An efficient method to compute the inverse Jacobian matrix in visual servoing

Jean-Thierry Lapresté 1 Frédéric Jurie 1 Michel Dhome 1 François Chaumette 2
1 LASMEA - Laboratoire des sciences et matériaux pour l'électronique et d'automatique
2 Lagadic - Visual servoing in robotics, computer vision, and augmented reality
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Rennes – Bretagne Atlantique , IRISA-D5 - SIGNAUX ET IMAGES NUMÉRIQUES, ROBOTIQUE
Abstract : The paper presents a method for estimating the inverse Jacobian matrix of a function, without computing the direct Jacobian matrix. The resulting inverse Jacobian matrix is shown to perform much better in modelling a relation $\theta= f^{-1}(x)$ than the classical Moore-Penrose inverse $J^+_f$ . Theoretical insight as well as comparisons in the domain of visual servoing are provided to demonstrate this assertion.
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Jean-Thierry Lapresté, Frédéric Jurie, Michel Dhome, François Chaumette. An efficient method to compute the inverse Jacobian matrix in visual servoing. IEEE Int. Conf. on Robotics and Automation, ICRA'04, 2004, New Orleans, Louisiana, France. pp.727-732. ⟨inria-00352026⟩

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