Shape visual servoing of a tether cable from parabolic features

In this paper we propose a visual servoing approach that controls the deformation of a suspended tether cable subject to gravity from visual data provided by a RGB-D camera. The cable shape is modelled with a parabolic curve together with the orientation of the plane containing the tether. The visual features considered are the parabolic coefficients and the yaw angle of that plane. We derive the analytical expression of the interaction matrix that relates the variation of the visual features to the velocities of the cable extremities. Singularities are demonstrated to occur if and only if the cable is taut horizontally or vertically. An image processing algorithm is also developed to extract in real-time the current features fitting the parabola to the cable from the observed point cloud. Simulations and experimental results demonstrate the efficiency of our visual servoing approach to deform the tether cable toward a desired shape configuration.