Kinematic Parameter Errors Research Articles

A unified calibration method for robot manipulators: hand-eye parameters, kinematic parameters and TCP position calibration

PurposeThe purpose of the paper is to propose an efficient, simple and concise unified robot calibration method that simultaneously considers errors in hand-eye parameters, kinematic parameters and tool center point (TCP) position.Design/methodology/approachThis paper proposes a unified robot calibration method. First, the initial hand-eye matrix and TCP position are computed without considering kinematic parameter errors. Second, the nominal TCP positions in the laser tracker coordinate system {S} are computed. The actual TCP positions in {S} are directly measured. Third, a unified parameter error calibration model is established, and the sequential quadratic programming algorithm is used for error identification. Finally, the identified errors are used for direct error compensation.FindingsSimulation results prove that the proposed scheme can accurately calibrate the hand-eye parameters, kinematic parameters and TCP position simultaneously. Experimental results reveal that the maximum value of the absolute positioning errors is reduced from 5.4725 mm to 0.4095 mm (reduced by 92.52%). Thus, the proposed approach meets the accuracy requirements of most robotic applications.Originality/valueThe main contributions of this paper are: (1) this scheme is efficient. The method can achieve fully automatic calibration by incorporating Kronecker products for the initial hand-eye matrix and TCP position computation. Thereby significantly improving the calibration efficiency and liberating the labor force. (2) This scheme is simple and concise. The hand-eye parameters, kinematic parameters and TCP position errors are modeled in a unified framework. Furthermore, the related redundant parameters are deleted.

Method for robot kinematic parameters identification based on position and orientation data obtained with laser tracker.

How to quickly and accurately identify the kinematic parameter errors is an important prerequisite for robot accuracy compensation. The laser tracker is used to measure and identify the kinematic parameters of the robot. The influence of laser tracker layout in robot pose measurement is analyzed, and the evaluation function of laser tracker layout is constructed to determine the optimal layout position. Then, the mapping relationship between the position and orientation deviation of the robot end and the deviation of each kinematic parameter is established, and the kinematic parameter identification model integrating the position and orientation information is constructed. The identification model is compared to the identification model based on position information to clarify the intrinsic reason of high accuracy. Next, aiming at the problem that the genetic algorithm is easy to prematurely converge to the local optimal solution, a hybrid genetic algorithm is constructed by introducing the simplex method to determine the optimal calibration pose set of the robot. On this basis, the results of robot kinematics parameter identification based on position measurement data, pose measurement data, and optimal calibration pose set are compared and analyzed through experiments, which verifies the effectiveness of the robot kinematics parameter identification model based on pose measurement data and optimization strategy.

An error compensation method for on-machine measuring blade with industrial robot

To achieve the seamless integration of precision grinding blade with timely measured data, an on-machine measurement system employing industrial robot is developed. The limitation to its widespread application lies in the accuracy of measurement, prompting the proposal of an error compensation method to address the measurement error within the implemented blade on-machine measurement system. To address the pre-travel error in the measuring device of the on-machine measurement system, an analysis of the factors influencing the pre-travel error of the contact probe is conducted. Subsequently, pre-travel error data is gathered utilizing the experimental calibration method involving a standard ball, and a prediction model employing the bilinear interpolation algorithm is established to facilitate error compensation. Employing pre-travel error compensation for the analysis of the operating body error in the on-machine measurement system, a spherical center distance constraint error model is derived through closed-loop kinematic calibration of the six-degrees-of-freedom industrial robot. Kinematic parameter error identification is conducted using a hybrid algorithm combining the L-M algorithm and the adaptive factor double-variable DE algorithm. This approach diminishes the spherical center distance measurement error, reducing it from 0.081 mm to 0.016 mm. Subsequently, experiment is conducted to measure blade machining allowances using an on-machine robotic measurement system, comparing the obtained data with measurement from a blue light scanner and a coordinate measuring machine (CMM). The results reveal average absolute deviations of 0.020 mm, 0.015 mm, and 0.016 mm in the three blade cross sections for the on-machine robotic measurement system and the blue light scanner, respectively. Correspondingly, the average absolute deviations for the on-machine robotic measurement system and the CMM in the three blade sections are 0.028 mm, 0.029 mm, and 0.029 mm. Moreover, the on-machine measurement system demonstrates commendable measurement repeatability, with a standard deviation of 0.003 mm.

