Proposed Self-calibration Method Research Articles

An integrated cable-driven parallel robot for space station servicing: Self-calibration and pose estimation

This paper presents an integrated cable-driven parallel robot designed for space station servicing. All components, including winches, sensors, controllers, and others, are integrated within its envelope, greatly simplifying the installation process of the robot. However, practical application of this integrated robot necessitates a rapid self-calibration method that relies solely on internal sensors. A self-calibration method utilizing the inertial measurement unit embedded in the robot is introduced to identify external attachment point coordinates. The entire calibration process takes less than 20 minutes, and the experimental results demonstrate that the proposed self-calibration method achieves higher accuracy compared to the existing method. Furthermore, the inertial measurement unit aids in estimating the robot's pose. An error-state Kalman filter is applied to fuse the inertial measurement unit outputs with cable length measurements, providing an optimal estimation of the robot's pose and velocity. In comparison to the existing forward kinematic algorithm, the proposed method exhibits superior estimation accuracy and numerical stability. Experimental results reveal a notable 50% performance improvement over the conventional method.

An Encoder-Based Relative Attitude Observation Method for Self-Calibration in Dual-Axis RINS

This study investigates an encoder-based relative attitude observation method for self-calibration in dual-axis rotational inertial navigation system (RINS). First, the calibration error of the gyroscope parameters caused by the velocity and position observations in systematic calibration is analyzed. Second, a relative attitude observation method utilizing photoelectric encoders for gyroscope parameters estimation is proposed. We apply the proposed method in our designed dual-axis RINS to verify its effectiveness in this work. Experimental results show that the calibration accuracy of the gyroscope can be improved to 0.0005 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^ \circ /h$</tex-math></inline-formula> in bias, and 0.98 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$ppm$</tex-math></inline-formula> in scale factor using the proposed method. The proposed self-calibration method can be utilized as a high-accuracy self-calibration method in dual-axis RINS when the vehicle is in static condition.

Mutual collimation self-calibration for dual-comb ranging-based multilateral coordinate measurement.

We propose a self-calibration method for multilateration based on dual-comb absolute distance measurement. By performing mutual collimation measurements between multilateral measurement bases, we could measure the system parameters in a multilateration system with high precision and efficiency. We demonstrated a multilateral coordinate measurement system based on the proposed self-calibration method. The system realized rapid coordinate measurement with micron-level precision in both tested directions.

Novel Self-Calibration Method for IMU Using Distributed Inertial Sensors

Inertial measurement unit (IMU) calibration is essential to ensure the successful operation of various navigation systems. This article describes a novel method for self-calibration of IMU with distributed sensor architectures. The IMU is composed of modules that are distributed along the measurement axes. Each module is equipped with a single-axis gyroscope and three-axis accelerometer sensors. The modules have also their own signal-conditioning circuits and processors. This enables single-axis calibration of the module with a servo system based on a piezoelectric actuator (PEA). The proposed IMU and calibration method are capable of on-site self-calibration. The calibration is performed with the sinusoidal movements generated by the servo system. Despite the limited displacement of the PEA, high angular velocity and tangential acceleration can be achieved with the servo system. Thus, the gyroscope sensor can be directly calibrated with the angular velocity produced by the servo system. On the other hand, the calibration parameters of the accelerometer are determined by using the tangential and centripetal acceleration produced by the servo system. With the proposed method, the bias, scale factor, and installation errors of accelerometer and gyroscope sensors can be determined. The method has been analyzed by conducting experiments with a prototype IMU. In addition, experiments on 3-DoF turntables have been conducted to confirm the effectiveness of the proposed self-calibration method.

A Disturbance Estimation Approach to Self-Calibration of Gimbal Resolver- to-Digital Conversion System

High-precision position measurement of the gimbal servo system is indispensable to accurate torque output of the control moment gyroscope (CMG). This article addresses the systematic error of the resolver caused by the nonideal output signals of the resolver in the gimbal resolver-to-digital (R/D) conversion system. Due to the limitation of the structure and installation space of the CMG, it is impractical to install additional high-precision sensors to calibrate the raw angular position. Thus, this article proposes a new self-calibration method based on the discrete extended state observer (DESO) to compensate the systematic error of the resolver. The systematic error of the resolver is observed through iterating the resolver systematic estimation error and the compensation table is generated by the output of the DESO. Then, the steady-state error and dynamic performance of the DESO is analyzed and simulated. Finally, the proposed self-calibration method is verified by experiments, which show that the angular position control accuracy is significantly improved, which enhances the speed precision of the gimbal servo system.

