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Registration of Six Degrees of Freedom Data with Proper Handling of Positional and Rotational Noise



Marek Franaszek


When two six degrees of freedom (6DOF) data are registered (e.g., robot-world/hand-eye calibration), a transformation is sought which minimizes the misalignment between the two datasets. Often, the measure of misalignment is the sum of the positional and rotational components. This measure has a dimensional mismatch between the positional component (unbounded and having length units) and the rotational component (bounded and dimensionless). The mismatch can be formally corrected by dividing the positional component by some scale factor with length units. However, the scale factor is arbitrarily set and depending on its value, more or less importance is associated with the positional component relative to the rotational component and this may result in a poorer registration. In this paper, a new method is introduced which uses the same form of bounded, dimensionless measure of misalignment for both components. Numerical simulations with a wide range of variances of positional and rotational noise show that obtained transformation is very close to ground truth. Additionally, the knowledge of the contribution of noise to the misalignment from individual components enables the formulation of a rational method to handle the noise in 6DOF data.
Journal of Research (NIST JRES) - 118.013
Report Number


Registration, robot-world/hand-eye calibration, pose determining systems, nonlinear least squares, noise


Franaszek, M. (2013), Registration of Six Degrees of Freedom Data with Proper Handling of Positional and Rotational Noise, Journal of Research (NIST JRES), National Institute of Standards and Technology, Gaithersburg, MD, [online], (Accessed June 25, 2024)


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Created June 6, 2013, Updated November 10, 2018