Error Compensation Algorithm Research Articles

A high-efficiency positioning error compensation method for a large parallel mechanism based on pose correction similarity

PurposeConsidering the influence of deformation error, the target poses must be corrected when compensating for positioning error but the efficiency of existing positioning error compensation algorithms needs to be improved. Therefore, the purpose of this study is to propose a high-efficiency positioning error compensation method to reduce the calculation time.Design/methodology/approachThe corrected target poses are calculated. An improved back propagation (BP) neural network is used to establish the mapping relationship between the original and corrected target poses. After the BP neural network is trained, the corrected target poses can be calculated with short notice on the basis of the pose correction similarity.FindingsUnder given conditions, the calculation time when the trained BP neural network is used to predict the corrected target poses is only 1.15 s. Compared with the existing algorithm, this method reduces the calculation time of the target poses from the order of minutes to the order of seconds.Practical implicationsThe proposed algorithm is more efficient while maintaining the accuracy of the error compensation.Originality/valueThis method can be used to quickly position the error compensation of a large parallel mechanism.

Fast fixed-time extended state observer based command filtering backstepping control of free-flying flexible-joint space robots

System parameter perturbations, external disturbances, and input saturation issues seriously affect the on-orbit operation precision and rapid response capabilities of the free-flying flexible-joint space robots (FFSR). To this end, a fixed-time extended state observer (ESO) based non-singular command filtering backstepping controller is proposed. The fast fixed-time ESO is designed to estimate the parameter perturbations and external disturbances. To avoid the “computational explosion” caused by multiple derivatives of the virtual control law in backstepping control, a second-order command filter is employed to obtain the derivative of virtual control laws. Meanwhile, to reduce the filtering errors induced by the command filter, a non-singular fixed-time filtering error compensation algorithm is developed. Furthermore, considering the constraints of control moment gyroscope (CMG) and joint motors, an anti-saturation compensation algorithm is introduced to drive the system out of the saturated region rapidly, thus reducing actuator saturation effects on the control system performance. Theoretical analysis shows the proposed controller can ensure the system tracking error converges to any arbitrarily small neighborhood of the origin within fixed time. Simulation results demonstrate that the designed non-singular fixed-time command filtering backstepping controller exhibits fast convergence speed and high tracking accuracy.

A novel phase measuring deflectometry based on polar coordinate

Phase measuring deflectometry (PMD) is a method measure the surface of a mirror. However, when measuring convex mirrors, Cartesian coordinate fringes experience extreme compression. To address this issue, this paper proposes a novel PMD based on polar coordinate. This new method defines two linearly independent phase modulation directions, using the orthogonal basis of polar coordinate. It establishes polar coordinate fringes with rotational symmetry and radial pre-modulation, effectively reducing the impact of extreme compression at the edges. To correct the phase errors in polar coordinate fringes, a phase error compensation algorithm based on greyscale gradient is introduced. The algorithm calculates the influence factor of the eight connected domains around the error points to be compensated, utilising the phase grey gradient. The wavefront gradient data obtained through polar coordinate fringes are radial and tangential. Hence, a surface reconstruction method is proposed based on the Zernike partial derivative polynomial based on polar coordinate. In this method, the tangential partial derivatives and radial partial derivatives of the first 36 terms of Zernike in polar coordinate to construct Gram matrix equations. As a result, linearly independent Zernike recovery coefficients are obtained from coupled aliasing gradient data. Compared to the Cartesian coordinate system, the proposed method significantly reduces the fitting coefficient errors. Experimental measurements of convex mirrors with radii of curvature of 200 mm and 100 mm were conducted. The results demonstrate that compared to traditional PMD, this technique not only effectively suppresses extreme compression and increases the measurement area but also improves measurement accuracy by six times.

