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The purpose of this paper is to propose a method that calibrates the hand-eye relationship for eye-to-hand configuration and afterwards a rectification to improve the accuracy of general calibration.

The hand-eye calibration of eye-to-hand configuration is summarized as a equation AX = XB which is the same as in eye-in-hand calibration. A closed-form solution is derived. To abate the impact of noise, a rectification is conducted after the general calibration.

Simulation and actual experiments confirm that the accuracy of calibration is obviously improved.

Only a calibration plane is required for the hand-eye calibration. Taking the impact of noise into account, a rectification is carried out after the general calibration and, as a result, that the accuracy is obviously improved. The method can be applied in many actual applications.

The purpose of this study is solving the hand–eye calibration issue for line structured light vision sensor. Only after hand–eye calibration the sensor measurement data can be applied to robot system.

In this paper, the hand–eye calibration methods are studied, respectively, for eye-in-hand and eye-to-hand. Firstly, the coordinates of the target point in robot system are obtained by tool centre point (TCP), then the robot is controlled to make the sensor measure the target point in multiple poses and the measurement data and pose data are obtained; finally, the sum of squared calibration errors is minimized by the least square method. Furthermore, the missing vector in the process of solving the transformation matrix is obtained by vector operation, and the complete matrix is obtained.

On this basis, the sensor measurement data can be easily and accurately converted to the robot coordinate system by matrix operation.

This method has no special requirement for robot pose control, and its calibration process is fast and efficient, with high precision and has practical popularized value.

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 present a fully automatic calibration method for hand-eye serial robot system is presented in this paper. The so-called “fully automatic” is meant to calibrate the robot body, the hand-eye relation, and the used measuring binocular system at the same time.

The calibration is done by controlling the joints to rotate several times one by one in the reverse order (i.e. from the last one to the first one), and simultaneously take pictures of the checkerboard patterns by the stereo camera system attached on the end-effector, then the whole robot system can be calibrated automatically from these captured images. In addition, a nonlinear optimization step is used to further refine the calibration results.

The proposed method is essentially based on an improved screw axis identification method, and it needs only a mirror and some paper checkerboard patterns without resorting to any additional costly measuring instrument.

Simulations and real experiments on MOTOMAN-UP6 robot system demonstrate the feasibility and effectiveness of the proposed method.

This paper aims to introduce a simple hand-eye calibration method that can be easily applied with different objective functions.

The hand-eye calibration is solved by using the closed form absolute orientation equations. Instead of processing all samples together, the proposed method goes through all minimal solution sets. Final result is chosen after evaluating the solution set for arbitrary objectives. In this stage, outliers can be excluded optionally if more accuracy is desired.

The proposed method is very flexible and gives more accurate and convenient results than the existing solutions. The mathematical error expression defined by the calibration equations may not be valid in practice, where especially systematic distortions are present. It is shown in the simulations that the solution which results the least mathematical error in systems may have incorrect, incompatible results in the presence of practical demands.

The performance of the calibration performed with the proposed method is compared with the reference methods in the literature. When the back-projection error is benchmarked, which corresponds to the point repeatability, the proposed approach is considered as the most successful method among all others. Due to its robustness, it is decided to make tooling-sensor calibrations by the recommended method, in the robotic non-destructive testing station in Ford-OTOSAN Kocaeli Plant Body Shop Department.

Arranging the well-known AX = XB calibration equation in quaternion representation as Q_A = Q_x × Q_B × Q_x reveals another common spatial rotation equation. In this way, absolute orientation solution satisfies the hand-eye calibration equations. The proposed solution is not presented in the literature as a standalone hand-eye calibration method, although some researchers drop a hint to the relative formulations.

The purpose of this paper is to propose a calibration method that can calibrate the relationships among the robot manipulator, the camera and the workspace.

The method uses a laser pointer rigidly mounted on the manipulator and projects the laser beam on the work plane. Nonlinear constraints governing the relationships of the geometrical parameters and measurement data are derived. The uniqueness of the solution is guaranteed when the camera is calibrated in advance. As a result, a decoupled multi‐stage closed‐form solution can be derived based on parallel line constraints, line/plane intersection and projective geometry. The closed‐form solution can be further refined by nonlinear optimization which considers all parameters simultaneously in the nonlinear model.

Computer simulations and experimental tests using actual data confirm the effectiveness of the proposed calibration method and illustrate its ability to work even when the eye cannot see the hand.

