David Samper

Articulated Arm Coordinate Measuring Machine Calibration by Laser Tracker Multilateration

A new procedure for the calibration of an articulated arm coordinate measuring machine (AACMM) is presented in this paper. First, a self-calibration algorithm of four laser trackers (LTs) is developed. The spatial localization of a retroreflector target, placed in different positions within the workspace, is determined by means of a geometric multilateration system constructed from the four LTs. Next, a nonlinear optimization algorithm for the identification procedure of the AACMM is explained. An objective function based on Euclidean distances and standard deviations is developed. This function is obtained from the captured nominal data (given by the LTs used as a gauge instrument) and the data obtained by the AACMM and compares the measured and calculated coordinates of the target to obtain the identified model parameters that minimize this difference. Finally, results show that the procedure presented, using the measurements of the LTs as a gauge instrument, is very effective by improving the AACMM precision.

Towards an effective identification strategy in volumetric error compensation of machine tools

The influence of technical parameters for volumetric error compensation in large-volume machine tools (MTs) is presented in this paper. The techniques presented are based on characterization models using nonlinear optimization procedures. The parameters presented allow for the characterization of different errors in the MT studied and depend on the kinematics and geometry of the system, regardless of the optimization methodology. The kinematics is affected by the MT errors on the number and type of axes and movements. To relate the coordinates of the tool to the coordinates of a laser tracker, a kinematic model of the MT that includes the measurement system must be defined. Kinematic models can be realized by using homogeneous transformation matrices or independent rotation and translation arrays according to the type of machine. Chebyshev, simple or Legendre polynomial regression functions can be used to characterize the geometric errors of the MT and are presented and compared. The distribution of measurement points, mesh or cloud, and optimization constraints of polynomial regressions are factors that also affect volumetric error compensation. Therefore, these parameters were studied and presented as well. In addition to the parameters discussed above, another parameter that affects the accuracy of data capture is the measurement noise. To improve the measurement accuracy, multilateration techniques need to be applied. Each of the aforementioned parameters has been studied by using a synthetic test generated by a parametric synthetic data generator. The selected parameters constitute a package of optimization improvement regardless of the optimization methodology, which have improved the nonlinear optimization from 60–70% to 98%.

An Overview of Kinematic and Calibration Models Using Internal/External Sensors or Constraints to Improve the Behavior of Spatial Parallel Mechanisms

This paper presents an overview of the literature on kinematic and calibration models of parallel mechanisms, the influence of sensors in the mechanism accuracy and parallel mechanisms used as sensors. The most relevant classifications to obtain and solve kinematic models and to identify geometric and non-geometric parameters in the calibration of parallel robots are discussed, examining the advantages and disadvantages of each method, presenting new trends and identifying unsolved problems. This overview tries to answer and show the solutions developed by the most up-to-date research to some of the most frequent questions that appear in the modelling of a parallel mechanism, such as how to measure, the number of sensors and necessary configurations, the type and influence of errors or the number of necessary parameters.

Study of self-calibration and multilateration in machine tool volumetric verification for laser tracker error reduction:

This article aims to present the influence of the measurement uncertainty of a commercial laser tracker on the volumetric verification of a machine tool through the study of verification procedures that are affected by measurement uncertainty, multilateration and laser tracker self-calibration. Self-calibration provides relative positioning between measuring coordinate systems (laser trackers) and the reference system from the measured points of the same mesh. The measured points are affected by the noise of each laser tracker; therefore, they provide positions that are different from the real positions of the laser trackers. By applying the technique of multilateration and by knowing the positions of the laser trackers, the measurement noise can be reduced. The range of the measurement noise reduction is influenced by the radial measurement noise of the laser tracker, the distance between the laser tracker and the measured point and the techniques that multilateration and laser tracker self-calibration employs. This article presents different laser tracker self-calibration procedures, a least squares adjustment, trilateration and quadrilateration as well as the scope and appropriateness of each method relative to the laser tracker measurement noise. Moreover, the influences of radial laser tracker noise on the trilateration and quadrilateration techniques are described as well as the influence of the distance between the laser tracker and the measured point on multilateration.

Modelling and calibration of parallel mechanisms using linear optical sensors and a coordinate measuring machine

This paper presents a new procedure for the modelling and calibration of a parallel mechanism by using linear optical sensors and a coordinate measuring machine. Three standard spheres, fixed to the moving platform, were measured by means of a coordinate measuring machine. Additionally, a control algorithm was developed to store sensor readings in each analysed position. These readings and the kinematic model allow us to obtain the calculated sphere coordinates. The use of high-accuracy linear optical sensors allows us to correct actuator backlash, thereby increasing the mechanism accuracy. The developed method defines an objective function that compares the measured and calculated coordinates of the three-sphere centres in order to obtain the identified model parameters that minimize this difference. This procedure combines both inverse and forward kinematics, and solves the nonlinear system loop of the kinematic model inside a second loop that optimizes the geometric parameters of the model. Numerical optimization techniques based on Levenberg–Marquardt algorithm are used to solve both optimization loops. Results show that the platform position and orientation errors are improved by more than one order of magnitude.

