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This paper aims to address the issue of model discontinuity typically encountered in traditional Denavit-Hartenberg (DH) models. To achieve this, we propose the use of a local Product of Exponentials (POE) approach. Additionally, a modified calibration model is presented which takes into account both kinematic errors and high-order joint-dependent kinematic errors. Both kinematic errors and high-order joint-dependent kinematic errors are analyzed to modify the model.

Robot positioning accuracy is critically important in high-speed and heavy-load manufacturing applications. One essential problem encountered in calibration of series robot is that the traditional methods only consider fitting kinematic errors, while ignoring joint-dependent kinematic errors.

Laguerre polynomials are chosen to fitting kinematic errors and high-order joint-dependent kinematic errors which can avoid the Runge phenomenon of curve fitting to a great extent. Levenberg–Marquard algorithm, which is insensitive to overparameterization and can effectively deal with redundant parameters, is used to quickly calibrate the modified model. Experiments on an EFFORT ER50 robot are implemented to validate the efficiency of the proposed method; compared with the Chebyshev polynomial calibration methods, the positioning accuracy is improved from 0.2301 to 0.2224 mm.

The results demonstrate the substantial improvement in the absolute positioning accuracy achieved by the proposed calibration methods on an industrial serial robot.

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.

A three-dimensional (3D) printing error simulation approach is proposed to analyze the influence of tilted vertical beams on the 3D printing accuracy. The purpose of this study is to analyze the influence of such errors on printing accuracy and printing quality for delta-robot 3D printer.

First, the kinematic model of a delta-robot 3D printer with an ideal geometric structure is proposed by using vector analysis. Then, the normal kinematic model of a nonideal delta-robot 3D robot with tilted vertical beams is derived based on the above ideal kinematic model. Finally, a 3D printing error simulation approach is proposed to analyze the influence of tilted vertical beams on the 3D printing accuracy.

The results show that tilted vertical beams can indeed cause 3D printing errors and further influence the 3D printing quality of the final products and that the 3D printing errors of tilted vertical beams are related to the rotation angles of the tilted vertical beams. The larger the rotation angles of the tilted vertical beams are, the greater the geometric deformations of the printed structures.

Three vertical beams and six horizontal beams constitute the supporting parts of the frame of a delta-robot 3D printer. In this paper, the orientations of tilted vertical beams are shown to have a significant influence on 3D printing accuracy. However, the effect of tilted vertical beams on 3D printing accuracy is difficult to capture by instruments. To reveal the 3D printing error mechanisms under the condition of tilted vertical beams, the error generation mechanism and the quantitative influence of tilted vertical beams on 3D printing accuracy are studied by simulating the parallel motion mechanism of a delta-robot 3D printer with tilted vertical beams.

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 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.

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.

Presents the kinematic calibration of an H4 parallel prototype robot using a vision‐based measuring device. Calibration is performed according to the inverse kinematic model method, using first the design model then a model developed for calibration purpose. To do so, the end‐effector pose (i.e. position and orientation) has to be measured with the utmost accuracy. Thus, first the practical accuracy of the low‐cost vision‐based measuring system is evaluated to have a precision in the order of magnitude of 10μ_it;m and 10^−3° for a 1,024×768 pixel CCD camera. Second, the prototype is calibrated using the easy‐to‐install vision system, yielding a final positioning accuracy of the end‐effector reduced from more than 1cm down to less than 0.5mm. Also provides a discussion on the use of such a method on commercial systems.

This paper aims to propose a novel robot kinematic calibration method based on the common perpendicular line (CPL) model to improve the absolute accuracy of industrial robots.

The deviation between the nominal and actual twists is considered the CPL transformation, which includes the rotation about the CPL and the translation along the CPL. By using the invariance of the reciprocal product of the two spatial lines, the previous deviation was analyzed in the neighbor space of the base frame origin. In this space, the line vector of the CPL contained only four independent parameters: two orientation elements and two moment elements. Thus, the CPL model has four independent parameters for the revolute joint and two parameters for the prismatic joint.

By simulations and experiment conducted on a SCARA robot and a 6-DOF PUMA robot, the effectiveness of the novel method for calibration of industrial robot is validated.

The CPL model avoided the normalization and orthogonalization in the iterative identification procedure. Therefore, identifying the CPL model was not only simpler but also more accurate than that of the traditional model. In addition, the results of the CPL transformation strictly conformed to the constraints of the twist.

This study aims to introduce a multi-configuration, three-finger dexterous hand with integrated high-dimensional sensors and provides an analysis of its design, modeling and kinematics.

A mechanical design scheme of the three-finger dexterous hand with a reconfigurable palm is proposed based on the existing research on dexterous hands. The reconfigurable palm design enables the dexterous hand to achieve four grasping modes to adapt to multiple grasping tasks. To further enhance perception, two six-axis force and torque sensors are integrated into each finger. The forward and inverse kinematics equations of the dexterous hand are derived using the D-H method for kinematics modeling, thus providing a theoretical model for index analysis. The performance is evaluated using three widely applied indicators: workspace, interactivity of fingers and manipulability.

The results of kinematics analysis show that the proposed hand has excellent dexterity. Additionally, three different experiments are conducted based on the proposed hand. The performance of the dexterous hand is also verified by fingertip force, motion accuracy test, grasping and in-hand manipulation experiments based on Feix taxonomy. The results show that the dexterous hand has good grasping ability, reproducing 82% of the natural movement of the human hand in daily grasping activities and achieving in-hand manipulations such as translation and rotation.

A novel three-finger dexterous hand with multi-configuration and integrated high-dimensional sensors is proposed. It performs better than the previously designed dexterous hand in actual experiments and kinematic performance analysis.

Rigid robotic hands are generally fast, precise and capable of exerting large forces, whereas soft robotic hands are compliant, safe and adaptive to complex environments. It is valuable and challenging to develop soft-rigid robotic hands that have both types of capabilities. The paper aims to address the challenge through developing a paradigm to achieve the behaviors of soft and rigid robotic hands adaptively.

The design principle of a two-joint finger is proposed. A kinematic model and a stiffness enhancement method are proposed and discussed. The manufacturing process for the soft-rigid finger is presented. Experiments are carried out to validate the accuracy of the kinematic model and evaluate the performance of the flexible body of the finger. Finally, a robotic hand composed of two soft-rigid fingers is fabricated to demonstrate its grasping capacities.

The kinematic model can capture the desired distal deflection and comprehensive shape accurately. The stiffness enhancement method guarantees stable grasp of the robotic hand, without sacrificing its flexibility and adaptability. The robotic hand is lightweight and practical. It can exhibit different grasping capacities.

It can be applied in the field of industrial grasping, where the objects are varied in materials and geometry. The hand’s inherent characteristic removes the need to detect and react to slight variations in surface geometry and makes the control strategies simple.

This work proposes a novel robotic hand. It possesses three distinct characteristics, i.e. high compliance, exhibiting discrete or continuous kinematics adaptively, lightweight and practical structures.