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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.

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.

This paper aims to propose a measurement principle and a calibration method of measurement system integrated with serial robot and 3D camera to identify its parameters conveniently and achieve high measurement accuracy.

A stiffness and kinematic measurement principle of the integrated system is proposed, which considers the influence of robot weight and load weight on measurement accuracy. Then an error model is derived based on the principle that the coordinate of sphere center is invariant, which can simultaneously identify the parameters of joint stiffness, kinematic and hand-eye relationship. Further, considering the errors of the parameters to be calibrated and the measurement error of 3D camera, a method to generate calibration observation data is proposed to validate both calibration accuracy and parameter identification accuracy of calibration method.

Comparative simulations and experiments of conventional kinematic calibration method and the stiffness and kinematic calibration method proposed in this paper are conducted. The results of the simulations show that the proposed method is more accurate, and the identified values of angle parameters in modified Denavit and Hartenberg model are closer to their real values. Compared with the conventional calibration method in experiments, the proposed method decreases the maximum and mean errors by 19.9% and 13.4%, respectively.

A new measurement principle and a novel calibration method are proposed. The proposed method can simultaneously identify joint stiffness, kinematic and hand-eye parameters and obtain not only higher measurement accuracy but also higher parameter identification accuracy, which is suitable for on-site calibration.

This paper aims to propose a united kinematic calibration method for a dual-machine system in automatic drilling and riveting. The method takes both absolute and relative pose accuracy into account, which will largely influence the machining accuracy of the dual-machine system and assembly quality.

A comprehensive kinematic model of the dual-machine system is established by the superposition of sub-models with pose constraints, which involves base frame parameters, kinematic parameters and tool frame parameters. Based on the kinematic model and the actual pose error data measured by a laser tracker, the parameters of coordinated machines are identified by the Levenberg–Marquardt method as a multi-objective nonlinear optimization problem. The identified parameters of the coordinated machines will be used in the control system.

A new calibration method for the dual-machine system is developed, including a comprehensive kinematic model and an efficient parameter identification method. The experiment results show that with the proposed method, the pose accuracy of the dual-machine system was remarkably improved, especially the relative position and orientation errors.

This method has been used in an aircraft assembly project. The calibrated dual-machine system shows a good performance on system coordination and machining accuracy.

This paper proposes a new method with high accuracy and efficiency for the dual-machine system calibration. The research can be extended to multi-machine and multi-robot fields to improve the system precision.

This paper aims to propose a calibration model for kinematic parameters identification of serial robot to improve its positioning accuracy, which only requires position measurement of the end-effector.

The proposed model is established based on local frame representation of the product of exponentials (local POE) formula, which integrates all kinematic errors into the twist coordinates errors; then they are identified with the tool frame’ position deviations simultaneously by an iterative least squares algorithm.

To verify the effectiveness of the proposed method, extensive simulations and calibration experiments have been conducted on a 4DOF SCARA robot and a 5DOF drilling machine, respectively. The results indicate that the proposed model outperforms the existing model in convergence, accuracy, robustness and efficiency; fewer measurements are needed to gain an acceptable identification result.

This calibration method has been applied to a variable-radius circumferential drilling machine. The machine’s positioning accuracy can be significantly improved from 11.153 initially to 0.301 mm, which is well in the tolerance (±0.5 mm) for fastener hole drilling in aircraft assembly.

An accurate and efficient kinematic calibration model has been proposed, which satisfies the completeness, continuity and minimality requirements. Due to generality, this model can be widely used for serial robot kinematic calibration with any combination of revolute and prismatic joints.

The purpose of this paper is to present a distance accuracy-based industrial robot kinematic calibration model. Nowadays, the repeatability of the industrial robot is high, while the absolute positioning accuracy and distance accuracy are low. Many factors affect the absolute positioning accuracy and distance accuracy, and the calibration method of the industrial robot is an important factor. When the traditional calibration methods are applied on the industrial robot, the accumulative error will be involved according to the transformation between the measurement coordinate and the robot base coordinate.