Diffraction-based self-calibration method for defocused speckle imaging

Defocused speckle imaging (DSI) is an optical technique where a diffuse object surface is illuminated by a laser source, and the scattered interference speckle field is sampled by a defocused camera. The recorded image contains a speckle pattern that characterizes the surface; if the object displaces or rotates, the speckles move within the camera view. Non-contact surface motion measurements are thus possible by simply tracking the speckle movements. The observed speckle motion magnitude scales proportional to the object distance, which makes DSI attractive for remote measurement applications. However, because DSI measurement sensitivity depends on the specific geometric arrangement, object range and orientation must be known to properly scale the measured speckle motions. In field conditions, manual extraction of the geometric parameters is challenging and time-consuming due to large distances and harsh conditions.To solve the scaling problem, a diffraction-based self-calibration method is proposed here to extract the geometric parameters from the captured speckle patterns directly with no additional sensors. The solution utilizes multi-longitudinal mode laser illumination combined with speckle pattern diffraction analysis. A laser with a multi-wavelength spectrum creates several copies of partially overlapping speckle patterns that propagate at slightly different directions. The related spatial speckle offset measured on the image sensor depends on the surface angle and scales proportional to the sampling distance. Therefore, all calibration parameters can be explicitly determined from a pair of speckle patterns recorded at axially separated focal planes.The speckle offset equations are derived from the general diffraction equation using simple geometric treatment. The speckle pattern dependence on the laser source spectrum is experimentally studied, and the proposed self-calibration method is demonstrated. The diffraction analysis can extract 500–1000 mm sampling distances at a 1.7% accuracy and determine 15–45˚ oblique surface angles at a 0.7˚ accuracy.

Knowledge-based self-calibration method of calibration phantom by and for accurate robot-based CT imaging systems

Modern X-ray imaging system with feature of low-dose and high spatial resolution imaging has become a prevalent noninvasive imaging technique in clinic. High-resolution imaging of cone-beam computed tomography (CBCT) system crucially relies on accurate geometric calibration. Accurate coordinates of bearing balls (BBs) on calibration phantom are essential prerequisites to precisely realize geometric calibration of CBCT systems. However, due to phantom-making error, BB position deviations may occur between the actual value and theoretical value, further resulting in estimation error of realistic parameters in geometric calibration. Current algorithms that can estimate BB coordinates are insufficient and not robust. In this study, we proposed a knowledge-based self-calibration method by means of a robot-based CT system to fill the vacancy. The moving knowledge from one single manipulator of dual manipulators is utilized for automatic self-calibration of the calibration phantom, which is then for accurate geometry calibration for the dual manipulator-based imaging system. Specifically, different projections of BBs can be obtained by moving the robotic manipulator, on which X-ray tube is installed several times, while the detector and the calibration phantom remain stationary. Hence, the actual BB coordinates can be estimated by minimizing two separate cost functions determined by reprojection errors and relocation errors of BBs. Simulation study shows that the mean of absolute distance values of the estimated coordinates are 0, 0.0164, and 0.0190 mm, and the standard deviation values of Gaussian noise are 0%, 10%, and 15% of a single pixel size on BB projection, respectively. Experiments demonstrate that the image quality of the reconstructed results has been improved to a large extent after utilizing the proposed self-calibration method. The performance is even superior to that of images acquired by performing geometric calibration on a high-precise calibration phantom with more BBs. The proposed method provides a flexible utility value to acquire high precision geometry and generate high-quality images for CBCT systems.

A self-calibration method for rotary tables’ five degrees-of-freedom error motions

The paper proposed a novel self-calibration method for five degrees-of-freedom error motions of rotary tables. Two encoders with multiple reading heads were installed on the spindle’s different positions to measure rotation angles. By analyzing indication differences between the reading heads, the two grid discs’ radial motions were obtained. After Fourier analysis, measurement errors caused by the installation errors of the grid discs were eliminated and two different positions’ error motions of the spindle were obtained. Therefore, the rotary table’s 5-DOF error motions, including angular positioning (ECC) error motions, radial (EXC, EYC) and tilt (EAC, EBC) error motions defined in ISO 230-7 and ANSI/AMSEB89.3.4, were self-calibrated. In order to verify the proposed self-calibration method, roundness errors of a cylinder were measured on a rotary table with a self-calibration system. During the measurement of the roundness errors, the error motions of the rotary table were measured simultaneously by the self-calibration system. After error compensations and eliminating influences of error motions of the rotary table, measurement data of the roundness errors were obtained. Compared with the calibration of three-point method for measuring roundness errors, the residual errors were less than ±0.5 μm. In order to verify dynamic measurement, external forces were loaded on the rotary table intentionally during the measurement process. The error motions of the rotary table changed with intermittent external forces, which were also detected accurately by the self-calibration system on line. After error compensations, the calibrations trend and magnitude with three-point method showed that error motions self-calibration of the rotary table are effectiveness and feasibility.

