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Paper details
Number 3 - September 2025
Volume 35 - 2025
Mathematical aspects of calibration by diffeomorphisms
Roberto Orozco, Joanna Ratajczak
Abstract
In this paper, we present a novel approach to calibrating robotic manipulators—calibration by diffeomorphisms. The
method is carried out in detail, placing special emphasis on the mathematical basis of the algorithm. The main idea is
based on the synergy of the theory of singular mappings and the large dense diffeomorphic metric mapping framework, a
method previously unused in robotic applications, together with reproducing kernel Hilbert spaces. The proposed solution
allows the determination of appropriate diffeomorphisms, which, as it were, adjust the arbitrarily chosen kinematics to
match a real one, thus taking into account inaccuracies arising from inaccurately determined parameters or a previously
unmodelled phenomenon, for example, due to high complexity or nonlinearities. The effectiveness of the calibration by
diffeomorphisms is illustrated using a numerical experiment for a manipulator with two degrees of freedom.
Keywords
kinematics, robot kinematics calibration, diffeomorphisms, calibration by diffeomorphisms