An improved kinematic calibration method for serial manipulators based on POE formula

Robotica ◽  
2018 ◽  
Vol 36 (8) ◽  
pp. 1244-1262 ◽  
Author(s):  
Chenguang Chang ◽  
Jinguo Liu ◽  
Zhiyu Ni ◽  
Ruolong Qi
Keyword(s):  
High Precision ◽  
Least Square Method ◽  
Calibration Method ◽  
Error Model ◽  
Least Square ◽  
Identification Accuracy ◽  
Kinematic Calibration ◽  
Serial Manipulators ◽  
Serial Robots ◽  
Generic Modeling

SUMMARYExisting measurement equipments easily determine position with high precision. However, they evaluate orientation with low precision. It is necessary to minimize the effect of measurement error on identification accuracy. In this study, a method for kinematic calibration based on the product of exponentials (POE) is presented to improve the absolute positioning accuracy of a sliding manipulator. An error model with uniform and generic modeling rules is established in which the tool frame is selected as the reference frame. Furthermore, the redundant parameters of the error model are removed. Subsequently, the actual kinematic parameters are identified by using the least square method. Finally, the process of the improved method is discussed. Kinematic calibration simulations of a sliding manipulator are implemented. The results indicate that the proposed method significantly improves the precision of the sliding manipulator. The improved POE kinematic calibration method offers convenience, efficiency, and high precision. The proposed method can be applied to all types of serial robots with n-DOF

Error Model and Calibration Analysis of the Flexible Coordinate Measuring Machine

2011 ◽  
Vol 121-126 ◽  
pp. 3273-3277 ◽  
Author(s):  
Fang Li ◽  
Shu Gui Liu ◽  
Lei Zhao
Keyword(s):  
Mathematical Model ◽  
Coordinate Measuring Machine ◽  
Least Square Method ◽  
Coefficient Matrix ◽  
Error Model ◽  
Least Square ◽  
Parameter Calibration ◽  
Measuring Machine ◽  
Improving Accuracy ◽  
The Mathematical Model

A new 5-DOF flexible coordinate measuring machine (CMM) is introduced in this paper, which uses REVO system produced by Renishaw. According to the D-H method, the mathematical model is built, and then the error model of the flexible CMM is derived. The parameter calibration based on the nonlinear least square method is analyzed theoretically. Due to the disadvantages of Gauss-Newton method, LM method is researched, which improved the singularity of the coefficient matrix. The calibration analysis is a basis for improving accuracy of the flexible CMM.

scholarly journals The tides in the south-western Kara sea. Tides calibration method effects

2017 ◽  
pp. 98-115
Author(s):  
G. N. Voinov ◽  
A. K. Naumov
Keyword(s):  
Sea Level ◽  
Least Square Method ◽  
Calibration Method ◽  
Kara Sea ◽  
Least Square ◽  
The South ◽  
Quality Estimation ◽  
Annual Series ◽  
Method Effects ◽  
Statistical Estimations

The estimates of the tides harmonic constants are given over the period from 1962 to 1993. They were received using a least square method according to AARI. Quality estimation of the sea level observations was performed. The annual series with bad observations were transformed by means of tides calibration. The Estimation of the tides fi ne structure – harmonics of the second and third degree of the potential according to analysis over the period from 1962–1985 was received. The statistical estimations of the sea level in the separate typical years were calculated using initial and corrected series.

scholarly journals A Kinematic Calibration Method of a 3T1R 4-Degree-of-Freedom Symmetrical Parallel Manipulator

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 357
Author(s):  
Fengxuan Zhang ◽  
Silu Chen ◽  
Yongyi He ◽  
Guoyun Ye ◽  
Chi Zhang ◽  
...  
Keyword(s):  
Parallel Manipulator ◽  
Kinematic Model ◽  
Calibration Method ◽  
Error Modeling ◽  
Degree Of Freedom ◽  
Least Square ◽  
Kinematic Calibration ◽  
Recursive Least Square ◽  
Local Product ◽  
Branched Chain

