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In spite of the vehicle, magnetic field interference can be reduced by some measures and techniques in ammunition design and manufacturing stage, the corruption of the vehicle magnetic field can still reach hundreds to thousands of nanoteslas. Besides, the magnetic field that the ferromagnetic materials generate in response to the strong magnetic field in the vicinity of the body. So, a real-time and accurate vehicle magnetic field calibration method is needed to improve the real-time measurement accuracy of the geomagnetic field for spinning projectiles.

Unlike the past two-step calibration method, the algorithm uses a linear model to calibrate the magnetic measurement error in real-time. In the method, the elliptical model of magnetometer measurement is established to convert the coefficients of hard and soft iron errors into the parameters of the elliptic equation. Then, the parameters are estimated by recursive least square estimator in real-time. Finally, the initial conditions for the estimator are established using prior knowledge method or static calibration method.

Studies show the proposed algorithm has remarkable estimation accuracy and robustness and it realizes calibration the magnetic measurement error in real-time. A turntable experiments indicate that the post-calibration residuals approximate the measurement noise of the magnetometer and the roll accuracy is better than 1°. The algorithm is restricted to biaxial magnetometers’ calibration in real-time as expressed in this paper. It, however, should be possible to broaden this method’s applicability to triaxial magnetometers' calibration in real-time.

Unlike the past two-step calibration method, the algorithm uses a linear model to calibrate the magnetic measurement error in real-time and the calculation is small. Besides, it does not take up storage space. The proposed algorithm has remarkable estimation accuracy and robustness and it realizes calibration the magnetic measurement error in real time. The algorithm is restricted to biaxial magnetometers’ calibration in real-time as expressed in this paper. It, however, should be possible to broaden this method’s applicability to triaxial magnetometers’ calibration in real-time.

The purpose of this paper is to propose an error model for serial robot kinematic calibration based on dual quaternions.

The dual quaternions are the combination of dual-number theory and quaternion algebra, which means that they can represent spatial transformation. The dual quaternions can represent the screw displacement in a compact and efficient way, so that they are used for the kinematic analysis of serial robot. The error model proposed in this paper is derived from the forward kinematic equations via using dual quaternion algebra. The full pose measurements are considered to apply the error model to the serial robot by using Leica Geosystems Absolute Tracker (AT960) and tracker machine control (T-MAC) probe.

Two kinematic-parameter identification algorithms are derived from the proposed error model based on dual quaternions, and they can be used for serial robot calibration. The error model uses Denavit–Hartenberg (DH) notation in the kinematic analysis, so that it gives the intuitive geometrical meaning of the kinematic parameters. The absolute tracker system can measure the position and orientation of the end-effector (EE) simultaneously via using T-MAC.

The error model formulated by dual quaternion algebra contains all the basic geometrical parameters of serial robot during the kinematic calibration process. The vector of dual quaternion error can be used as an indicator to represent the trend of error change of robot’s EE between the nominal value and the actual value. The accuracy of the EE is improved after nearly 20 measurements in the experiment conduct on robot SDA5F. The simulation and experiment verify the effectiveness of the error model and the calibration algorithms.

Existing calibration methods mainly focus on the camera laser-plane calibration of a single laser-line length, which is not convenient and cannot guarantee the consistency of the results when several three-dimensional (3D) scanners are involved. Thus, this study aims to provide a unified step for different laser-line length calibration requirements for laser profile measurement (LPM) systems.

3D LPM is the process of converting physical objects into 3D digital models, wherein camera laser-plane calibration is critical for ensuring system precision. However, conventional calibration methods for 3D LPM typically use a calibration target to calibrate the system for a single laser-line length, which needs multiple calibration patterns and makes the procedure complicated. In this paper, a unified calibration method was proposed to automatically calibrate the camera laser-plane parameters for the LPM systems with different laser-line lengths. The authors designed an elaborate planar calibration target with different-sized rings that mounted on a motorized linear platform to calculate the laser-plane parameters of the LPM systems. Then, the camera coordinates of the control points are obtained using the intersection line between the laser line and the planar target. With a new proposed error correction model, the errors caused by hardware assembly can be corrected. To validate the proposed method, three LPM devices with different laser-line lengths are used to verify the proposed system. Experimental results show that the proposed method can calibrate the LPM systems with different laser-line lengths conveniently with standard steps.

The repeatability and accuracy of the proposed calibration prototypes were evaluated with high-precision workpieces. The experiments have shown that the proposed method is highly adaptive and can automatically calibrate the LPM system with different laser-line lengths with high accuracy.

In the repeatability experiments, there were errors in the measured heights of the test workpieces, and this is because the laser emitter had the best working distance and laser-line length.

