motor voltage sensor is most affected by temperature, and the 206B sensor can withstand a maximum temperature of 125 °C. In view of its temperature influence, the least square method is used to compensate the error. The compensated voltage sensor error is reduced to 1~3.048%, which effectively improves the accuracy of the turbine motor voltage detection device and can accurately receive the downward signal of rotary steering drilling, so as to greatly reduce the drilling cost.

Error Compensation for Low-Density Circular Gratings Based on Linear Image-Type Angular Displacement Measurements

The image-type angular displacement measurement method based on linear image recognition has garnered attention because of its higher frequency response, strong fault tolerance, and high robustness. In the small-size image angular displacement measuring device, due to the limited pixel size, the circular grating cannot place more lines when realizing single-channel absolute coding recognition on a small diameter grating disk. This leads to larger errors in angular displacement measurement when the line density of the grating disk is low. To improve the measurement accuracy of small-scale displacement, the present work aimed to reduce this error by studying the error compensation method involving low-density grating disks. First, the mechanism of linear image-type angular displacement measurements is described, and a measurement algorithm based on linear scan images is proposed. Second, the measurement error model for low-density grating disks is established according to the proposed measurement algorithm. Third, a simplified error compensation algorithm based on a harmonic model is developed. Finally, simulations and experiments are performed to verify the performance of the proposed algorithm. Simulation results show that the developed harmonic compensation algorithm can effectively reduce the error caused by the low-density circular grating. When the proposed error compensation algorithm is applied to a grating disk with a 62 mm diameter and 2 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">^N</i> lines, the measurement accuracy is improved from 8.14” to 4.78”. The proposed error compensation algorithm can significantly improve the accuracy of linear image-type angular displacement measurements involving low-density grating disks, and the results presented herein laid a foundation for improving the accuracy and engineering applicability of angular displacement measurement technology.

A Low-Cost Digital Twin-Driven Positioning Error Compensation Method for Industrial Robotic Arm

In robotic arms, transmission error will cause positioning error, which increases with the wear and tear of the transmission mechanism. Positioning error will degrade the performance of the robotic arm. It is necessary to carry out intelligent maintenance for the robotic arm. In this article, a low-cost digital twin (DT)-driven positioning error compensation method is proposed for robotic arm. The DT model of the robotic arm is first established, including the physical layer, data transfer layer, model layer, functional layer, and application service layer. A low-cost attitude sensor is then applied to provide actual information of the robotic arm to the DT model. When the DT model senses the positioning error of the robotic arm, it reduces the positioning error by adjusting the motor angle. The effectiveness of the proposed method is finally verified by the experimental results under different conditions.

Calibration and error compensation of scanner-based robotic belt grinding system

Turbine blade is one of the key components of turbomachinery, and the machining quality of its airfoil surface has an important impact on the operating efficiency, service life, and safety of the turbine. Robotic abrasive belt grinding has become an important means of blade airfoil surface machining. Based on the self-developed robot grinding system, this paper proposes a scanner-based system calibration method to determine the relationships among coordinate systems of measurement, robot base, tool, and workpiece. An accurate and efficent calibration method of workpiece coordinate system based on rapid surface segmentation of point cloud using CAD model is established. An blade error surface is constructed by B-spline interpolation to compensate system errors such as absolute positioning error of robot, calibration error, and blade shape error. The calibration process is illustrated at the end of this paper. The effectiveness of the calibration and error compensation methods proposed in this paper are verified by the simulation results.

Study on FOG scale factor error calibration in start-up stage based on GWO-GRU

The fiber optic gyroscope (FOG) is the core component of the inertial system, which has been widely utilized in aviation, maritime, automotive, and other fields. The scale factor is one of the critical parameters to characterize the dynamic performance of the FOG. Due to the temperature sensitivity of the optoelectronic devices, the scale factor errors will be caused with the temperature change. The traditional compensation method usually compensates the output of the FOG in a stable working state. Without considering the difference between the characteristics of the FOG in the start-up stage and the stable working state, the compensation accuracy of the traditional method cannot meet the demand for quick start-up in application areas. According to the above analysis, a novel scale factor error compensation method based on the grey wolf optimization (GWO) and gated recurrent unit (GRU) neural network is proposed in this paper. Furthermore, a new experiment is designed to calibrate the scale factor error in the start-up stage, which can reduce the calibration time and ensure the calibration accuracy. The experimental results demonstrate the proposed method significantly improves the compensation accuracy compared with other methods, such as the multilayer perceptrons (MLPs) and the traditional GRU network.

