Discrete-time robot visual feedback systems with nonlinear depth adaptation: stability analysis and experiments

In this paper, a nonlinear adaptive visual feedback scheme is designed to perform 3D positioning tasks, consisting in the regulation of the relative pose between a robotic camera and a rigid object of interest. The dynamical system of robotic camera-object interaction is expressed in terms of image features, i.e. 2D points tracking in the image plane. Since the visual sampling period is not negligible at the current state of technology, a discrete-time representation of the camera-object interaction model is first derived. By exploiting nonlinear controllability properties, a Lyapunov-based discrete-time control law is designed to ensure asymptotic stability in the image reference set-point. Moreover, a 3D adaptation procedure, in a case of unknown object depth, ensures ultimate boundedness of the whole state vector.