Kinematic calibration of a laser tracker based on nonlinear optimization of a refined geometric error model

This paper presents a kinematic calibration of a 6-RRRPRR parallel kinematic mechanism with offset RR-joints that would be applied in space positioning field. In order to ensure highly accurate and highly effective calibration process, the complete error model, which contains offset universal joint errors, is established by differentiating inverse kinematic model. A calibration simulation comparison with non-complete error model shows that offset universal joint errors are crucial to improve the calibration accuracy. Using the error model, an optimal calibration configuration selection algorithm is developed to determine the least number of measurement configurations as well as the optimal selection of these configurations from the feasible configuration set. To verify the effectiveness of kinematic calibration, a simulation and experiment were performed. The results show that the developed approach can effectively improve accuracy of a parallel kinematic mechanism with relatively low number of calibration configurations.

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Kinematic calibration of serial robot using dual quaternions

Industrial Robot the international journal of robotics research and application ◽

10.1108/ir-10-2018-0221 ◽

2019 ◽

Vol 46 (2) ◽

pp. 247-258 ◽

Cited By ~ 3

Author(s):

Guozhi Li ◽

Fuhai Zhang ◽

Yili Fu ◽

Shuguo Wang

Keyword(s):

Kinematic Analysis ◽

Quaternion Algebra ◽

Error Model ◽

Kinematic Calibration ◽

Dual Quaternion ◽

Robot Calibration ◽

Geometrical Meaning ◽

Content Type ◽

Dual Quaternions ◽

Serial Robot

Purpose The purpose of this paper is to propose an error model for serial robot kinematic calibration based on dual quaternions. Design/methodology/approach 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. Findings 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. Originality/value 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.

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A Complete, Continuous, and Minimal Product of Exponentials-Based Model for Five-Axis Machine Tools Calibration With a Single Laser Tracker, an R-Test, or a Double Ball-Bar

Journal of Manufacturing Science and Engineering ◽

10.1115/1.4042582 ◽

2019 ◽

Vol 141 (4) ◽

Cited By ~ 2

Author(s):

Peng Xu ◽

Benny C. F. Cheung ◽

Bing Li

Keyword(s):

Machine Tool ◽

Machine Tools ◽

Rigid Bodies ◽

Error Model ◽

Laser Tracker ◽

Calibration Model ◽

Transformation Matrices ◽

Double Ball Bar ◽

Ball Bar ◽

Five Axis

Calibration is an important way to improve and guarantee the accuracy of machine tools. This paper presents a systematic approach for position independent geometric errors (PIGEs) calibration of five-axis machine tools based on the product of exponentials (POE) formula. Instead of using 4 × 4 homogeneous transformation matrices (HTMs), it establishes the error model by transforming the 6 × 1 error vectors of rigid bodies between different frames resorting to 6 × 6 adjoint transformation matrices. A stable and efficient error model for the iterative identification of PIGEs should satisfy the requirements of completeness, continuity, and minimality. Since the POE-based error models for five-axis machine tools calibration are naturally complete and continuous, the key issue is to ensure the minimality by eliminating the redundant parameters. Three kinds of redundant parameters, which are caused by joint symmetry information, tool-workpiece metrology, and incomplete measuring data, are illustrated and explained in a geometrically intuitive way. Hence, a straightforward process is presented to select the complete and minimal set of PIGEs for five-axis machine tools. Based on the established unified and compact error Jacobian matrices, observability analyses which quantitatively describe the identification efficiency are conducted and compared for different kinds of tool tip deviations obtained from several commonly used measuring devices, including the laser tracker, R-test, and double ball-bar. Simulations are conducted on a five-axis machine tool to illustrate the application of the calibration model. The effectiveness of the model is also verified by experiments on a five-axis machine tool by using a double ball-bar.

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Prediction of machining accuracy based on a geometric error model in five-axis peripheral milling process

Proceedings of the Institution of Mechanical Engineers Part B Journal of Engineering Manufacture ◽

10.1177/0954405413516611 ◽

2014 ◽

Vol 228 (10) ◽

pp. 1226-1236 ◽

Cited By ~ 17

Author(s):

Guofu Ding ◽

Shaowei Zhu ◽

Elssawi Yahya ◽

Lei Jiang ◽

Shuwen Ma ◽

...

Keyword(s):

Milling Process ◽

Geometric Error ◽

Error Model ◽

Machining Accuracy ◽

Peripheral Milling ◽

Five Axis

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A General Approach for Geometric Error Modeling of Lower Mobility Parallel Manipulators

Journal of Mechanisms and Robotics ◽

10.1115/1.4003845 ◽

2011 ◽

Vol 3 (2) ◽

Cited By ~ 29

Author(s):

Haitao Liu ◽

Tian Huang ◽

Derek G. Chetwynd

Keyword(s):

Systematic Approach ◽

Parallel Manipulators ◽

Geometric Error ◽

Error Modeling ◽

Kinematic Calibration ◽

Accuracy Improvement ◽

Linear Map ◽

Homogeneous Transformation Matrix ◽

Lower Mobility ◽

Source Errors

This paper presents a general and systematic approach for geometric error modeling of lower mobility manipulators. The approach can be implemented in three steps: (1) development of a linear map between the pose error twist and source errors within an individual limb using the homogeneous transformation matrix method; (2) formulation of a linear map between the pose error twist and the joint error intensities of a lower mobility parallel manipulator; and (3) combination of these two models. The merit of this approach lies in that it enables the source errors affecting the compensatable and uncompensatable pose accuracy of the platform to be explicitly separated, thereby providing designers and/or field engineers with an informative guideline for the accuracy improvement achievable by suitable measures, i.e., component tolerancing in design, manufacturing and assembly processes, and kinematic calibration. Three typical and well-known parallel manipulators are taken as examples to illustrate the generality and effectiveness of this approach.

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