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

Contribution to improving the accuracy of serial robots

The goal of the present study is to improve the accuracy of six-revolute industrial robots using calibration methods. These methods identify the values of the calibrated robot model to improve the correspondence between the real robot and the mathematical model used in its controller. The calibrated robot model adds error parameters to the nominal model, which correspond to the geometric errors of the robot as well as the stiffness behavior of the robot. The developed methods focus on using low cost measurement equipment. For instance, the first work makes a comparison between a robot calibration performed using a laser tracker and a stereo camera (MMT optique) separately. The accuracy performance is validated using a telescoping ballbar for each of the two methods. While the calibration result is the same for both methods, the price of a laser tracker is more than twice the price of a stereo camera. The method is tested using an ABB IRB120 robot, a Faro ION laser tracker, and a Creaform CTrack stereo camera to calibrate the robot. A Renishaw QC20-W ballbar is used to validate the accuracy. A novel measurement system to measure a set of poses is described in the second work. The device is an extension of a known approach using an hexapod (a Stewart-Gough platform). One fixture is attached to the robot base and the other to the robot end-effector, each having three magnetic cups. By taking six ballbar measurements at a time, it is possible to measure 144 poses of the triangular fixture attached to the robot end-effector with respect to the base fixture. The position accuracy of the device is 3.2 times the accuracy of the QC20-W ballbar: ± 0.003 mm. An absolute robot calibration using this novel 6D measurement system is performed in the third work of this thesis. The robot is calibrated in 61 configurations and the absolute position accuracy of the robot after calibration is validated with a Faro laser tracker in about 10,000 robot configurations. The mean distance error is improved from 1.062 mm to 0.400 mm in 50 million pairs of measurements throughout the complete robot workspace. To allow a comparison, the robot is also calibrated using the laser tracker and the robot accuracy validated in the same 10,000 robot configurations

Calibration of a serial robot using a laser tracker

The positioning performance of an industrial robot ABB IRB 1600-6/1.45 has been studied with a laser tracker. Performing some axis-by-axis analyses, we found that axes 2, 3 and 6 have a non-geometrical behavior. A 34-parameter model was used to represent the real robot. This error model takes into account the geometrical errors due to fabrication as well as four error parameters related to stiffness (in axes 2 and 3) and four other error parameters used to fit a second-order Fourier series to the non-linear behavior of axis 6. The Nelder-Mead non linear optimization technique was used to find the error parameters that best fit the measures acquired with the laser tracker. An algebraic solution for the inverse kinematics is not possible for the 34-parameter model. We therefore propose a numerical and iterative inverse algorithm to recalculate the robot targets into so-called fake targets. No more than three iterations are needed to accurately obtain the joint angles corresponding to a given pose of the end-effector. Similar tests to the ones proposed by the ISO 9283 norm are performed to compare the accuracy of the nominal and improved robot models. The validation of the accuracy is done with a large number of measures. For the 34-parameter model the mean / maximum position errors are reduced from 0.979 mm / 2.326 mm to 0.329 mm / 0.916 mm (verification performed with around 1000 measurements), at a 6 kg payload, for eight points on the endeffector and for the complete robot workspace (or almost complete, since we had to avoid some obstacles). Analyses were performed with the expected errors. They allow to “pre-validate” the models without having to take extra measurements. It was found that this pre-validation is very close to the real validation