Pose Selection Based on a Hybrid Observation Index for Robotic Accuracy Improvement

The problem of the insufficient accuracy performance of industrial robots in high-precision manufacturing is addressed in this paper. Firstly, a kinematic error model based on an M-DH model was presented. Secondly, a hybrid observability index O6 was proposed to select the optimal poses for parameter identification. O6 is the combination of O1 and O3. The optimal poses were obtained by using the IOOPS algorithm. Thirdly, the fitness function for parameter identification was established, and the Levenberg–Marquardt (LM) algorithm was applied for the accurate identification of kinematic parameter errors. Finally, several experiments were conducted to evaluate the performance of the proposed hybrid observability index O6. The average position error and average attitude error of Staubli TX60 robot were reduced by 89% and 49%. The results show that the proposed hybrid observability index O6 has great stability and effectiveness for robot calibration.

Simultaneous compensation of geometric and compliance errors for robotics with consideration of variable payload effects

In order to satisfy the high accuracy requirements of robotic applications, it is necessary to consider not only the geometric errors but also the compliance errors which are caused by the self-gravity of the link and the external payloads. A general error model is developed based on the modified Denavit-Hartenberg (DH) model. For the parameters in the error model, there is a coupling between the compliance coefficients and the link parameters, making it difficult to use only the compliance coefficients to compute the compliance errors due to external payloads. As the external payload for the robot manipulator varies, the parameter identification of the model should be conducted again. In this paper, a novel algorithm using a variable payload method is proposed to first identify the compliance coefficients using different payloads and end effector position information. Second, the kinematic parameter errors and link parameters are identified with the given compliance coefficients. Then, the algorithm generates a modified trajectory using the calibrated DH tables for the precision compensation. Simulation and experimental results demonstrate that the positioning accuracy can be improved by 80 % to 90 % even under different payloads. The root mean square, mean, maximum, and standard deviation of the residual errors by using the proposed algorithm could outperform the conventional kinematic algorithm.

Positioning accuracy improvement for target point tracking of robots based on Extended Kalman Filter with an optical tracking system

Although industrial robots have been successfully used in a wide spectrum of applications for production automation, they still face challenges for many high precision tasks especially in low-volume high-mix production due to their low absolute positioning accuracy. To respond to such rapidly changing production tasks, an efficient means is required to determine the pose relationship between the robot and the workpiece without human intervention such as teaching the robot. For this purpose, the paper proposes the use of the Extended Kalman Filter (EKF) with an optical tracking system to improve the robot positioning accuracy with a particular focus on the target point tracking of the end-of-arm tool, which is an essential part for many robotic tasks. To this end, a comprehensive kinematic error model is first derived for the end-of-arm tool that accounts for the errors in the Denavit-Hartenberg (D-H) parameters, the positioning errors of the robot base and the end-of-arm tool installation. Then, by using the optical tracking system, the pose of the end-of-arm tool relative to the workpiece can be determined in an efficient way. Based on the EKF algorithm, the kinematic parameter errors of the system can be estimated online to compensate the positioning error of the target point during the robot movement. Simulation and experimental tests have been performed to demonstrate the effectiveness of the proposed method. The proposed approach utilizes the given trajectory to design a compensation scheme where the kinematic parameter errors of the robot are estimated during the motion and then the positioning error of the end-of-arm tool is compensated at the target point. As a result, this approach can improve the target point accuracy of the robot without continuous feedback to reduce the tracking error along the trajectory in real time. It is easy to implement and suitable for low-volume, high-mix scenarios to determine the pose relationship between the robot and the workpiece without human intervention.