By using this proposed method and device, the calibration of the 3D scanning laser device can be done in an automatic way.

The calibration efficiency of a laser camera device is increased.

The authors proposed a unified calibration method for LPM systems with different laser-line lengths that consist of a motorized linear joint and a calibration target with elaborately designed ring patterns; the authors realized the automatic parameter calibration.

For some special manipulators such as the ones work at the space station, nuclear or some other unmanned environments, the overload, collision, vibration, temperature change or release of the internal stress would affect the structural parameters. And thus the operation precision might constantly decrease in long-term use. In these unmanned environments, the unattended manipulators should calibrate itself when they execute high precision operations or proceed self-maintenances. The purpose of this paper is to propose an automatic visual assistant on-line calibration (AVOC) method based on multi-markers.

A camera fixed on the end of the manipulator is used to measure one to three identification points, which forms an unstable multi-sensor eye-in-hand system. A Gaussian motion method which combines the linear quadratic regulator control and extended Kalman filter together is proposed to make the manipulator track the planned trajectories when its inaccurate structural parameters form uncertain motion errors. And a Monte-Carlo method is proposed to form a high precision and stable signal acquisition when the visual system has measurement errors and intermittent signal feedback. An automatic sampling process is adopted to select the optimal measurement points basing on their variances.

Data analysis and experiment results prove the efficiency and feasibility of the method proposed in this paper. With this method, the positioning accuracy is largely promoted from about 2 mm to 0.04–0.05 mm.

Experiments were carried out successfully on a manipulator in a life sciences glove box that will work at the Chinese space station. It is a low cost and efficient manipulator calibration method. The whole autonomic calibration process takes less than 10 min and requires no human intervention. In addition, this method not only can be used in the calibration of other unmanned articulated manipulator that works in deep ocean, nuclear industry or space but also be useful for the maintenance work in modern factories owing a lot of industrial robots.

This paper aims to propose a hand–eye calibration method of arc welding robot and laser vision sensor by using semidefinite programming (SDP).

The conversion relationship between the pixel coordinate system and laser plane coordinate system is established on the basis of the mathematical model of three-dimensional measurement of laser vision sensor. In addition, the conversion relationship between the arc welding robot coordinate system and the laser vision sensor measurement coordinate system is also established on the basis of the hand–eye calibration model. The ordinary least square (OLS) is used to calculate the rotation matrix, and the SDP is used to identify the direction vectors of the rotation matrix to ensure their orthogonality.

The feasibility identification can reduce the calibration error, and ensure the orthogonality of the calibration results. More accurate calibration results can be obtained by combining OLS + SDP.

A set of advanced calibration methods is systematically established, which includes parameters calibration of laser vision sensor and hand–eye calibration of robots and sensors. For the hand–eye calibration, the physics feasibility problem of rotating matrix is creatively put forward, and is solved through SDP algorithm. High-precision calibration results provide a good foundation for future research on seam tracking.

The purpose of this paper is to describe a calibration method developed to improve the absolute accuracy of a novel three degrees‐of‐freedom planar parallel robot. The robot is designed for the precise alignment of semiconductor wafers and, even though its complete workspace is slightly larger, the accuracy improvements are performed within a target workspace, in which the positions are on a disc of 170 mm in diameter and the orientations are in the range ±17°.

The calibration method makes use of a single optimization model, based on the direct kinematic calibration approach, while the experimental data are collected from two sources. The first source is a measurement arm from FARO Technologies, and the second is a Mitutoyo coordinate measurement machine (CMM). The two sets of calibration results are compared.

Simulation confirmed that the model proposed is not sensitive to measurement noise. An experimental validation on the CMM shows that the absolute accuracy inside the target workspace was improved by reducing the maximum position and orientation errors from 1.432 mm and 0.107°, respectively, to 0.044 mm and 0.009°.

This paper presents a calibration method which makes it possible to accurately identify the actual robot's base frame (base frame calibration), at the same time as identifying and compensating for geometric errors, actuator offsets, and even screw lead errors. The proposed calibration method is applied on a novel planar robot, and its absolute accuracy was found to improve to 0.044 mm.

With the improvement of modern aircraft requirements for safety, long life and economy, higher quality aircraft assembly is needed. However, due to the manufacturing and assembly errors of the posture adjustment mechanism (PAM) used in the digital assembly of aircraft large component (ALC), the posture alignment accuracy of ALC is difficult to be guaranteed, and the posture adjustment stress is easy to be generated. Aiming at these problems, this paper aims to propose a calibration method of redundant actuated parallel mechanism (RAPM) for posture adjustment.