Analysis of Tsai calibration method using two- and three-dimensional calibration objects

Camera calibration is a fundamental process for both photogrammetric and computer vision. Since the arrival of the direct linear transformation method and its later revisions, new methods have been developed by several authors, such as: Tsai, Heikkilä and Zhang. Most of these have been based on the pinhole model, including distortion correction. Some of these methods, such as Tsai method, allow the use of two different techniques for determining calibration parameters: a non-coplanar calibration technique using three-dimensional (3D) calibration objects, and a coplanar technique that uses two-dimensional (2D) calibration objects. The calibration performed by observing a 3D calibration object has good accuracy, and produces very efficient results; however, the calibration object must be accurate enough and requires an elaborate configuration. In contrast, the use of 2D calibration objects yields less accurate results, is much more flexible, and does not require complex calibration objects that are costly to produce. This article compares these two different calibration procedures from the perspective of stereo measurement. Particular attention was focused on the accuracy of the calculated camera parameters, the reconstruction error in the computer image coordinates and in the world coordinate system and advanced image-processing techniques for subpixel detection during the comparison. The purpose of this work is to establish a basis and selection criteria for choosing one of these techniques for camera calibration, according to the accuracy required in each of the many applications using photogrammetric vision: robot calibration methods, trajectory generation algorithms, articulated measuring arm calibration, and photogrammetric systems.

Volumetric Verification of Multiaxis Machine Tool Using Laser Tracker

This paper aims to present a method of volumetric verification in machine tools with linear and rotary axes using a laser tracker. Beyond a method for a particular machine, it presents a methodology that can be used in any machine type. Along this paper, the schema and kinematic model of a machine with three axes of movement, two linear and one rotational axes, including the measurement system and the nominal rotation matrix of the rotational axis are presented. Using this, the machine tool volumetric error is obtained and nonlinear optimization techniques are employed to improve the accuracy of the machine tool. The verification provides a mathematical, not physical, compensation, in less time than other methods of verification by means of the indirect measurement of geometric errors of the machine from the linear and rotary axes. This paper presents an extensive study about the appropriateness and drawbacks of the regression function employed depending on the types of movement of the axes of any machine. In the same way, strengths and weaknesses of measurement methods and optimization techniques depending on the space available to place the measurement system are presented. These studies provide the most appropriate strategies to verify each machine tool taking into consideration its configuration and its available work space.

Efficient volumetric error compensation technique for additive manufacturing machines

Purpose – This paper aims to present a methodology for volumetric error compensation. This technique is applied to an Objet Eden350V 3D printer and involves a custom measurement strategy. Design/methodology/approach – The kinematic model of the printer is explained, and its error model is simplified to 18 independent error functions. Each error function is defined by a cubic Legendre polynomial. The coefficients of the polynomials are obtained through a Levenberg–Marquardt optimization process. This optimization process compares, in an iterative algorithm, nominal coordinates with actual values of the cloud of points. The points are built in the faces of a gauge artefact as conical sockets defining one unique point for each socket. These points are measured by a coordinate measuring machine self-centring measurement process. Findings – Most of the errors of the 3D printer are systematic. It is possible to obtain an improvement of 70 per cent in terms of global mean error reduction in single points within ...

Teaching Camera Calibration by a Constructivist Methodology

This article describes the Metrovisionlab simulation software and practical sessions designed to teach the most important machine vision camera calibration aspects in courses for senior undergraduate students. By following a constructivist methodology, having received introductory theoretical classes, students use the Metrovisionlab application to carry out a series of practical exercises with the aim of learning in a simple way: 1) the basic functioning of a camera; 2) how to calibrate a camera; 3) the most important calibration methods and their special characteristics; and 4) the generation and use of synthetic calibration points. Evaluations based on student feedback confirm that the use of Metrovisionlab as a teaching tool facilitates the learning process.

Empirical analysis of the efficient use of geometric error identification in a machine tool by tracking measurement techniques

Volumetric verification is becoming increasingly accepted as a suitable technique with which to improve machine tool accuracy. In the same way, the use of laser trackers to obtain machine error information using the new Active Target motorised retro-reflector allows the verification of all types of machine tool throughout their workspaces. Non-linear optimisation methods and machine tool kinematic models are the mainstays of this technique. Whereas the latter provide the relationship between the nominal coordinates, the geometric errors of the machine and laser tracker measurement, the former reduces the combined influence of geometric errors by obtaining their approximation functions. However, within these two procedures, several factors affect the scope of the produced verification results. The present paper focuses on the analysis of the adequacy of commercial measurement techniques using laser trackers and the new motorised retro-reflector in a real milling machine. An examination is also made regarding the influence of the optimisation sequence defined by the identification strategy, as well as the impact of the number of measured points in relation to the employed regression functions.