This paper proposes a method for kinematic calibration of a 3T1R, 4-degree-of-freedom symmetrical parallel manipulator driven by two pairs of linear actuators. The kinematic model of the individual branched chain is established by using the local product of exponentials formula. Based on this model, the model of the end effector’s pose error is established from a pair of symmetrical branched chains, and a recursive least square method is applied for the parameter identification. By installing built-in sensors at the passive joints, a calibration method for a serial manipulator is eventually extended to this parallel manipulator. Specifically, the sensor installed at the second revolute joint of each branched chain is saved, replaced by numerical calculation according to kinematic constraints. The simulation results validate the effectiveness of the proposed kinematic error modeling and identification methods. The procedure for pre-processing compensation on this 3T1R parallel manipulator is eventually given to improve its absolute positioning accuracy, using the inverse of the calibrated kinematic model.

Simultaneous identification of joint stiffness, kinematic and hand-eye parameters of measurement system integrated with serial robot and 3D camera

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Jinlei Zhuang ◽  
Ruifeng Li ◽  
Chuqing Cao ◽  
Yunfeng Gao ◽  
Ke Wang ◽  
...  
Keyword(s):  
Measurement System ◽  
Measurement Accuracy ◽  
Joint Stiffness ◽  
Calibration Method ◽  
Identification Accuracy ◽  
Kinematic Calibration ◽  
Content Type ◽  
3D Camera ◽  
Serial Robot ◽  
Measurement Principle

Purpose 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. Design/methodology/approach 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. Findings 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. Originality/value 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.

scholarly journals Self-Calibration of an Industrial Robot Using a Novel Affordable 3D Measuring Device

Sensors ◽  
2018 ◽  
Vol 18 (10) ◽  
pp. 3380 ◽  
Author(s):  
Martin Gaudreault ◽  
Ahmed Joubair ◽  
Ilian Bonev
Keyword(s):  
Industrial Robot ◽  
Low Cost ◽  
Least Square Method ◽  
Calibration Method ◽  
Least Square ◽  
Geometrical Parameters ◽  
Robot Arm ◽  
Measuring Device ◽  
Self Calibration ◽  
Position Errors

This work shows the feasibility of calibrating an industrial robot arm through an automated procedure using a new, low-cost, wireless measuring device mounted on the robot’s flange. The device consists of three digital indicators that are fixed orthogonally to each other on an aluminum support. Each indicator has a measuring accuracy of 3 µm. The measuring instrument uses a kinematic coupling platform which allows for the definition of an accurate and repeatable tool center point (TCP). The idea behind the calibration method is for the robot to bring automatically this TCP to three precisely-known positions (the centers of three precision balls fixed with respect to the robot’s base) and with different orientations of the robot’s end-effector. The self-calibration method was tested on a small six-axis industrial robot, the ABB IRB 120 (Vasteras, Sweden). The robot was modeled by including all its geometrical parameters and the compliance of its joints. The parameters of the model were identified using linear regression with the least-square method. Finally, the performance of the calibration was validated with a laser tracker. This validation showed that the mean and the maximum absolute position errors were reduced from 2.628 mm and 6.282 mm to 0.208 mm and 0.482 mm, respectively.

Camera Calibration Based on Snell’s Law

2005 ◽  
Vol 128 (3) ◽  
pp. 548-557 ◽  
Author(s):  
Psang Dain Lin ◽  
Chi-Kuen Sung
Keyword(s):  
Camera Calibration ◽  
Least Square Method ◽  
Calibration Method ◽  
Least Square ◽  
Camera System ◽  
Optical Elements ◽  
Snell’S Law ◽  
Snell's Law ◽  
Geometric Relationship ◽  
Pinhole Model

In this paper we present a camera calibration method using Snell’s Law. Traditional camera calibration is based on the pinhole model, which is an approximation algorithm using untrue geometrical assumptions and giving a single lumped result for the various optical elements in the camera system. Using full modeling of lens geometry, the proposed method establishes the geometric relationship between images and objects via Snell’s Law. A matrix equation that relates the intrinsic/extrinsic parameters of image the plane and six pose parameters of each element is determined from sensitivity analysis. These parameters can be identified using the least square method by observing points with known coordinates. An illustrative example using a two-camera stereo coordinate measurement system demonstrates that system performance via the proposed method is better than the pinhole model.