Autonomous ground vehicle gravity anomaly measurement and dynamic error compensation

Abstract To address the issue that dynamic gravity anomaly measurement is overly dependent on GNSS and can’t be measured autonomously at this stage, this paper proposes an autonomous ground vehicle dynamic gravity anomaly measurement method based on a strapdown inertial navigation system (SINS), odometer (OD), barometer and platform gravimeter. The SINS/OD /barometer integrated navigation solution delivers high-precision navigation parameters, completes the calculation of correction terms, and performs the autonomous dynamic gravity anomaly measurement combined with the primary measurement results of the platform gravimeter. Numerical calculations provide the requirements for the application of the proposed method, and the cut-off frequency for extracting gravity anomalies is 0.02 Hz, as determined by power spectral density analysis. In order to further improve the measurement accuracy and account for dynamic errors caused by vehicle maneuvering, a long-short-term memory (LSTM) model of recurrent neural network (RNN) is introduced. A series of experiments under multiple circumstances with repeated lines were conducted in Tianjin, China, and the static measurements along the line were taken using CG-5 to provide true values of gravity anomalies. The results demonstrate that the autonomous measurement scheme can achieve accuracy comparable to GNSS-assisted, and that dynamic error compensation algorithm based on LSTM improves the dynamic gravity measurements accuracy significantly without sacrificing the spatial resolution of gravity anomalies.

Research on six-joint industrial robotic arm positioning error compensation algorithm based on motion decomposition and improved CIWOA-BP neural network

Motion errors in the trajectory of a six-joint industrial robotic arm’s end-effector can significantly impact machining precision. Complex milling operations can lead to deviations from the intended path due to the robotic arm’s structural characteristics. These errors often exhibit periodic and position-dependent variations, underscoring the need for meticulous control measures. To address this challenge, we propose a novel motion decomposition-based error compensation technique for a six-joint industrial robotic arm. This approach involves breaking down the robot’s motion trajectory into distinct components and constructing prediction models for each component using a BP neural network. These models are then optimized using the Whale Optimization Algorithm (CIWOA) and an adaptive chaotic mapping clustering approach to improve efficiency and global optimization. The proposed method is applied to various motion types of the robotic arm, resulting in substantial enhancements in absolute positioning accuracy. Experimental validation confirms the reliability of the CIWOA-BP neural network prediction model and the effectiveness of the nonparametric accuracy compensation method in refining motion planning precision.

Automatic compensation system for eccentricity error of absolute optical encoder.

Eccentric error is a vital part of high-precision optical encoder error. An automatic error compensation system is designed to lower the eccentric error of the encoder. On the periphery of the fan-shaped code path of the traditional encoder disk, a set of radial code paths is drawn. This radial code path is composed of several concentric circles with alternating light and dark lines. The direction of the radial code path is perpendicular to the direction of the fine code path. When the encoder rotates, the eccentricity of the encoder disk is measured by the moiré fringe signal output from the radial code channel. Based on the eccentricity error compensation algorithm, the eccentricity error of the encoder disk is compensated in real time to enhance the accuracy of the encoder. The experimental results of an encoder show that the mean square error of the encoder before the eccentricity error compensation is 21.25 arc seconds, and it is 3.66 arc seconds after compensation by this algorithm. The algorithm can significantly compensate the error caused by the eccentricity of the encoder and greatly improve the accuracy of the encoder.

Compound-choking theory and artificial neural networks-based hybrid modeling for supersonic ejectors

As the core component of ejector refrigeration systems, the research of ejector mechanisms has always been a hot topic. Based on the compound-choking theory, this paper studies the relationship between the entrainment ratio and critical back pressure and designs a neural network-based online error compensation mechanism for supersonic ejectors. Firstly, a thermodynamic model of the ejector is developed by combining the ideal gas model, the compound-choking theory, and the constant-pressure mixing theory. Then, the thermodynamic relationship between the entrainment ratio and critical back pressure is derived by introducing the idea of a hypothetical mixing cross section. Compared with the existing results, our method is able to improve critical back pressure prediction accuracy by virtue of the actual entrainment ratio. Therefore, a new adaptive error compensation algorithm is proposed for supersonic ejectors based on neural networks. Thus, the proposed scheme can be regarded as a hybrid modeling method for supersonic ejectors, which combines thermodynamic laws and data-driven artificial intelligence algorithms. Experimental data from ejector refrigeration systems with R141b, R245fa, water vapor and R134a are used in this paper to verify the validity of the model. The simulation results show that our method can effectively predict the critical back pressure, and all the prediction errors are less than 10%.