Design and calibration of the accurate torque measurement systems of the precision robot reducer detector

The input and output torque testing is crucial for improving the quality of Industry robot reducers. In this study, the TMMISR and TMMOSR for a vertical-type robot reducer detector were designed. The length of measurement chain between the torque transducer and the tested reducer was shorten. The overall stiffness of this instrument has been improved through structural optimization. The characteristics of the two main parts of the torque-measurement errors were also analyzed. A high precision torque calibrator with a standard torque output is used to handle the torque calibration process. An error compensation method based on a backpropagation neural network was adopted for the error compensation process in this study. After error compensation, torque-measurement precision of 0.1% can be achieved by the reducer detector over the full torque measurement scale, and the instrument can be used for both static and dynamic measurements.

High-precision magnetorheological finishing based on robot by measuring and compensating trajectory error.

The 6-DOF industrial robot has wide application prospects in the field of optical manufacturing because of its high degrees of freedom, low cost, and high space utilisation. However, the low trajectory accuracy of robots will affect the manufacturing accuracy of optical components when the robots and magnetorheological finishing (MRF) are combined. In this study, aiming at the problem of the diversity of trajectory error sources of robot-MRF, a continuous high-precision spatial dynamic trajectory error measurement system was established to measure the trajectory error accurately, and a step-by-step and multistage iterations trajectory error compensation method based on spatial similarity was established to obtain a high-precision trajectory. The experimental results show that compared with the common model calibration method and general non-model calibration method, this trajectory error compensation method can achieve accurate compensation of the trajectory error of the robot-MRF, and the trajectory accuracy of the Z-axis is improved from PV > 0.2 mm to PV < 0.1 mm. Furthermore, the finishing accuracy of the plane mirror from 0.066λ to 0.016λ RMS and the finishing accuracy of the spherical mirror from 0.184λ RMS to 0.013λ RMS using the compensated robot-MRF prove that the robot-MRF has the ability of high-precision polishing. This promotes the application of industrial robots in the field of optical manufacturing and lays the foundation for intelligent optical manufacturing.

A method of geometric error identification and compensation of CNC machine tools based on volumetric diagonal error measurements

A method of geometric error identification and compensation of CNC machine tools based on volumetric diagonal error measurements

Development of Voltage Control Algorithm for Improving System Stability in Korean Distribution Grids

Problems with overvoltage and reverse energy flow arise as the percentage of distribution energy resources (DERs) in distribution system rises. This paper implements a MATLAB/Simulink linked model that communicates with the OpenDSS engine. The point of common coupling (PCC) voltage typically mitigates using the inverter outputs control. However, case overvoltage issues occur in distribution networks and the influence of the volt–var control effect is insufficient to reduce PCC voltage to a stable range. To improve the reactive control effect, this paper proposes active power control and voltage error compensation methods that maximize the reactive power control effect. The DER management system (DERMS) platform was constructed to analyze the effect of changing DER output values. The DERMS data are organized based on real distribution line (D/L) system data where overvoltage occurred in Korea and the control effect of the real system is analyzed. This control method analysis can be used to develop an inverter control scheme for the over voltage issues described in this paper.

Methods for Underwater Gravity Measurement Error Compensations Based on Correlation Analysis

The measurement of Earth’s gravitational field is important in geophysics, geodynamics, geodesy, oceanography, and space science. The ocean covers 71% of the earth’s surface; therefore, measuring the ocean’s gravitational field is crucial. Compared with shipborne gravimetry, underwater gravimetry near the seafloor is closer to gravity sources and can obtain short-wavelength gravity information that is useful for small-scale deposit detection and seawater intrusion monitoring. This article focuses on gravimetric errors caused by the poor dynamics of the carrier; an error compensation method for underwater gravimetry based on correlation analysis is proposed. By analyzing the error sources that affect the dynamics of the carrier, the relationship between the gravimetry error and impact factors related to the dynamics was established, and the model’s parameters were estimated by the least-squares fitting method. The experimental data show that this method can effectively compensate for gravimetric errors caused by carrier dynamics and provide the theoretical basis and algorithm model for underwater gravimetry in the bottom-tracking mode.

Active projection nonlinear γ correction method for fringe projection profilometry.

In fringe projection profilometry (FPP), the luminance nonlinearity generated by the superimposed γ effect of the projector and camera can lead to distortion of the intensity of the sinusoidal phase-shift fringe, resulting in a reduction of measurement precision and resolution. Traditional phase error compensation and γ-correction methods need to focus on the projector's optimal performance. However, commercial projectors often have huge apertures and are, therefore, unable to project a perfectly focused sinusoidal fringe image. This paper proposes an easy-to-implement active projection error correction method with high precision that is insensitive to projector defocus. After calibrating the projector to establish the nonlinear γ-response model of the optical measurement system, inverse γ compensation is performed. By generating and projecting a set of precorrected sinusoidal fringes, the camera can capture the high-quality sinusoidal fringe image and decrease the phase measurement error caused by the nonlinear γ effect of the FPP system. Computer simulations and experiments verify the effectiveness and feasibility of the proposed method for estimating and correcting the nonlinear γ distortion of the FPP system. The experimental results show that using the proposed active projection method to compensate for the error of the three-step phase-shift algorithm can achieve a high-precision measurement, and the influence of the system's nonlinear γ effect on the measurement accuracy is significantly suppressed.