First, the kinematics model of the PAM is established, and the influence of the coupling relationship between the axes of the numerical control locators (NCL) is analyzed. Second, the calibration method based on force closed-loop feedback is used to calibrate each branch chain (BC) of the PAM, and the solution of kinematic parameters is optimized by Random Sample Consensus (RANSAC). Third, the uncertainty of kinematic calibration is analyzed by Monte Carlo method. Finally, a simulated posture adjustment system was built to calibrate the kinematics parameters of PAM, and the posture adjustment experiment was carried out according to the calibration results.

The experiment results show that the proposed calibration method can significantly improve the posture adjustment accuracy and greatly reduce the posture adjustment stress.

In this paper, a calibration method based on force feedback is proposed to avoid the deformation of NCL and bracket caused by redundant driving during the calibration process, and RANSAC method is used to reduce the influence of large random error on the calibration accuracy.

The purpose of this study is to improve the position and posture accuracy of posture alignment mechanism. The automatic drilling and riveting machine is an important equipment for aircraft assembly. The alignment accuracy of position and posture of the bracket type posture alignment mechanism has a great influence on the operation effect of the machine. Therefore, it is necessary to carry out the kinematic calibration.

Based on analysis of elastic deformation of the bracket and geometric errors of the posture alignment mechanism, an improved method of kinematic calibration was proposed. The position and posture errors of bracket caused by geometric errors were separated from those caused by gravity. The method of reduction of dimensions was applied to deal with the error coefficient matrix in error identification, and it did not change the coefficient of the error terms. The target position and its posture were corrected to improve the error compensation accuracy. Furthermore, numerical simulation and experimental verification were carried out.

The simulation and experimental results show that considering the influence of the elastic deformation of the bracket on the calibration effect, the error identification accuracy and compensation accuracy can be improved. The maximum value of position error is reduced from 5.33 mm to 1.60 × 10⁻¹ mm and the maximum value of posture error is reduced from 1.07 × 10⁻³ rad to 6.02 × 10⁻⁴ rad, which is superior to the accuracy without considering the gravity factor.

This paper presents a calibration method considering the effects of geometric errors and gravity. By separating position and posture errors caused by different factors and correcting the target position and its posture, the results of the calibration method are greatly improved. The proposed method might be applied to any parallel mechanism based on the positioner.

This study aims to find a novel solution to the calibration of three-axis magnetometers to suppress errors of sensors. The nature of the calibration process is parameter estimation and hence the purpose of the paper is to calculate the error parameters and eliminate sensor errors and obtain the true value of the pure magnetic field.

The paper puts forward a calibration method using an alternative iteration looping optimization (AILO) to estimate the parameters. The proposed method divided the parameters to be estimated into two parts: a portion less than one and the other greater than one. Parameters with different orders of magnitude are calculated respectively, which let one part to be a known quantity and the other part is derived by the known quantity; the derived quantity is used to calculate the known quantity again, and looping iteration multiple times until the iteration termination condition is satisfied.

The simulation and experimental results indicate that the calibration accuracy is improved at least by two orders by the proposed method compared to the two-step method and the linear decreasing weight particle swarm optimization (LDW-PSO) algorithm which proves the validity of the proposed method.

The proposed method can improve the calibration accuracy of total magnetic field, which provides a reference to the calibration of three-axis magnetometers.

A calibration method based on the AILO is proposed in this paper, which is used to improve the calibration accuracy of the three-axis magnetometer.

In a dual-robot system, the relative position error is a superposition of errors from each mono-robot, resulting in deteriorated coordination accuracy. This study aims to enhance relative accuracy of the dual-robot system through direct compensation of relative errors. To achieve this, a novel calibration-driven transfer learning method is proposed for relative error prediction in dual-robot systems.

A novel local product of exponential (POE) model with minimal parameters is proposed for error modeling. And a two-step method is presented to identify both geometric and nongeometric parameters for the mono-robots. Using the identified parameters, two calibrated models are established and combined as one dual-robot model, generating error data between the nominal and calibrated models’ outputs. Subsequently, the calibration-driven transfer, involving pretraining a neural network with sufficient generated error data and fine-tuning with a small measured data set, is introduced, enabling knowledge transfer and thereby obtaining a high-precision relative error predictor.

Experimental validation is conducted, and the results demonstrate that the proposed method has reduced the maximum and average relative errors by 45.1% and 30.6% compared with the calibrated model, yielding the values of 0.594 mm and 0.255 mm, respectively.

First, the proposed calibration-driven transfer method innovatively adopts the calibrated model as a data generator to address the issue of real data scarcity. It achieves high-accuracy relative error prediction with only a small measured data set, significantly enhancing error compensation efficiency. Second, the proposed local POE model achieves model minimality without the need for complex redundant parameter partitioning operations, ensuring stability and robustness in parameter identification.