Measurement method for large aperture angle incomplete spherical surface stitching based on confocal focusing

In traditional stitching measurements, the central sub-aperture is usually used as the reference and is not suitable for incomplete spherical surfaces without central sub-aperture. The measurement of each sub-aperture requires manual readjusting the position and attitude of the measured component, resulting in low measurement accuracy and low measurement efficiency. In response to this issue, this study proposed a method based on confocal focusing for large aperture angle incomplete spherical surface stitching measurement. Automatically and accurately determine the position of the common focus through confocal focusing technology, the positioning accuracy of the measured component is improved. A sub-aperture stitching model was built, coordinate mapping rotation algorithm and overlapping area error compensation algorithm were applied to the surface shape of each sub-aperture, achieving stitching measurement of large aperture angle incomplete spherical surfaces. Finally, the confocal interference stitching measurement system was built to carry out stitching experiments of sphere and large aperture angle incomplete spherical surface. The stitching experimental results indicated that the method increases the measurement accuracy of PV by 2.2 times, increases the measurement accuracy of RMS by 2.3 times, and increases the measurement efficiency by 1.6 times. Therefore, this method provides a high-precision measurement method for detecting large aperture angle spherical surface shape.

Simulation of motion error compensation of CNC with multi-axis linkage

Motion errors can significantly affect the machining accuracy of MACNC. To reduce the motion errors in the operation of CNC, an error compensation algorithm is proposed in the study. Firstly, the motion error measurement and identification method is proposed, and in this way, the MECA based on the third spline fitting is proposed Finally, the effectiveness is verified by simulation experiments. The proposed error measurement method has high measurement accuracy, and the MECA can effectively reduce the machining error value, and its processing time is only 0.012s. The measurement accuracy of the error measurement method proposed in the study reached 98.95%, which was 4.49% and 4.88% higher than the minimum measurement accuracy based on wavelet denoising and genetic algorithm, respectively. When the number of iterations was 5, all three measurement methods achieved the minimum measurement accuracy, and the minimum measurement accuracy of the proposed measurement method was 91.00%, Compared with the minimum measurement accuracy of 93.65% and 94.26% based on wavelet denoising and genetic algorithm, it has decreased by 2.65% and 3.26%, respectively. When disturbed, the accuracy rate of the error compensation algorithm proposed by the research is 93.9%, which is 2%, 2% and 3.5% higher than the minimum values of 91.9%, 91.9% and 90.4% of the three error compensation algorithms based on BP neural network, Particle swarm optimization algorithm and genetic algorithm, respectively. The above results show that the MECA can effectively achieve the error compensation of MACNC, with a fast processing speed, which can effectively workshop Machining efficiency and quality.

Evaluation of surface quality and error compensation for optical aspherical surface grinding

Optical aspherical lenses are widely used in the aerospace, electronics, and optical communication industries. Grinding is the primary processing method used to ensure their precision. It is difficult for traditional evaluation indexes to fully reflect the optical properties of optical surfaces after grinding. This paper presents a novel method for characterizing surface quality of optical aspherical surface oriented to the application of optical properties. The proposed evaluation indicators include the profile error, surface roughness, slope error, and projection-area scale-deviation value, which can be used to comprehensively evaluate the surface quality. Subsequently, a novel grinding compensation method for the optical aspherical surface is proposed, and its compensation precision is evaluated using the abovementioned evaluation indicators. The results show that the maximum surface-shape error decreases to less than 150 nm; additionally, the central cusp point is restrained. The precision and efficiency of error compensation for the optical aspherical surface are significantly better than those of the conventional method. The proposed evaluation indicators can be applied to reflect the features of optical aspheric surface directly. The high efficiency and precision compensation of optical aspherical surface can be achieved with the proposed evaluation method and modified error compensation algorithm.