Kinematic Parameter Identification and Error Compensation of Industrial Robots Based on Unscented Kalman Filter with Adaptive Process Noise Covariance

Kinematic calibration plays a pivotal role in enhancing the absolute positioning accuracy of industrial robots, with parameter identification and error compensation constituting its core components. While the conventional parameter identification method, based on linearization, has shown promise, it suffers from the loss of high-order system information. To address this issue, we propose an unscented Kalman filter (UKF) with adaptive process noise covariance for robot kinematic parameter identification. The kinematic model of a typical 6-degree-of-freedom industrial robot is established. The UKF is introduced to identify the unknown constant parameters within this model. To mitigate the reliance of the UKF on the process noise covariance, an adaptive process noise covariance strategy is proposed to adjust and correct this covariance. The effectiveness of the proposed algorithm is then demonstrated through identification and error compensation experiments for the industrial robot. Results indicate its superior stability and accuracy across various initial conditions. Compared to the conventional UKF algorithm, the proposed approach enhances the robot’s accuracy stability by 25% under differing initial conditions. Moreover, compared to alternative methods such as the extended Kalman algorithm, particle swarm optimization algorithm, and grey wolf algorithm, the proposed approach yields average improvements of 4.13%, 26.47%, and 41.59%, respectively.

A novel calibration method for kinematic parameter errors of industrial robot based on Levenberg–Marquard and Beetle Antennae Search algorithm

In this paper, a new kinematic parameter error calibration method based on the Levenberg–Marquard and the beetle antennae search algorithm is proposed to enhance the positioning accuracy of the industrial robot. Firstly, the Modified Denavit–Hartenberg model is chosen to establish the kinematic model for the industrial robot. Secondly, the kinematic parameter errors are calibrated by Levenberg–Marquard algorithm and then obtain the kinematic parameter errors of the industrial robot. Thirdly, these kinematic parameter errors are taken as the center values for the initial individual of the beetle antennae search algorithm. The kinematic parameter errors are accurately calibrated using the beetle antennae search algorithm to obtain the best value for the kinematic parameter errors. Finally, experimental verification results demonstrate that the positioning error of the industrial robot is decreased from 0.7332 mm to 0.1392 mm by using the proposed Levenberg–Marquard and beetle antennae search algorithm. The results also demonstrate that the proposed Levenberg–Marquard and beetle antennae search algorithm calibrate the kinematic parameter errors of the industrial robot effectively and enhance the positioning accuracy of the industrial robot significantly.

A matrix-solving hand-eye calibration method considering robot kinematic errors

Hand-eye calibration is one of the practical solutions for enhancing the robotic machining accuracy of complex freeform surfaces. The hand-eye parameters identification, however, is inevitably affected by the robot kinematic errors. In this paper, a matrix-solving hand-eye calibration method is proposed to overcome the challenge by taking into consideration the position constraint based robot kinematics identification. In the calibration framework, the calibration of hand-eye parameters is performed for solving the rotation matrix and translation vector, and the corresponding calibration strategies are proposed based on the axial translation under robot end-effector coordinate frame and the robot relocalization, respectively. Then the hand-eye parameters are corrected in the form of matrix compensation by using the differential matrix of the robot pose errors. A uniform sampling method for robot pose screening is further designed to automatically acquire spherical point clouds by the laser scanner when the robot poses change. Based on these steps, the combined identification model of robot kinematic parameter errors and hand-eye parameters is developed according to the position constraint that the position of the criterion sphere in the robot base coordinate frame is invariant. By virtue of the least square method, the kinematic parameter errors of the robot are calculated to compensate the hand-eye calibration accuracy. The calibration experiments are investigated by robotic scanning of the criterion sphere and two typical complex workpiece of car bodywork and blade, and the results are particularly compared with the uncompensated method and the state-of-the-art methods, showing the effectiveness and applicability of the proposed method.

Kinematic Calibration Method for Six-Hardpoint Positioning Mechanisms Using Optimal Measurement Pose

