# Robot calibration

Robot calibration is the process of determining the various parameters of the robot mechanics in order to obtain a complete kinematic model of the robot . The calibration of robot, tool and workpiece ( cell calibration ) can reduce or minimize the existing inaccuracies. The calibration can also increase process reliability.

The positioning accuracy of industrial robots (IR) is often insufficient for certain tasks. Problems can arise when replacing robots and when programming precision applications, which can be very time-consuming and costly to resolve.

## Parameters and error influences

The international standard ISO 9283 defines various performance criteria for IR and suggests test methods for their determination. The most important parameters are absolute accuracy (accuracy of pose or path, AP) and repeatability (repeatability of pose and path, RP). These are the commonly used criteria.

Repeat accuracy is not only crucial when programming the robot through teaching ("teach-in"), but also in every more demanding process. This is independent of whether the robot is only "taught" or whether the data was generated by "offline programming".

However, if the movement program is created using 3D simulation (“offline programming”), the absolute accuracy of an IR is also important. It is generally negatively influenced by various factors. The axis zero positions as well as the length and angle errors between the individual robot elements are of the greatest importance. These, in connection with the variable load on the flange of an IR, represent the greatest sources of error. Changes in length due to temperature fluctuations also contribute to the change in position of a robot, which, depending on the robot program or heating of the machine, can make a contribution significantly above the repeat accuracy .

## Measuring systems

There are various options for measuring the position of industrial robots, for example approaching sample workpieces, using ultrasonic sensors , laser interferometry , theodolites , measuring probes or laser triangulation . There are also camera systems that can be installed in the robot cell or on the IR itself and capture the position of a reference object. Providers of measuring systems are, for example, the companies Automated Inspection (formerly HGV Vosseler), Carl Zeiss, Dynalog, EngRoTec Solutions, FARO, Leica, Metris, NDI, Perceptron, Wiest and Teconsult.

## Mathematical basics

The robot errors detected by means of position measurement can be minimized with numerical optimization as part of a compensation calculation. To do this, a complete kinematic model of the geometric structure must first be created, the parameters of which are then determined by mathematical optimization. From the input and output variables in vector notation, the general system behavior can be formulated using the vector model function as follows:

{\ displaystyle {\ begin {aligned} {\ vec {p}} & = (p_ {1}, \ ldots, p_ {n}) ^ {\ text {T}}, \ {\ vec {p}} \ in {\ text {R}} ^ {\ text {n}} \\ {\ vec {x}} & = ({\ vec {x}} _ {1}, \ ldots, {\ vec {x}} _ {m}) ^ {\ text {T}}, \ {\ vec {x}} _ {i} \ in {\ text {R}} ^ {\ text {k}}, \ {\ vec {x }} \ in {\ text {R}} ^ {\ text {mxk}} \\ {\ vec {y}} _ {M} & = ({\ vec {y}} _ {M1}, \ ldots, {\ vec {y}} _ {Mm}) ^ {\ text {T}}, \ {\ vec {y}} _ {Mi} \ in {\ text {R}} ^ {\ text {l}} , \ {\ vec {y}} _ {M} \ in {\ text {R}} ^ {\ text {mxl}} \\ {\ vec {y}} _ {S} & = ({\ vec { y}} _ {S1}, \ ldots, {\ vec {y}} _ {Sm}) ^ {\ text {T}}, \ {\ vec {y}} _ {Si} \ in {\ text { R}} ^ {\ text {l}}, \ {\ vec {y}} _ {S} \ in {\ text {R}} ^ {\ text {mxl}} \\ & \\ {\ vec { y}} _ {M} & = {\ vec {f}} ({\ vec {p}}, {\ vec {x}}), \ {\ vec {f}} \ in {\ text {R} } ^ {\ text {mxl}} \\ & \\ {\ underset {{\ vec {p}} \ in {\ text {R}} ^ {\ text {n}}} {min}} & \ left \ {r \ right \} {\ text {with}} r = \ lVert {\ vec {y}} _ {M} - {\ vec {y}} _ {S} \ rVert ^ {2} = \ lVert {\ vec {f}} ({\ vec {p}}, {\ vec {x}}) - {\ vec {y}} _ {S} \ rVert ^ {2} {\ text {and}} r \ in {\ text {R}} \ end {aligned}}}

The variables k, l, m, n and their links describe the dimensions of the individual vector spaces. The minimization of the residual error r to identify an optimal parameter vector p results from the difference between the two output vectors using the Euclidean norm.

For the solution of the kinematic optimization problems are u. a. Least squares descent method , for example a modified quasi-Newton method . This method supplies corrected kinematics parameters for the measured machine, which can then be entered in the robot controller, for example, in order to adapt the computer model used there to the real kinematics.

## Results

The absolute positioning accuracy of industrial robots varies between a few tenths and several millimeters, depending on the manufacturer, age and use. A positioning accuracy of approx. 0.5 mm can usually be achieved by calibration, which, if the working volume is limited, can also approach the otherwise usual repeatability of a robot of approx. 0.1 mm.

## Application examples

In-line measuring cell for body measurements

In the industry there is e.g. Currently there is a general trend towards the substitution of machine tools or special machines by industrial robots for certain production tasks whose accuracy requirements can be met by calibrated robots. A current example is shown in the figure: in-line measurement technology in the body shop, where the "measurement tunnels" with many expensive sensors, e.g. T. be replaced by IR, which each lead only one sensor. This can significantly reduce the total costs of a measuring cell. In addition, if there is a model change, the system can be reused without any structural changes thanks to simple reprogramming.

Further examples of precision applications are the robot-assisted roller hemming in the body shop of e.g. B. EngRoTec Solutions, the assembly of mobile phones, drilling, riveting and milling in aircraft construction as well as increasingly medical applications.

## Summary

By using efficient calibration methods, it is possible to achieve an absolute positioning accuracy of 0.1 mm with industrial robots available on the market today - especially parallel kinematic robots - in order to improve interchangeability, simplify off-line programming and new, high-precision applications to enable.

## literature

• Lukas Beyer: Increased accuracy of industrial robots, especially with parallel kinematics. Dissertation, Helmut Schmidt University Hamburg. Shaker Verlag , Aachen 2005, ISBN 3-8322-3681-3
• Klaus Schröer: Identification of calibration parameters of kinematic chains. Dissertation, Technical University of Berlin. Hanser Fachbuchverlag, Munich 1993, ISBN 3446176500
• Ulrich Wiest: Kinematic calibration of industrial robots. Dissertation, University of Karlsruhe. Shaker Verlag, Aachen 2001, ISBN 3-8265-8609-3
• NN: ISO 9283 - Manipulating industrial robots. Performance criteria and related test methods. ISO, Geneva 1998
• Y. Zhang and F. Gao, “A calibration test of Stewart platform,” 2007 IEEE International Conference on Networking, Sensing and Control, IEEE, 2007, pp. 297-301.