Robust Self-Constructing Fuzzy Neural Network-Based Online Estimation for Industrial Product Quality

Online estimation for product quality is crucial for improving industrial process efficiency. However, model degradation and outliers usually challenge industrial quality estimation models. To tackle the above problems, a robust self-constructing fuzzy neural network (RSC-FNN) is developed in the article. In the RSC-FNN, the rules can be automatically created or pruned, obtaining the online self-constructing mechanism (OSCM). First, an online error compensation algorithm is developed to generate new rules. Second, the model performance and contribution of existing rules are evaluated online to delete redundant rules. Thus, the OSCM effectively improves the structural adaptability and compactness of the RSC-FNN. Moreover, the correntropy-induced criterion, which can handle complex outliers, is modified for the parameter learning algorithm. Hence, the adverse effect of outliers can be suppressed during the parameter updating process. Besides, we analyze the convergence of the RSC-FNN to ensure its feasibility in industrial applications. Finally, two industrial applications are studied to test the effectiveness of the RSC-FNN. Compared with other FNN <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> , the results indicate that the RSC-FNN performs better in learning efficiency, structure compactness, and robustness.

Research on High-Precision Position Detection Based on a Driven Laser Spot in an Extreme Ultraviolet Light Source

Laser-spot-location detection technology based on photodetectors is widely used in the aerospace, medical, military and communication fields. However, most of the current research focuses on continuous laser detection in the visible and near-infrared bands, and the real-time high-precision position detection of a long-wave infrared pulsed laser is lacking. In this paper, a spot-position detection system based on a four-quadrant detector is designed for a 10.6 μm CO2-driven laser in extreme ultraviolet light source, and a second-order extended error compensation algorithm based on a Gaussian-spot model is proposed. Finally, the algorithm is verified and analyzed experimentally by a spot-position detection system under both focusing and defocusing conditions. The experimental results show that the root-mean-square error, maximum absolute error and average absolute error of the second-order error compensation algorithm are significantly reduced compared with the traditional algorithm, and the detection accuracy of the spot-position is better than 9 μm. The above results show that this spot-position detection system has obvious advantages and high accuracy, which can realize the high-precision real-time detection of a laser’s spot position to obtain accurate spot position information, provide feedback adjustments for subsequent beam pointing control, and provide a theoretical basis for the beam pointing stability of the extreme ultraviolet light source system.

A Study on Refraction Error Compensation Method for Underwater Spinning Laser Scanning Three-Dimensional Imaging.

Laser scanning 3D imaging technology, because it can obtain accurate three-dimensional surface data, has been widely used in the search for wrecks and rescue operations, underwater resource development, and other fields. At present, the conventional underwater spinning laser scanning imaging system maintains a relatively fixed light window. However, in low-light situations underwater, the rotation of the scanning device causes some degree of water fluctuation, which warps the light strip data that the system sensor receives about the object's surface. To solve this problem, this research studies an underwater 3D scanning and imaging system that makes use of a fixed light window and a spinning laser (FWLS). A refraction error compensation algorithm is investigated that is based on the fundamentals of linear laser scanning imaging, and a dynamic refraction mathematical model is established based on the motion of the imaging device. The results of the experiment on error analysis in an optimal underwater environment indicate that the error in reconstructing the radius is decreased by 60% (from 2.5 mm to around 1 mm) when compensating for the measurement data of a standard sphere with a radius of 20 mm. Moreover, the compensated point cloud data exhibit a higher degree of correspondence with the model of the standard spherical point cloud. Furthermore, we examine the impact of physical noise, measurement distance, and partial occlusion of the object on the imaging system inside an authentic underwater setting. This study is a good starting point for looking at the refractive error of an underwater laser scanning imaging system. It also provides to us some ideas for future research on the refractive error of other scanning imaging methods.