Only a laser pointer is required for this calibration method and this method can work without any manual measurement. In addition, this method can also be applied when the robot is not within the camera field of view.

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.

The purpose of this paper is to present a visual detection approach to predict the poses of target objects placed in arbitrary positions before completing the corresponding tasks in mobile robotic manufacturing systems.

A hybrid visual detection approach that combines monocular vision and laser ranging is proposed based on an eye-in-hand vision system. The laser displacement sensor is adopted to achieve normal alignment for an arbitrary plane and obtain depth information. The monocular camera measures the two-dimensional image information. In addition, a robot hand-eye relationship calibration method is presented in this paper.

First, a hybrid visual detection approach for mobile robotic manufacturing systems is proposed. This detection approach is based on an eye-in-hand vision system consisting of one monocular camera and three laser displacement sensors and it can achieve normal alignment for an arbitrary plane and spatial positioning of the workpiece. Second, based on this vision system, a robot hand-eye relationship calibration method is presented and it was successfully applied to a mobile robotic manufacturing system designed by the authors’ team. As a result, the relationship between the workpiece coordinate system and the end-effector coordinate system could be established accurately.

This approach can quickly and accurately establish the relationship between the coordinate system of the workpiece and that of the end-effector. The normal alignment accuracy of the hand-eye vision system was less than 0.5° and the spatial positioning accuracy could reach 0.5 mm.

This approach can achieve normal alignment for arbitrary planes and spatial positioning of the workpiece and it can quickly establish the pose relationship between the workpiece and end-effector coordinate systems. Moreover, the proposed approach can significantly improve the work efficiency, flexibility and intelligence of mobile robotic manufacturing systems.

The purpose of this paper is to propose a novel measurement technique and a modelless calibration method for improving the positioning accuracy of a three-axis parallel kinematic machine (PKM). The aim is to present a low-cost calibration alternative, for small and medium-sized enterprises, as well as educational and research teams, with no expensive measuring devices at their disposal.

Using a chessboard pattern on a ground-truth plane, a digital indicator, a two-dimensional eye-in-hand camera and a laser pointer, positioning errors are explored in the machine workspace. With the help of these measurements, interpolation functions are set up per direction, resulting in an interpolation vector function to compensate the volumetric errors in the workspace.

Based on the proof-of-concept system for the linear-delta PKM, it is shown that using the proposed measurement technique and modelless calibration method, positioning accuracy is significantly improved using simple setups.

In the proposed method, a combination of low-cost devices is applied to improve the three-dimensional positioning accuracy of a PKM. By using the presented tools, the parametric kinematic model is not required; furthermore, the calibration setup is simple, there is no need for hand–eye calibration and special fixturing in the machine workspace.

The purpose of this study is to design a robotic inline measurement system for spot welding quality control to achieve process requirement without any operator during the manufacturing flow.

A robot manipulator carries a stereo-camera and an ultrasonic control probe. The center position of the spot welding point is determined by evaluating the results of the edge, gradient and symmetry approaches from the methods proposed up to now in the literature to increase reliability. The center position of the spot welding point, determined in the camera reference plane, is transferred to the robot base plane coordinates with the hand–eye calibration proposed in this manuscript. Weld quality is checked by the ultrasonic test probe located at the spot welding point.

While operators can only control welding quality, the developed station can also evaluate the quality based on geometric accuracy by processing the deviation of the position of the spot welding points. The proposed calibration method and the results of other methods in the literature are presented in this study by comparing it with synthetic data in simulations and in practical application.

The quality control is performed not only for the spot welding made with robots but also for the manual welds as well. Because of vision configuration, and reliability issues, maximum allowable offset by the correct spot position is limited to 20 mm to position the manipulator for testing. The installation and pretest works of the developed robotic welding quality control station are completed in the Body Shop Area of Ford Otosan factory in Kocaeli/Turkey. The results of the robotic control process are monitored by the quality assurance team. Integration of automation with the production line will be completed and an inline measurement will be done.

In this paper, a new hand–eye calibration method based on simple and closed-form analytical solutions has been presented. The objective function is defined as reducing the deviation in the point projection, rather than reducing the error in the calibration equation. To increase reliability, combining the results of existing centering algorithms for the detection of the strongly deformed spot welding spot center, although it is normally in a circular form, has been suggested.