In this manuscript, a distance accuracy-based industrial robot kinematic calibration model is proposed. First, a simplified kinematic model of the robot by using the modified Denavit–Hartenberg (MDH) method is introduced, then the proposed distance error-based calibration model is presented; the experiment is set up in the next section.

The experimental results show that the proposed calibration model based on MDH and distance error can improve the distance accuracy and absolute position accuracy dramatically.

The proposed calibration model based on MDH and distance error can improve the distance accuracy and absolute position accuracy dramatically.

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.

The purpose of this paper is to describe a calibration method developed to improve the accuracy of a six degrees-of-freedom medical robot. The proposed calibration approach aims to enhance the robot’s accuracy in a specific target workspace. A comparison of five observability indices is also done to choose the most appropriate calibration robot configurations.

The calibration method is based on the forward kinematic approach, which uses a nonlinear optimization model. The used experimental data are 84 end-effector positions, which are measured using a laser tracker. The calibration configurations are chosen through an observability analysis, while the validation after calibration is carried out in 336 positions within the target workspace.

Simulations allowed finding the most appropriate observability index for choosing the optimal calibration configurations. They also showed the ability of our calibration model to identify most of the considered robot’s parameters, despite measurement errors. Experimental tests confirmed the simulation findings and showed that the robot’s mean position error is reduced from 3.992 mm before calibration to 0.387 mm after, and the maximum error is reduced from 5.957 to 0.851 mm.

This paper presents a calibration method which makes it possible to accurately identify the kinematic errors for a novel medical robot. In addition, this paper presents a comparison between the five observability indices proposed in the literature. The proposed method might be applied to any industrial or medical robot similar to the robot studied in this paper.

Calibrating kinematic parameters is one of the efficient ways to improve the robot's positioning accuracy. A method based on the product-of-exponential (POE) formula to calibrate the kinematic parameters of serial industrial robots is proposed. The paper aims to discuss these issues.

The forward kinematics is established, and the general positioning error model is deduced in an explicit expression. A simplified model of robot's positioning error is established as both the error of reference configuration and the error of rigid displacement of the base coordinating system with respect to the measuring coordinating system are equivalently transferred to the zero position errors of the robot's joints. A practical calibration model is forwarded only requiring 3D measuring based on least-squares algorithm. The calibration system and strategy for calibrating kinematic parameters are designed.

By the two geometrical constrains between the twist coordinates, each joint twist only has four independent coordinates. Due to the equivalent error model, the zero position error of each joint can cover the error of reference configuration and rigid displacement of the robot base coordinating system with respect to the measuring coordinating system. The appropriate number of independent kinematic parameters of each joint to be calibrated is five.

It is proved by a group of calibration experiments that the calibration method is well conditioned and can be used to promote the level of absolute error of end effector of industrial robot to 2.2 mm.

The purpose of this paper is to develop a means of the kinematic calibration of a parallel manipulator with full-circle rotation.

An error-mapping model based on the space vector chain is formulated and parameter identification is proposed based on double ball-bar (DBB) measurements. The measurement trajectory is determined by the motion characteristics of this mechanism and whether the error sources can be identified. Error compensation is proposed by modifying the inputs, and a two-step kinematic calibration method is implemented.

The simulation and experiment results show that this kinematic calibration method is effective. The DBB length errors and the position errors in the end-effector of the parallel manipulator with full-circle rotation are greatly reduced after error compensation.

By establishing the mapping relationship between measured error data and geometric error sources, the error parameters of this mechanism are identified; thus, the pose errors are unnecessary to be measured directly. The effectiveness of the kinematic calibration method is verified by computer simulation and experiment. This proposed calibration method can help the novel parallel manipulator with full-circle rotation and other similar parallel mechanisms to improve their accuracy.