Nonlinear error compensation algorithm for signal resolution of chromatic confocal measurements

The mechanisms of the nonlinear error, primarily stemming from the deviation of the polynomial model fitting the wavelength-distance mapping relationship in chromatic confocal measurement, have been elucidated. A compensation method is proposed for the nonlinear error, based on a regression tree model. Through calibration experiments using our chromatic confocal sensor, an impressive improvement of over 40 % in precision could be achieved by our proposed compensation method, which advances from ±1 μm to ±0.6 μm within a 4 mm measurement range.

Error compensation of a 2TPR&amp;2TPS parallel mechanism based on particle swarm optimization

This paper solves the problem of the precise compensation of the pose error of a 2TPR&amp;2TPS parallel mechanism. First, the inverse solution of the mechanism is solved, the error source of the mechanism is analyzed, and a closed-loop vector method error model based on the inverse solution is established. Then, the ball screw commutation gap is measured with a high-precision grating ruler, and a laser tracker is used to measure the comprehensive position error of the mechanism under the set trajectory (circle). Finally, an error compensation algorithm based on the particle swarm algorithm is constructed, the measured trajectory data are substituted into the compensation algorithm, the position accuracy of the mechanism is significantly improved, and the compensation effect is remarkable. The compensation algorithm has good versatility, is simple and feasible, and can be applied to the error compensation of various mechanisms.

Drift Error Compensation Algorithm for Heterodyne Optical Seawater Refractive Index Monitoring of Unstable Signals.

The refractive index measurement of seawater has proven significance in oceanography, while an optical heterodyne interferometer is an important, highly accurate, tool used for seawater refractive index measurement. However, for practical seawater refractive index measurement, the refractive index of seawater needs to be monitored for long periods of time, and the influence of drift error on the measurement results for these cases cannot be ignored. This paper proposes a drift error compensation algorithm based on wavelet decomposition, which can adaptively separate the background from the signal, and then calculate the frequency difference to compensate for the drift error. It is suitable for unstable signals, especially signals with large differences between the beginning and the end, which is common in actual seawater refractive index monitoring. The authors identify that the primary cause of drift error is the frequency instability of the acousto-optic frequency shifter (AOFS), and the actual frequency difference was measured through experimentation. The frequency difference was around 0.1 Hz. Simulation experiments were designed to verify the effectiveness of the algorithm, and the standard deviation of the optical length of the results was on the scale of 10-8 m. Liquid refractive index measurement experiments were carried out in a laboratory, and the measurement error was reduced from 36.942% to 0.592% after algorithm processing. Field experiments were carried out regarding seawater refractive index monitoring, and the algorithm-processing results are able to match the motion of the target vehicle. The experimental data were processed with different algorithms, and, according to the comparison of the results, the proposed algorithm performs better than other existing drift error elimination algorithms.

Geometric error calibration and analysis of rotary axes on a five-axis dispensing machine

Geometric rotary axis errors are one of the main factors affecting the dispensing positioning accuracy of five-axis vision dispensing machines. Hence, the accurate detection and compensation of these error terms is an important and challenging problem. In this study, a decoupling identification method for both position-dependent geometric errors and position-independent geometric errors of a rotary dispensing table is proposed based on vision measurement technology. According to this strategy, the screw theory and exponential product formula are used to establish a kinematic model of the end-effector, followed by the definition of the mapping relationship between position-independent geometric errors and axis posture. Then, to separate the coupling error terms of the rotating axes, a step-by-step identification strategy is proposed based on the least squares method. Furthermore, a coordinate search-based error compensation algorithm is developed, which avoids the inverse singular value problem and is insensitive to the error model. Finally, the effectiveness of the proposed identification algorithm and compensation algorithm is experimentally validated.