A Target-Based Self-Calibration Method for Terrestrial Laser Scanners and its Robust Solution

Fundamental systematic errors in point cloud data are inevitable due to a variety of factors, ranging from the external environment during scanning or observation by a terrestrial laser scanner (TLS), to the assembly of the instrument. For low-cost scanners, error terms may be further accentuated and include, in addition to systematic errors, random or even serious errors that directly affect the coordinates of each point in the point cloud, which are directly related to the quality of the point cloud data and subsequent processing. To address the above issues, we attempted to propose a robust target-based self-calibration method for TLS at the algorithmic level without considering the network design and measurement configuration, and derived its solution by normalizing the residual vector and calculating an equivalent covariance matrix based on the IGGIII function. After validating the simulated and measured data, the experimental results showed that the proposed self-calibration method could effectively eliminate the random and gross errors associated with the observations; improved the accuracy of the points from centimeter to millimeter level; and increased the accuracy of the corrected checkpoints by 58%, 47% and 33% respectively compared to the three existing methods. However, the proposed method was unable to take into account the attenuation of parameter correlations and further refinement in terms of measurement configurations would be subsequently required.

Improved Self-Calibration of a Multilateration System Based on Absolute Distance Measurement.

Multilateration tracking systems (MLTSs) are used in industrial three-dimensional (3D) coordinate measuring applications. For high-precision measurement, system parameters must be calibrated properly in advance. For an MLTS using absolute distance measurement (ADM), the conventional self-calibration method significantly reduces estimation efficiency because all system parameters are estimated simultaneously using a complicated residual function. This paper presents a novel self-calibration method that optimizes ADM to reduce the number of system parameters via highly precise and separate estimations of dead paths. Therefore, the residual function to estimate the tracking station locations can be simplified. By applying a suitable mathematical procedure and solving the initial guess problem without the aid of an external device, estimation accuracy of the system parameters is significantly improved. In three self-calibration experiments, with ADM repeatability of approximately 3.4 µm, the maximum deviation of the system parameters estimated by the proposed self-calibration method was 68.6 µm, while the maximum deviation estimated by the conventional self-calibration method was 711.9 µm. Validation of 3D coordinate measurements in a 1000 mm × 1000 mm × 1000 mm volume showed good agreement between the proposed ADM-based MLTS and a commercial laser tracker, where the maximum difference based on the standard deviation was 17.7 µm. Conversely, the maximum difference was 98.8 µm using the conventional self-calibration method. These results confirmed the efficiency and feasibility of the proposed self-calibration method.

An improved self-calibration method with consideration of inner lever-arm effects for a dual-axis rotational inertial navigation system

In high-precision navigation applications, a well-designed self-calibration method is a convenient approach to ensuring the positioning performance of a rotational inertial navigation system (RINS). Benefiting from the gimbal structure, traditional inertial measurement unit (IMU) sensor errors, including gyro drifts, accelerometer biases, scale factor errors and installation errors, could be estimated through a filter process under a proper rotation scheme. However, when the IMU rotates, inner lever-arm effects may bring additional errors to the observations, which may reduce the self-calibration accuracy. In this paper, an improved self-calibration method that includes consideration of the inner lever-arm effect is proposed for a dual-axis RINS. Based on analysis of the error propagation characteristics, a novel rotation scheme with variable angular rate is designed. By adopting the proposed self-calibration method, traditional IMU sensor errors can achieve much higher accuracy, and the inner lever-arm parameters can also be well calibrated simultaneously. Long-term vehicle navigation indicates that the positioning accuracy was significantly enhanced after the compensation of the calibration results, fully illustrating the effectiveness of the proposed method in ameliorating navigation performance for the dual-axis RINS.

