Theoretical Basics - Kinematic Calibration of Industrial Robots

Although the offline-programming technology has very much advanced, approximately 95% of all industrial robots are still programmed with the teach-in procedure. This is above all due to the imperfect positioning accuracy of industrial robots nowadays. For this reason, the target should be the improvement in this accuracy.

Despite the high repeated accuracy of industrial robots nowadays these robots present inconstant operational characteristics caused by temperature influences. For the use of industrial robots as measuring robots for quality assurance, it is necessary to keep the relative repeated accuracy at a constant level - regardless of any temperature influences.

Model

On the basis of the mechanical configuration of an industrial robot, a model which may be parameterized is set up; the unknown parameters of this model have to be determined in the course of a special identification process. The model considers geometric deviations of the robot e.g. length deviation, errors in the robot zero position and displacement of axes. The non-geometric effects are shaped sufficiently exact by a linear joint elasticity. For the calculation of the static torques, which are necessary to identify the coefficient of the linear elasticity, a faster algorithm was conceived.

Inverse

The complete robot model represents the basis for the compensation of Cartesian errors. As there is no fully closed form of the parameterized and inverse kinematics, a first-order approximation is inferred. A given target position is overlapped with the expected Cartesian error in such a manner that the tip of the tool of the real robot takes up the desired target position. The fast approximation of the inverse kinematics was fully integrated into the real robot control and allows a compensation of the errors that occur on all intermediate and end points of the robot trajectory in real time.

Measuring

A precondition for identifying the parameters of the model is the measurement of the robot TCP.
Several measuring procedures and sensor systems used for the measurement of robots are presented. Sensors with a large visibility area are applied in order to measure the targets fixed to the robot arm. They provide 6D measured values of the TCP. Small, inexpensive sensors are fixed to the robot arm in order to measure the targets inside the work space of the robot. But these sensors only provide 3D measured values. The distance between the robot TCP and the measuring system, measured by the length of a winded thread, only provides 1D measured values. Depending on the measured dimensions, suitable procedures for the calibration of robots will be conceived.

6D-Calibration

The root of the 6D calibration is the formation of a target functional that is minimized in order to identify the parameter of the model. It quantifies the non-conformities that result from the theoretical and the real measured robot’s poses. In order to not only consider positional errors but also non-conformities as to orientation, a residue operator is introduced. It is demonstrated that it is sufficient to examine the figures of the Euclidean basis vectors below this illustration in order to get a suitable measure of the pose errors.

The 6D measured values are generated by measuring targets on a measured body.
This procedure is not only a criteria for the quality of the measurements but also allows to determine the position of the member for the purpose of highest approximation.
Satisfying initial values for the unknown parameters of the model are very important for the convergence of the numeric procedures for solutions.

A general procedure is presented that allows an estimate of the most important unknown parameters with a minimum of measurements. With the help of field tests, the suitability of these estimates and the error compensation is demonstrated. Measured values are presented which show that, regardless to the payload, the aimed positioning accuracy inside the whole work space of the robot lies clearly below one millimetre.

3D-Calibration

Concerning the 3D calibration, the robot is fitted with a sensor for the point wise measurement of targets on a measured body in accordance with the “eye to hand” principle. In this case, the metric information of the targets is an important part as to the creation of the target functional.
Though, already during the general operation, the TCP of a robot presents a temperature drift of several tenths of a millimetre. For the survey and the compensation of temperature drifts the procedure of drift calibration was conceived.

At the time of the robot’s initial operation, a reference measurement is performed on the calibration ball that is temperature invariant. If this measurement is repeated at a later date, the deformations of the robot caused by temperature drifts can be proven in the form of a drift as to the measured values.

The model parameters are now determined in such a way that the measured drift corresponds with the modelled drift as best as possible. If the drift compensation on the calibration ball is carried out cyclically, a closed loop control is formed together with the error compensation inside the robot control. This closed control loop largely works against the unsteady operation of the robot. Several test proved that the repeated accuracy of the robot can so be held, regardless of the temperature, at approximately 0.04 mm. For the first time ever, due to this procedure, industrial robots could be used as supports for measuring systems for the permanent survey of quality characteristics in one production line. The suitability for industry was proven in a field test by carrying out 21.000 calibrations with a car manufacturer over a period of seven months.