On visual servoing based on efficient second order minimization
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:
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A denotes the control law using the current value of the interaction matrix.
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B and D denote respectively the ESM control laws MJP and PJM proposed in [12] (i.e. control laws given by (18), (19)).
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C and E denote the modified ESM control laws (23), (24).
These control strategies will be compared in two applications:
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camera positioning with respect to a set of points using point coordinates or spherical moments as features,
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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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2020, Computers and Electrical EngineeringCitation Excerpt :In [22], after mathematically explaining a set of minimization techniques and comparing them to each other, it has been concluded based on the experimental results that the ESM control schemes have the best performance, and that the PMJ method results in higher convergence rates and better 3D camera trajectories between the two schemes. Furthermore, in [23], after showing that there is a limitation to the validity of the PMJ method, and that the use of this control scheme does not necessarily ensure a better system behavior especially in the tasks where large rotational motions are involved, a new appropriate formula for the PMJ controller has been proposed and validated. In the rest of this section, a brief explanation about the ESM control schemes and their shortcomings is presented, then, the proposed controller is described, and finally, the stability of this controller is analytically proved.
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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.