A self-calibration method for gyro scale factor asymmetry in rotational inertial navigation system

In the rotational inertial navigation system (RINS), the inertial measurement unit (IMU) rotates around the motor shaft, which will stimulate the gyro scale factor asymmetry, so it needs to be effectively calibrated and compensated. In this paper, the influence of gyro scale factor asymmetry on angular velocity error, angle error and velocity error is analysed, and a self-calibration method for it is proposed in the RINS using velocity errors as measurements. A self-calibration rotation strategy is designed for the dual-axis RINS so as to carry out self-calibration for the scale factor asymmetry of x-gyro, y-gyro and z-gyro. The feasibility of this scheme is verified by theoretical analysis and simulation. Experiments are carried out on a set of dual-axis RINS based on fiber optic gyroscope, and the scale factor asymmetry calibration results of three gyros are 2.56 ppm, 10.01 ppm and 0.88 ppm, respectively. In the navigation experiment, the navigation error is improved by 57.45% after compensating the gyro scale factor asymmetry error, which fully illustrates the significance of the proposed self-calibration method in improving the navigation performance of RINS.

A self-calibration method of inner lever arms for dual-axis rotation inertial navigation systems

In an inertial navigation system (INS), it is generally assumed that three accelerometers in an inertial measurement unit measure the acceleration input at the same point in space. However, there are error vectors between the respective sensitive point of the three accelerometers and the theoretical measurement point, typically termed as inner lever arms (ILAs). In strapdown INS, the ILAs coupled with the carrier’s angular motion lead to a decline in navigation accuracy, while for dual-axis rotational INS (RINS), the ILAs coupled with the gimbals’ angular motion further introduce new navigation errors. Therefore, the calibration and compensation for the ILAs are important for enhancing the systemic reliability. In this paper, an ILA self-calibration method is proposed by leveraging the rotation gimbals of the RINS. To be able to obtain all the ILA parameters, we establish an error model by considering the ILAs, and design a reasonable rotation scheme to ensure all parameters observable. The simulations and experiments show that the proposed self-calibration method is able to accomplish the rapid and accurate estimation of all the ILAs and the velocity stage and slope errors are greatly corrected after compensation by the calibration results.

The Self-Calibration Method for the Vertex Distance of the Elliptical Paraboloid Array

The elliptical paraboloid array plays an important role in precision measurement, astronomical telescopes, and communication systems. The calibration of the vertex distance of elliptical paraboloids is of great significance to precise 2D displacement measurement. However, there are some difficulties in determining the vertex position with contact measurement. In this study, an elliptical paraboloid array and an optical slope sensor for displacement measurement were designed and analyzed. Meanwhile, considering the geometrical relationship and relative angle between elliptical paraboloids, a non-contact self-calibration method for the vertex distance of the elliptical paraboloid array was proposed. The proposed self-calibration method was verified by a series of experiments with a high repeatability, within 3 μ m in the X direction and within 1 μ m in the Y direction. Through calibration, the displacement measurement system error was reduced from 100 μ m to 3 μ m . The self-calibration method of the elliptical paraboloid array has great potential in the displacement measurement field, with a simple principle and high precision.

Geometric Self-Calibration of YaoGan-13 Images Using Multiple Overlapping Images.

Geometric calibration is an important means of improving the absolute positioning accuracy of space-borne synthetic aperture radar imagery. The conventional calibration method is based on a calibration field, which is simple and convenient, but requires a great deal of manpower and material resources to obtain ground control points. Although newer cross-calibration methods do not require ground control points, calibration accuracy still depends on a periodically updated reference image. Accordingly, this study proposes a geometric self-calibration method based on the positioning consistency constraint of conjugate image points to provide rapid and accurate calibration of the YaoGan-13 satellite. The proposed method can accurately calibrate geometric parameters without requiring ground control points or high-precision reference images. To verify the absolute positioning accuracy obtained using the proposed self-calibration method, YaoGan-13 Stripmap images of multiple regions were collected and evaluated. The results indicate that high-accuracy absolute positioning can be achieved with a plane accuracy of 3.83 m or better for Stripmap data, without regarding elevation error. Compared to the conventional calibration method using high-accuracy control data, the difference between the two methods is only about 2.53 m, less than the 3-m resolution of the image, verifying the effectiveness of the proposed self-calibration method.

Lab-built terrestrial laser scanner self-calibration using mounting angle error correction

Systematic errors generated from internal misalignments of a lab-built terrestrial laser scanner (TLS) need to be calibrated to improve the positional accuracy of point-cloud. Hence, an angle measurement error model was established by the ray-tracing method involving five types of mounting angle errors, which were estimated by two-face method and network method. Experimental results show that the two errors including mirror tilt error and vertical index offset error are regarded as main systematic errors for lab-built TLS, and consequently the positional accuracy of the point-cloud can be improved in horizontal and vertical directions. The proposed self-calibration method can be used for other TLS by adjusting the angle measurement error model.

