On visual servoing based on efficient second order minimization

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Abstract

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.

Section snippets

Mathematical background of the “efficient second order minimization”

In this section, the mathematical background of the ESM given in [12] are recalled.

Validations

In the remainder of this paper, the following notations will be used:

  • A denotes the control law using the current value of the interaction matrix.

  • B and D denote respectively the ESM control laws MJP and PJM proposed in [12] (i.e. control laws given by (18), (19)).

  • C and E denote the modified ESM control laws (23), (24).

These control strategies will be compared in two applications:

  • camera positioning with respect to a set of points using point coordinates or spherical moments as features,

  • visual

Conclusion

In this paper the validity of the “Efficient Second order Minimization” for visual servoing applications has been discussed. Based on this discussion, new revised formulas of ESM-based control laws have been proposed. The revised control laws have also been compared to the control law using the current value of the interaction matrix and the ESM control law based on the mean of the Jacobian pseudo-inverse in two different applications (camera positioning with respect to a set of points, and

Omar Tahri was born in Fez, Morocco, in 1976. He got his Masters in photonics, images and system control from the Louis Pasteur University, Strasbourg, France, in 2000 and received his Ph.D degree in computer science from the University of Rennes, France, in March 2004. His research interests include robotics and computer vision, especially visual servoing.

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    Omar Tahri was born in Fez, Morocco, in 1976. He got his Masters in photonics, images and system control from the Louis Pasteur University, Strasbourg, France, in 2000 and received his Ph.D degree in computer science from the University of Rennes, France, in March 2004. His research interests include robotics and computer vision, especially visual servoing.

    Youcef Mezouar was born in Paris, France, in 1973. He received the Ph.D. degree in computer science from the University of Rennes 1, Rennes, France, in 2001. He was a Postdoctoral Associate in the Robotics Laboratory of the Computer Science Department, Columbia University, New York, NY. Since 2002, he has been with the Robotics and Vision Group, Laboratoire des Sciences et Materiaux pour l’Electronique et d’Automatique (LASMEA)–Centre National de la Recherche Scientifique (CNRS), Aubiere, France. His current research interests include robotics, computer vision, vision-based control, and mobile robots navigation.

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