Study on Two-Step Method for Robot Dynamics Parameters Calibration

2012 ◽  
Vol 605-607 ◽  
pp. 1557-1562 ◽  
Author(s):  
Qing Xuan Jia ◽  
Tong Li ◽  
Gang Chen
Keyword(s):  
Inverse Method ◽  
Least Square Method ◽  
Calibration Method ◽  
Least Square ◽  
Second Step ◽  
Robot Dynamics ◽  
Joint Movement ◽  
Step Method ◽  
Multidimensional Matrix ◽  
Pseudo Inverse

In order to obtain accurate dynamics parameters, a two-step method for robot dynamics parameters calibration is presented. In the first step a multidimensional matrix is constituted through transforming the configurations of robot manipulators and the product of quality and centroid coordinate about links is solved by using the least square method. In the second step decoupling dynamic equation of robot is deduced based on Newton-Euler algorithm, and through planning specific joint movement, the inertia tensor and centroid coordinate of robot links are calibrated making use of the pseudo inverse method. By the above two steps, the entire calibration of robot dynamic parameters is achieved. The correctness and feasibility of the presented calibration method is manifested by simulations and experiments.

A Camera Calibration Method Based on Free Points

2011 ◽  
Vol 130-134 ◽  
pp. 1885-1888
Author(s):  
Jing Lei Zhang ◽  
Kai Bo Fan ◽  
Yan Jiao Wang
Keyword(s):  
Standard Deviation ◽  
Ccd Camera ◽  
Least Square Method ◽  
Calibration Method ◽  
Initial Guess ◽  
Least Square ◽  
Camera Model ◽  
Extrinsic Parameters ◽  
The Mean ◽  
Constraint Method

A new accurate calibrating technique for intrinsic parameters and extrinsic parameters of CCD camera is described. The camera model is derived by the pinhole projection theory. Then other parameters of the model are resolved under the radial alignment constraints and orthogonal constraints. In order to get a fine initial guess for the nonlinear searching solution, the least square method is introduced, and finally uses radial alignment constraint method to get the results. The experimental results show that the mean absolute differences in x direction and y direction are 0.0070 and 0.1430 separately while the standard deviation are 0.5006 and 1.2046 separately.

The Novel Calibration Method for 3-DOF Measurement System

2011 ◽  
Vol 120 ◽  
pp. 440-443
Author(s):  
Kwang Il Lee ◽  
Jin Seok Jang ◽  
Hyun Woo Lee ◽  
Suk Jin Kim ◽  
Sang Ryong Lee ◽  
...  
Keyword(s):  
Measurement System ◽  
Measurement Accuracy ◽  
Least Square Method ◽  
Calibration Method ◽  
Measured Data ◽  
Least Square ◽  
The Novel ◽  
Squareness Error ◽  
Misalignment Error ◽  
Calibration Parameters

In this paper, a novel calibration method is developed to improve the measurement accuracy of 3-DOF measurement system. The squareness error between three sensors and misalignment error with respect to reference coordinate of machine tool are calibration parameters. To estimate these parameters, reference ball is used and moved in the measuring ranges of 3-DOF measurement system. The relation between calibration parameters, position of reference ball, measured data of sensors are defined using geometric constraint and estimated using least square method. Finally, simulation is done to check the feasibility of developed calibration method. The result of simulation revealed the validation of developed method.

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