In this study, a kinematic calibration method is proposed. The method selects the optimal measurement poses based on the observability index O1, and is used for six-hardpoint positioning mechanisms, which can identify and compensate for kinematic parameter errors of the mechanism. The calibration method is based on the derived error model. In order to improve the problem that measurement noise affects calibration accuracy, the proposed calibration method selects specific poses for calibration based on the observability index O1, effectively improving the calibration accuracy. The reason for using O1 is that we compared the performance of the five observability indices through simulation, and the results show that the calibration based on O1 has the highest accuracy. In order to achieve pose selection based on observability indices, the DETMAX algorithm has been improved to achieve better performance of selection. Finally, an overall evaluation of the proposed calibration method is conducted, and the results show that the method can accurately identify kinematic parameter errors, with a fast error convergence speed. Compared with the traditional method, the proposed method has higher accuracy, reducing the mean position error by 78.4% and the mean attitude error by 70.6%. The proposed method is instrumental in the accurate kinematic calibration of six-hardpoint positioning mechanisms, and can effectively improve the accuracy of the mechanism, thus improving the pose accuracy of the primary mirror of the ground-based large aperture telescope.

Error identification and compensation regarding the kinematic parameter of the MD-PEF for tibial deformity correction

The correction accuracy of an external fixator is crucial to the treatment outcome of deformity correction and patient safety. In this study, the mapping model is established between the pose error and kinematic parameter error of the motor-driven parallel external fixator (MD-PEF). Subsequently, the kinematic parameter identification and error compensation algorithm of the external fixator is established based on the least squares method. An experimental platform based on the developed MD-PEF and Vicon motion capture system is constructed for kinematic calibration experiments. Experimental results show that the correction accuracy of the MD-PEF after calibration is as follows: translation accuracy dE1 = 0.36 mm, axial translation accuracy dE2 = 0.25 mm, angulation accuracy dE3 = 0.27°, and rotation accuracy dE4 = 0.2°. The accuracy detection experiment verifies the kinematic calibration results, which further validates the feasibility and reliability of the error identification and compensation algorithm constructed by the least squares method. The calibration approach used in this work also provides an effective way to improve the accuracy of other medical robots.

Joint space-based optimal measurement configuration determination method for Stewart platform kinematics calibration

The accuracy problem is one of the most concerning problems for the industrial application of a Stewart platform, and kinematic calibration is a feasible way to solve it. Although various calibration methods have been proposed, there is still room for improvement in the accuracy and robustness of these studies. In this article, a dimensionless error model is investigated, and the kinematic parame-ter errors are identified via the least-square method. Moreover, a novel method for measurement configurations selected based on the joint space is proposed. The simulation results show that the identification accuracy of the proposed method is better than that of the conventional method whose measurement configurations are uniformly selected in the workspace. A measurement method of the calibration experiment is suggested by the AICON 3D system - MoveInspect XR. The experimental results indicate that the position and orientation accuracy of the proposed method enhanced by 5% and 11% relative to the uniform selection method.

Kinematic parameters calibration of industrial robot based on RWS-PSO algorithm

The positioning accuracy of an industrial robot has a significant impact on its application in precision manufacturing, and it is necessary to calibrate robot kinematic parameters. Previous studies have established numerous nonlinear equations to solve the kinematic parameters, which are complicated and time consuming. A standard particle swarm optimization (PSO) algorithm is limited by long running time and low solution efficiency. Therefore, in this study, a dynamic particle swarm optimization algorithm based on roulette wheel selection (RWS-PSO) is proposed to realize the kinematic parameters calibration. First, a kinematics model is constructed using the standard Denavit-Hartenberg (D-H) method, and the theoretical and actual values of the spatial position of the robot endpoint are obtained via forward kinematics and a Laser Tracker, respectively. Next, the kinematic parameters calibration problem is transformed into a solution of a high-dimensional nonlinear equation using the proposed RWS-PSO algorithm. In the proposed RWS-PSO algorithm, the inertia factor is considered as linearly decreasing and the number of particles is selected by the roulette wheel selection (RWS) to improve its computational efficiency. The proposed RWS-PSO and standard PSO algorithms are compared based on various indices by simulation. The results reveal that the time cost of the RWS-PSO algorithm is much lower than that of the standard PSO algorithm on the basis of high precision and a reduced running time of approximately 53%. Finally, the kinematic parameter errors obtained by the two algorithms are compensated. According to the experimental results, the positioning accuracy of the robot in three ( x-, y-, and z-) directions is improved by 78%, 46%, and 67%, respectively, compared to that of before compensation, which proves that the RWS-PSO algorithm is effective and practical for kinematic parameters calibration.

