Computing the polar decomposition with applications
SIAM Journal on Scientific and Statistical Computing
The calibration index and taxonomy for robot kinematic calibration methods
International Journal of Robotics Research
Efficient randomized algorithms for robust estimation of circular arcs and aligned ellipses
Computational Geometry: Theory and Applications
Fundamentals of Manipulator Calibration
Fundamentals of Manipulator Calibration
Kinematic-parameter identification for serial-robot calibration based on POE formula
IEEE Transactions on Robotics
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Currently, the results of a robot calibration procedure are expressed generally in terms of the position and orientation error for a set of locations and orientations, which have been obtained from the previously identified kinematic parameters. In this work, a technique is presented to evaluate the calibration uncertainty for a robot arm calibrated using the circle point analysis method. The method developed is based on the probability distribution propagation calculation recommended by the Guide to the Expression of Uncertainty of Measurement and on the Monte Carlo method. This method makes it possible to calculate the uncertainty in the identification of each single robot parameter, and thus, to estimate the robot positioning uncertainty due to the calibration uncertainty, rather than based on a single set locations and orientations that are previously defined for a unique set of identified parameters. Additionally, this technique allows for the establishment of the best possible conditions for the data capture test, which identifies parameters and determines which of them have the least possible calibration uncertainty. This determination is based on the variables involved in the data capture process by propagating their influence up to the final robot accuracy.