2D 1/2 Visual Servoing

In this paper, the problem of estimating the partial camera displacement from two images of a static object is studied. The classical approach to linearly estimate the motion parameters is based on the computation of the essential matrix. In this paper, we propose another approach, based on the estimation of an homography matrix related to a chosen plane of an unknown object. Simulations and experiments on a real scene show that this method gives a more robust reconstruction of the motion parameters, especially in the singular cases. The motion parameters are used to design a new vision-based control scheme, called 2D 1/2 visual servoing. Indeed, visual features and data extracted from the partial displacement allow us to design a decoupled control law controlling the six camera d.o.f. The robustness of our visual servoing scheme with respect to camera calibration errors is also analyzed: the necessary and sufficient conditions for local asymptotic stability are easily obtained. Then, thanks to the simple structure of the system, sufficient conditions for global asymptotic stability are established. Finally, experimental results with an eye-in-hand robotic system confirm the improvement in the stability and robustness of the 2D 1/2 visual servoing with respect to classical position-ba- sed and image-based visual servoings.