A Novel Calibration Method for Robot Kinematic Parameters Based on Improved Manta Ray Foraging Optimization Algorithm

The positioning accuracy has a significant impact on the application of the robotic arm. In this study, a novel method based on improved manta ray foraging optimization (MRFO) algorithm is presented for kinematic parameters calibration, which can reduce the absolute positioning error of the manipulator. The error model of the robot is established according to the Denavit–Hartenberg (D–H) method. The redundancy of the model is analyzed, and the redundant parameters are eliminated. The kinematic parameter identification of the robot is transformed into a nonlinear optimization problem. The original MRFO algorithm is improved by using the natural selection strategy and adaptive parameter control strategy to improve searching performance and convergence speed. The calibration experiment of the self-designed 6-DOF robot arm is carried out. A measurement method for measuring the position of the robot end using a 3-D scanner is introduced. The improved MRFO (IMRFO) algorithm is used to identify the kinematic parameter errors of the robot. The experimental results show that by using the IMRFO algorithm to calibrate the parameter error, the position error of the robot end is reduced from 10.2357 to 0.5483 mm or by 94.6%. The results show that the IMRFO algorithm proposed in this article has high identification accuracy and fast convergence speed, which can effectively identify the kinematic parameter error of the robot.

Model-based kinematic and non-kinematic calibration of a 7R 6-DOF robot with non-spherical wrist

This paper presents a model-based kinematic and non-kinematic calibration method for a 7R 6-DOF robot with non-spherical wrist. By using the proposed method, kinematic errors, compliance errors from external load and self-gravity are particularly compensated. Firstly, kinematic error model is built based on modified DH (MDH) model, meanwhile calibration models for compliance and inertial parameters are derived by proper linearization of stiffness model. Secondly, to derive a suitable minimal model for practical application, model reduction and parameter identifiability analysis are conducted by considering parameter properties defined in controller. Finally, a step-by-step procedure for error parameter estimation is proposed with laser tracker as measuring device: (1) kinematic parameter errors are identified when the robot is not loaded. (2) compliance parameters are identified when the robot is loaded. (3) inertial parameters are calibrated together with kinematic errors, if deformations from self-gravity need to be compensated. Simulations and experiments on a 7R 6-DOF industrial painting robot are conducted to verify that the proposed calibration method can improve accuracy of the robot under no load and loaded conditions.

Two-Step Validation of a New Wireless Inertial Sensor System: Application in the Squat Motion

The use of Inertial Measurement Units (IMUs) can provide embedded motion data to improve clinical application. The objective of this study was to validate a newly designed IMU system. The validation is provided through two main methods, a classical sensor validation achieved on a six-degrees-of-freedom hexapod platform with controlled linear and rotation motions and a functional validation on subjects performing squats with segmental angle measurement. The kinematics of the sensors were measured by using an optoelectronic reference system (VICON) and then compared to the orientation and raw data of the IMUs. Bland–Altman plots and Lin’s concordance correlation coefficient were computed to assess the kinematic parameter errors between the IMUs and VICON system. The results showed suitable precision of the IMU system for linear, rotation and squat motions.

Kinematic Calibration of Parallel Robots Based on L-Infinity Parameter Estimation

Pose accuracy is one of the most important problems in the application of parallel robots. In order to adhere to strict pose error bounds, a new kinematic calibration method is proposed, which includes a new pose error model with 60 error parameters and a different kinematic parameter error identification algorithm based on L-infinity parameter estimation. Parameter errors are identified by using linear programming to minimize the maximum difference between predictions and workspace measurements. Simulation results show that the proposed kinematic calibration has better kinematic parameter error estimation and fewer pose errors when measurement noise is less than kinematic parameter errors. Experimental results show that maximum position and orientation errors, respectively, based on the proposed method are decreased by 86.48% and 87.85% of the original values and by 14.32% and 18.23% of those based on the conventional least squares method. The feasibility and validity of the proposed kinematic calibration are verified by improved pose accuracy of the parallel robot.

