On visual servoing based on efficient second order minimization

This paper deals with the Efficient Second order Minimization (ESM) and the image-based visual servoing schemes. In other words, it deals with the minimization based on the pseudo-inverse of the mean of the Jacobians or on the mean of Jacobian Pseudo-inverses. Chronologically, it has been noticed in Tahri and Chaumette (2003) [22] that ESM generally improves the system behavior when compared with the system in which only the simple Jacobian Pseudo-inverses are used. Subsequently, a mathematical explanation has been given in Malis (2004) [12]. In this paper, the proofs given by Malis are discussed and it will be shown that there is a limitation to the validity of the ESM. We will also show that the use of ESM does not necessarily ensure a better system behavior, especially in the situations where large rotational motions are involved. Further, a new appropriate formula of the ESM is proposed and validated using several kinds of features.