Splicing Measurement and Compensation of Straightness Errors for Ultra-Precision Guideways.

The straightness error of guideways is one of the key indicators of an ultra-precision machine, which plays an important role in the machining accuracy of a workpiece. In order to measure the straightness error of a long-distance ultra-precision guideway accurately, a splicing measurement for the straightness error of a guideway using a high-precision flat mirror and displacement sensor was proposed in this paper, and the data splicing processing algorithm based on coordinate transformation was studied. Then, comparative experiments on a splicing measurement and direct measurement of the straightness error were carried out on a hydrostatic guideway grinder. The maximum difference between the two measurements was 0.3 μm, which was far less than the straightness error of 5.8 μm. The experiment demonstrated the correctness of the proposed splicing measurement method and data processing algorithm. To suppress the influence of the straightness error on machining accuracy, a straightness error compensation algorithm based on error rotation transformation and vertical axis position correction was proposed, and the grinding experiment of a plane optics with a size of 1400 mm × 500 mm was carried out. Without error compensation grinding, the flatness error of the element was 7.54 μm. After error compensation grinding, the flatness error was significantly reduced to 2.98 μm, which was less than the straightness errors of the guideways. These results demonstrated that the straightness error of the grinding machine had been well suppressed.

Improving Accuracy of Real-Time Positioning and Path Tracking by Using an Error Compensation Algorithm against Walking Modes.

Wide-range application scenarios, such as industrial, medical, rescue, etc., are in various demand for human spatial positioning technology. However, the existing MEMS-based sensor positioning methods have many problems, such as large accuracy errors, poor real-time performance and a single scene. We focused on improving the accuracy of IMU-based both feet localization and path tracing, and analyzed three traditional methods. In this paper, a planar spatial human positioning method based on high-resolution pressure insoles and IMU sensors was improved, and a real-time position compensation method for walking modes was proposed. To validate the improved method, we added two high-resolution pressure insoles to our self-developed motion capture system with a wireless sensor network (WSN) system consisting of 12 IMUs. By multi-sensor data fusion, we implemented dynamic recognition and automatic matching of compensation values for five walking modes, with real-time spatial-position calculation of the touchdown foot, enhancing the 3D accuracy of its practical positioning. Finally, we compared the proposed algorithm with three old methods by statistical analysis of multiple sets of experimental data. The experimental results show that this method has higher positioning accuracy in real-time indoor positioning and path-tracking tasks. The methodology can have more extensive and effective applications in the future.

Coupling error modeling and compensation of beam-column endplate connection system

To investigate the composition form and evolution law of similar errors between full-scale prototype joints and reduced-scale model joints in steel structure beam-column connections, a full-scale benchmark model test and a 1:2 reduced-scale model test of beam-column end-plate connections were carried out respectively, focusing on the similarities and differences between the hysteretic curves of the two. The test results show that there is an irreparable gap between the test results of the two models without considering the similarity error, and the test results of the scaled model cannot accurately represent the full-scale model. Based on the test results, finite element models are established, and a calculation method to compensate the similarity error of the scale model is proposed. The relative independence between similarity error and test operation error is proved. The similarity error can be accurately simulated by response surface method based on multi-factor correlation. This paper focuses on three test error sources, namely, boundary conditions, plate thickness differences and bolt specification differences, meanwhile the contribution weights of the three error sources and their influence forms on the hysteretic curve are well investigated. Based on the proposed error compensation algorithm, the test results of the scale model are compensated and compared with full scale test results, which proves the effectiveness of the error correction algorithm. The compensated scale model test results are in good agreement with the prototype data, and the error is decreased from 70% to 5%.