Galaxy Rotation Parameters from OB2 Stars with Proper Motions and Parallaxes from the Gaia EDR3 Catalog

We have analyzed the kinematics of OB2 stars with proper motions and parallaxes selected by Xu et al. from the Gaia EDR3 catalog. The relative parallax errors for all the stars in this sample do not exceed 10%. Based on a sample of 9750 stars, the group velocity components $${{(U,V,W)}_{ \odot }} = $$ (7.21, 7.46, 8.52) ± (0.13, 0.20, 0.10) km/s were obtained and the parameters of the angular velocity of rotation of the Galaxy: $${{\Omega }_{0}} = 29.712 \pm 0.062$$ km/s/kpc, $$\Omega _{0}^{'} = - 4.014 \pm 0.018$$ km/s/kpc2, and $$\Omega _{0}^{{''}} = 0.674 \pm 0.009$$ km/s/kpc3. The circular velocity of rotation of the solar neighborhood around the center of the Galaxy is $${{V}_{0}} = 240.7 \pm 3.0$$ km/s for the assumed distance of the Sun to the galactic center $${{R}_{0}} = 8.1 \pm 0.1$$ kpc. It is shown that the influence of the systematic correction to the trigonometric parallaxes of the Gaia EDR3 catalog with the value $$\Delta \pi = - 0.040$$ mas does not exceed the $$\sim {\kern 1pt} 1\sigma $$ level of the errors of the sought-for kinematic parameters of the model. Based on the proper motions of OB stars, the following variances of the residual velocities were found: $$({{\sigma }_{1}},{{\sigma }_{2}},{{\sigma }_{3}}) = (11.79,9.66,7.21) \pm (0.06,0.05,0.04)$$ km/s. It is shown that the first axis of this ellipsoid slightly deviates from the direction to the center of the Galaxy $${{L}_{1}} = 12.4^\circ \pm 0.1^\circ $$ , and the third axis is oriented almost exactly to the north pole of the Galaxy, $${{B}_{3}} = 83.7^\circ \pm 0.1^\circ $$ .

Kinodynamic Model Identification: A Unified Geometric Approach

A robot's dynamic model depends on both the kinematic and mass-inertial parameters of a robot. Robot model identification therefore typically begins with kinematic identification; the mass-inertial parameters are then identified with the identified kinematic parameters used in the dynamic model. In this article we show that poorly identified kinematic parameters can lead to an uncorrectable bias in the dynamic model, leading to errors in the mass-inertial parameters that are many times that of kinematic parameter errors. We instead argue that a unified kinodynamic identification leads to more accurate identification of both the kinematic and mass-inertial parameters. A linearly weighted kinodynamic objective function is proposed, in which the weight can be interpreted from a maximum likelihood perspective as the relative accuracy of the kinematic sensors vis-à-vis the dynamic sensors. Recursive algorithms for computing exact analytic gradients of the kinodynamic objective function are newly derived, leading to robust and fast-converging identification algorithms. Extensive numerical and hardware experiments demonstrate the advantages of our unified kinodynamic identification procedure.

Robot Calibration Method Based on Extended Kalman Filter–Dual Quantum Behaved Particle Swarm Optimization and Adaptive Neuro-Fuzzy Inference System

This paper combines the extended Kalman filter (EKF), dual quantum-behaved particle swarm optimization (DQPSO), and adaptive neuro-fuzzy inference system (ANFIS) to propose a novel robot calibration method. Robot precision is influenced by kinematic and non-kinematic error sources. The EKF algorithm is robust for the nonlinear system with Gaussian noise to identify kinematic parameter errors for kinematic calibration. However, if inappropriate covariance matrices are selected, the EKF algorithm may converge to an incorrect solution. To increase the effectiveness of the EKF algorithm, we propose a DQPSO algorithm that consists of the QPSO-1 and QPSO-2 algorithms. The QPSO-1 algorithm adapts the covariance matrices of measurement noise and process noise, while the QPSO-2 algorithm optimizes the kinematic parameter errors estimated by the EKF algorithm. In addition, the used ANFIS predicts and compensates the non-kinematic error for non-kinematic calibration. Experiments have been performed on a five-bar parallel robot to confirm the effectiveness of the proposed method. The experimental results demonstrate that the proposed method significantly improves the positional accuracy, and is better than the previous methods.