E. Malis. Contributions à la modélisation et à la commande en asservissement visuel. Thèse de l'Université de Rennes 1, Mention traitement du signal et télécommunications, Novembre 1998.
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Our work is concerned with robotics and vision, and more precisely visual servoing. It consists in the design of methods that do not need the model of the observed objects or a precise calibration of the system. First, the problem of the Euclidean reconstruction (up to a scale factor), from two images of a unknown static object, has been studied. It has been highlighted that the best linear solution for a robust reconstruction of the camera displacement is to use an homography matrix. Thus, an algorithm for the linear estimation of this matrix has been proposed. Then, two new visual servoing schemes, based on the partial Euclidean reconstruction, are proposed. The closed-loop system is analyzed in order to obtain the robustness domain of a proportional control law with respect to the system calibration errors. Later, it has been shown that, thanks to the decoupled structure of the considered systems, it is possible to considerably increase the robustness domain with an adaptive control law. The new methods have been tested on a Cartesian robot and on a redundant robot, and then compared to the classic ones. The obtained results confirm the improvement in the stability of our methods. Finally, the visual servoing techniques have been extended to the use of several cameras observing different parts of the scene. The multi-camera visual servoing has been designed as a part of the task function approach. The particular choice of the task function allows us to simplify the design of the control law and the stability analysis. In the end, a positioning task of a cumbersome object has been realized using two cameras mounted on a manipulator robot
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