On visual servoing based on efficient second order minimization

This paper deals with the Efficient Second orderMinimization (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] thatESM generally improves the systembehaviorwhen comparedwith 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. © 2009 Elsevier B.V. All rights reserved. Visual servoing techniques are quite effective since they close the control loop over the vision sensor. This yields a high robustness to disturbances as well as to calibration errors. Visual servoing schemes can be distinguished according to the space where the visual features were defined. In position-based visual servo (PBVS) [1], the features are defined in the 3D space. The control scheme using PBVS ensures a nice decoupling between the degrees of freedom (dofs). For this reason, adequate 3D trajectories can be obtained, such as a geodesic for the orientation and a straight line for the translation. However, position-based visual servoing might be affected by potential instabilities due to image noise [2]. Inversely, in image-based visual servo (IBVS) [3], the visual servo is performed on the image. A compromise can be obtained by combining features in image and partial 3D data [4]. Briefly, we recall that the time variation ṡ of the visual features s can be expressed linearly with respect to the relative camera–object kinematics screw V = (v,ω):