Ana Cristina Majarena

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.

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.

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.

Calibration, non-geometric error modelling and correction methods for Articulated Arm Coordinate Measuring Machines

The different accuracy and repeatability requirements of articulated Arm Coordinate Measuring Machines (AACMM) and robots make it necessary to consider different kinematic parameters identification techniques covering the characteristic operational parameters in each case. This paper presents a data capture technique for subsequent identification of an AACMM kinematic model parameters, using nominal data reached by a ball bar and a kinematic coupling. Also this paper addresses the performance evaluation of the algorithm and objective functions used, based on a new approach, including terms regarding measurement accuracy and repeatability.

Laser Tracker Error Modeling and Kinematic Calibration Strategy

Calibration of Laser Tracker systems is based most times in the determination of its geometrical errors. Some standards as the ASME B89.4.19 [1] and the VDI 2617-10 [2] describe different tests to calculate the geometric misalignments that cause systematic errors in Laser Tracker measurements. These errors are caused not only because of geometrical misalignments and other sources of error must also be taken in count. In this work we want to state the errors in a kinematic form. Errors will be split in two different components, geometric and kinematic errors. The first ones depend on the offsets, tilts and eccentricity of the mechanical and optical components of the system. Kinematic errors are different for every position of the Laser tracker, so they will be formulated as functions of three system variables: distance (R), vertical angle (V) and horizontal angle (H) usually called d, φ and θ. The goal of this work is to set up an evaluation procedure to determine geometric and kinematic errors of Laser Trackers.

Teaching Mechanism Calibration to Engineering Students

A new practical application for teaching mechanism calibration to engineering students in senior undergraduate courses is presented in this paper. The modelling, characterization and calibration of kinematic mechanisms is performed. This application presents a special interest in kinematic mechanisms in areas such as industry and research. The application interface allows the students to carry out the different steps of the calibration procedure in an easy way, to change different variables and to analyze results. This application therefore presents an important utility as a teaching tool for the learning process and analysis of the different steps in the mechanism optimization. The application developed allows students: to design their own mechanisms and to analyze the mechanism workspace by changing some design parameters, to test accuracy and repeatability of mechanism components, to introduce the mechanism kinematic model, to evaluate the mechanism performance before calibration, to calibrate the mechanism and, finally, to analyze the improvement in the system accuracy.

Software simulation platform for learning techniques for identifying kinematic parameters of industrial robots

This paper presents the simulation software of capture and analysis of data for parameter identification of robot kinematic models developed for learning the discipline and the practical sessions under the activity for courses for master and postgraduate students adapted to the EHEA. After the content of the theoretical sessions, the software will be used for practical sessions, from a constructivist approach, encouraging independent learning of the students. This parametric software covers most important aspects of a robot calibration procedure and the influences on accuracy: 1) kinematic modeling, 2) data capture procedure, 3) parameter identification methods, 4) evaluation of the calibration. Also it allows to understand how each influence spreads to the final error and how to minimize sources of error in the process to establish optimal conditions for the highest possible accuracy in the parameters identified.

Pant‐tilt Platform Design Based on Parallel Kinematics

A new long distance measurement system design, based on parallel kinematics, is presented in this paper. This system has two degrees of freedom for positioning and orientating two high precision cameras. In this document is presented the system design. Several configurations have been analyzed and the components needed such as actuators, linear captators (to measure the displacement), spherical ball‐and‐socket joints and universal joints, have been selected. The developed model allows us to obtain the kinematic joint variables, depending on geometric parameters, by means of the resolution of opened chains for each leg. The direct model allows us to obtain the platform position and orientation for a determined displacement values. Once the matrix transformation (which describes the coordinates of the platform reference system respect to the base reference system) is obtained, the actuators elongation can be found out through the inverse model with numeric or geometric methods. The design optimization, by m...