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The positioning error is always very low. Experimental results have validated this control law in the case of positioning tasks.

It is first based on a gradient approach and then on a Levenberg-Marquardt-like approach. Therefore, we have developed a newĬontrol law derived from the particular shape of the cost function. We have shown that the classical control laws fail in this case due to the strong non linearities in the corresponding cost function. The modeling has first been based on the hypothesis of Lambertian scene. , is used as input of the control scheme. More precisely, the luminance of all pixels in the image, that is We proposed to use directly photometric features as input of the control scheme This may lead to complex and time consuming image processing algorithms, and may increase the effect of image noise. That are used to build the visual featuresġ )) involved in the control scheme. One of the main problems in visual servoing is to extract and track robustly the image measurements Visual servoing of a special sphere using a fisheye camera: initial image on the left and desired image on the right. Simulation results have shown a wideĬonvergence domain even in the presence of points depth estimation errors.Ĥ. The three other features used to control the robot orientation are based on a particular rotation matrix. The decoupling property has been obtained by using distances on the sphere, which are invariant to any rotation. The control scheme obtainedįor a set of points is similar. The control scheme developed has been shown to be robust to both robot and camera calibration errors, as well as to point depth estimation error.

The interests of these features have been experimentally validated at the Beckman Institute (seeĨ.3.4 ) using a catadioptric sensor mounted on a mobile robot (see Figģ ). As for a point, it can be represented by its spherical coordinates, which are suitable for catadioptric sensors with a dead angle in their center. The classical geometrical features such as points, segments, straight lines and spheres have been revisited using this model, and for each of them, a new set of minimal and decoupled It also allows considering the same modeling forĬlassical perspective cameras and omnidirectional vision sensors such as fish-eye and catadioptric sensors. The approach we developed is based on the spherical projection model since it provides interesting geometrical properties. This study is directly related to the search of adequate visual features, as described in Sectionģ.1.

Roméo Tatsambon Fomena, François Chaumette. New Results Visual servoing Visual features from a spherical projection model

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