Distortion Rectifying for Dynamically Measuring Rail Profile Based on Self-Calibration of Multiline Structured Light

Dynamically measuring rail profile using the structured-light vision suffers from random vibrations on the line laser projector, which would cause distorted rail profiles. This paper presents a simple and effective distortion rectifying method to address this issue. The distorted rail profile is rectified by easily projecting it onto an auxiliary plane which is parallel to the cross section of rail. In order to establish the auxiliary plane, three profiles formed by radiating multiline structured light on rail are used to fit the rail longitudinal axis. More importantly, only one of the light planes is required to be calibrated beforehand. The others are calibrated online with the proposed self-calibration method, which is based on collinearity and parallelity constraints on the scene points of different rail profiles and requires only one image of the scene. Apart from evaluating the implementation with comprehensive experiments, we compare our method against other published works. The results exhibit its effectiveness and superiority in terms of the dynamic measurement of the rail profile.

A new self-calibration method for electronic current transformers

Compared with traditional current transformers (CTs), electronic current transformers (ECT) have the following advantages: (1) no saturation problem, (2) wider measurement range, (3) smaller footprint, (4) lighter weight, and (5) easier for digitization. Hence, the ECT is one of the critical components in the development of intelligent substations. Since the majority of the sensing elements of ECTs are semiconductor materials, their accuracy and sensitivity are influenced by the ambient temperature. Moreover, the quiescent output voltage of the semiconductor-based ECT is also affected by the ambient temperature. This paper proposes a self-calibration method with the ability of quiescent-output-voltage compensation and sensitivity compensation. The proposed design can automatically adjust the quiescent output voltage and the sensitivity variation when the temperature changes. The experimental test results demonstrate that an ECT with the proposed self-calibration method can achieve Class 0.5 for measuring CTs and Class 5P20 for protective CTs.

An Accelerometers-Size-Effect Self-Calibration Method for Triaxis Rotational Inertial Navigation System

Rotational inertial navigation system (RINS) could improve navigation performance by rotating the inertial measurement unit (IMU) with gimbals, and error parameters could be self-calibrated as well. However, accelerometers size effect would cause more influence on navigation accuracy in RINS than a strapdown inertial navigation system because of gimbals rotation, which should be calibrated and compensated for high-end application. In this paper, size effect and other IMU errors are calibrated through optimal estimation with navigation errors in triaxis RINS. The rotation scheme is designed by the characteristics of size effect and other errors, and all errors are verified to be observable by piece-wise constant system method and singular value decomposition method. The self-calibration method is tested by simulations and experiments. The calibration repeatability of size-effect parameters is less than 0.15 cm, while other IMU errors reach higher calibration accuracy compared with traditional methods. Navigation experiments indicate that the sharply changing velocity errors are greatly corrected after compensation, and position and velocity accuracy have improved 30% and 70%, respectively, during 12-h navigation experiment. Therefore, the navigation performance of RINS could be further improved in both the short term and long term with the proposed self-calibration method.

Stylus Tip Center Position Self-Calibration Based on Invariable Distances in Light-Pen Systems.

The light-pen coordinate measuring machine (LPCMM for short) is portable and flexible to measure features including invisible ones in-situ. Since different styluses are needed to measure different features and even during the process of measuring a single workpiece with complicated configurations, to improve the system measurement accuracy it is beneficial to calibrate the stylus tip center position after it is mounted to the light-pen before measurement in an industrial field. A novel and simple method aiming at self-calibrating the position of the tip center based on invariable distances is presented. The distinguishing feature of the proposed method is that the center position of the tip can be calibrated by using a kinematic seat with an inverted cone hole without any external reference and auxiliary devices. Calibration is based on that the distance between the tip center and that of any LED is invariable when the light-pen is swung smoothly with its spherical tip firmly touching the fixed cone seat. To ensure the repeatability of the algorithm some error constraint parameters are given. Based on invariable distances, the tip center position in the light-pen coordinate system can be obtained. Experiment results show that the self-calibration method has the advantage of good repeatability, with standard deviations 0.027, 0.023 and 0.014 mm in U, V and W directions, respectively. Experimental results of measuring a circle and a gauge block indirectly demonstrate the accuracy of the proposed self-calibration method.