Thermal error modeling of machine tool based on dimensional error of machined parts in automatic production line

Thermally induced error has proven to be the major source of machining error for the machine tool working in a non-temperature-controlled workshop. Current research on thermal error modeling and compensation is implemented based on the measured thermal deformation of machine tool, and the data is obtained referring to spindle idling rather than metal cutting condition, resulting in the disadvantages of the established model with low adaptability to varying conditions. In this paper, a modeling and compensation method based on the dimensional error of the machined parts is proposed to address the issue and verified through machine tools in an automatic production line. Compared with the modeling based on thermal deformation, the method formulates a more direct relations between temperature rise and machining error. The thermal error modeling is carried out by measuring the dimension deviation of the inner hole diameter of the motor end cover and the screened representative temperature variables. Meantime, considering the temperature coefficient in model is difficult to converge when modeling with the single-day data, the unified modeling with the multi-day data is realized by improving the conventional multiple linear regression model. Finally, the generalized model used for thermal error compensation in x direction of the machine tool is obtained. The real-time compensation of the thermal error based on the established model is realized with the machine tool machining in mass production. The verification results show that this error modeling and compensation method can reduce the machining error of the end cover by more than 52%, irrespective of experiencing various complicated working conditions. Stability and robustness of the modeling are also validated through application on the other machine tool with the same configuration and real machining over seven days.

Research on Continuous Error Compensation of a Sub-Arc-Second Macro/Micro Dual-Drive Rotary System.

In this paper, a sub-arc-second macro/micro dual-drive rotary system is designed, and the continuous compensation of the system error and its experimental research are completed. First, the macro-drive system is driven by a direct-drive motor, and the micro-drive system uses a piezoelectric ceramic to drive the micro-drive rotary mechanism; the system uses a micro-drive system to compensate the motion error of the macro-drive system, and uses circular grating to feedback the displacement of the macro/micro total output turntable to form a macro/micro dual-drive closed-loop control system. Second, based on the establishment of the system error model, the design of the system’s continuous error compensation scheme is completed. Finally, the positioning accuracy testing of the system, direct error compensation of the macro-drive, manual error compensation of the macro-drive, error compensation performance of the micro-drive part and macro/micro compensation of the system are carried out in the study. The results show that the repeated positioning error and the positioning error of the system are reduced by 78.8% and 95.2%, respectively, after macro/micro compensation. The correctness and effectiveness of the designed system design, error compensation and control method are verified through performance tests, and its positioning accuracy is verified to the sub-arc-second (0.1 arcsecond) level. The research in this paper has important reference value for the development of ultra-precision macro/micro dual-drive technology.

A two-step machining and active learning approach for right-first-time robotic countersinking through in-process error compensation and prediction of depth of cuts

• Two-step process method for online compensation and prediction of machining errors • Data-driven models require large training datasets for accurate predictions • Training data is very expensive to obtain for high-value manufacturing processes • Active learning is used to identify the most informative data for model training • Right-first-time robotic machining and reduced inspection costs are achieved Robotic machining processes are characterised by errors arising from the limitations of the industrial robots. These robot-related errors can compromise the overall manufacturing process performance, resulting in final products with dimensions different from the nominal specifications. To avoid accumulation of errors through several manufacturing stages, a quality inspection step is usually performed after the cutting operation. This work presents an innovative two-step manufacturing method for achieving right-first-time characteristics in robotic machining operations through in-process inspection and compensation of the systematic errors, whilst collecting suitable training data for building predictive models. The key idea behind the proposed method is based on the observation that under certain conditions, the robotic machining errors remain largely consistent, and therefore by splitting the process into two similar steps and having an inspection step in between, a prediction and then compensation of the systematic errors would be possible. A Gaussian Process Regression (GPR) framework is applied for the creation of robust process models that predict the post-process inspection result from in-process signal features, with the associated confidence intervals. An active learning algorithm that makes online decisions on the inspection task based on the current confidence of the models, is also proposed. The two-step machining method and the active learning approach were both tested on a robotic countersinking process experiment. The results showed that the in-process inspection and error compensation of the proposed two-step machining method was able to achieve final countersink depths very close to the desired target, confirming the potential for right-first-time robotic machining. In addition, the active learning results highlighted the ability of the algorithm to reduce the number of required post-process inspections, thus saving both time and costs, whilst also identifying novel data relevant for the model training.