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Theoretical Basics – Kinematic Calibration of Industrial Robots

Although off-line programming technology is well advanced, approximately 95% of all industrial robots are currently programmed using the teach-in method. This is mainly due to the poor positioning accuracy of today’s industrial robots. Therefore, their absolute positioning accuracy needs to be improved. Despite the high repeatability of today’s industrial robots, they exhibit transient behaviour due to temperature effects. When using industrial robots as measuring robots in quality assurance, it is necessary to keep the relative repeatability constant regardless of temperature effects.


Based on the mechanical structure of an industrial robot, a parametrizable model is created whose unknown parameters are to be determined in the course of an identification process. The model takes into account geometric deviations of the robot, such as length deviations, zero-position errors and axis misalignments. The non-geometric effects are adequately modelled by linear joint elasticities. A fast algorithm has been developed to calculate the static torques required to identify the linear elasticity coefficients.


The complete robot model forms the basis for the compensation of Cartesian errors. As there is no closed form of the parameterised inverse kinematics, a 1st order approximation is derived. A given target position is overlaid with the expected Cartesian error so that the tool tip of the real robot will hit the desired target point. The fast approximation of the inverse kinematics is fully integrated into the real robot controller and allows error compensation at all intermediate and end points of the robot trajectory in real time.


A prerequisite for the identification of the model parameters is the measurement of the robot TCP. Various measurement methods and sensor systems used to measure the robot in this thesis are presented. Sensors with a large field of view are used to measure targets attached to the robot’s hand. They provide 6-dimensional measurements of the TCP. Small, low-cost sensors are attached to the robot’s hand to measure targets in the robot’s workspace. They only provide 3-dimensional readings. The distance between the TCP robot and the measurement system, measured over the length of an unwound thread, even provides only 1-dimensional measurements. Depending on the dimensions measured, appropriate robot calibration procedures will be developed.


The essence of 6D calibration is the formation of an objective function that is minimised to identify the model parameters. It quantifies the errors that result from the theoretical pose of the robot and the actual pose measured. A residual operator is introduced to account for orientation errors in addition to positioning errors. It is shown that it is sufficient to examine the images of the Euclidean basis vectors under this operator to obtain a suitable measure of the pose errors.

The 6-dimensional measurements are generated by measuring targets on a measuring scale. This approach not only provides a quality criterion for the quality of the measurements, but also allows the position of the body to be determined in terms of a best approximation. The generation of good initial values for the unknown model parameters is crucial for the convergence of the numerical solution methods.

A general procedure is presented that allows the estimation of the most important unknowns with a minimum number of measurements. Practical experiments demonstrate the suitability of parameter estimation and error compensation. Measurements are presented which show that the positioning accuracies achieved throughout the robot’s working space are well below one millimetre, regardless of the payload.


During 3D calibration, the robot carries an “eye-in-hand” sensor for point measurement of targets on a measuring scale. An essential component in the construction of the target function is the metric information of the targets.

However, the TCP of a robot already exhibits a temperature drift of a few tenths of a millimetre during normal operation due to thermal deformation of the robot structure. To record and compensate for temperature drift, the drift calibration procedure has been developed.

During commissioning of the robot, a reference measurement is made on a temperature invariant calibration sphere. If this measurement is repeated at a later date, temperature-related deformations of the robot can be detected in the form of a drift in the measured values.

The model parameters of the robot are now set so that the measured drift matches the modelled drift as closely as possible. When drift compensation is performed cyclically on the calibration sphere, together with the error compensation built into the robot controller, the result is a control loop that largely counteracts the unsteady operating behaviour of the robot. Tests have shown that the robot’s repeatability can be maintained at around 0.04mm, regardless of temperature. This was the first time that industrial robots could be used as measurement system carriers for the continuous recording of quality characteristics on a production line. The industrial suitability of the method has been demonstrated in a practical field test at an automotive manufacturer with 21,000 calibrations over a seven-month period.


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