On the efficient second order minimization and image-based visual servoing

This paper deals with the efficient second order minimization (ESM) and the image-based visual servoing schemes. In other word, it deals with the minimization based on the pseudo-inverses of the mean of the Jacobians or on the mean of Jacobian Pseudo-inverses. Chronologically, it has been noted by Tahri and Chaumette (2003) that the (ESM) improves generally the system behavior compared to the case where only the simple Jacobian Pseudo- inverses is used. Subsequently, a mathematical explanation has been given by Malis (2004). In this paper, the proofs given by Malis are considered to deal with their validity. It will be shown that there is a limitation to the the validity of this method and some precautions should be taken, for adequate application of it. In other words, we will show that the use of ESM does not necessary ensures a better system behavior, especially in the cases where large rotational motions are considered.