Stability and Convergence Analysis of 3D Feature-Based Visual Servoing

Visual control based on image features has received much attention for its inherent robustness against camera calibration errors, modelling uncertainties and the capability to keep the object in the Field of View (FoV) of the camera. Nevertheless, some drawbacks related to the basin of convergence and the existence of local minima, which make the camera to get stuck in undesired equilibrium points, are still worth being investigated. Nowadays, the availability of cheap and lightweight RGB-D cameras makes the use of three-dimensional features natural. By using an RGB-D camera in an eye-in-hand configuration, this letter proposes an in-depth stability and convergence analysis of 3D feature-based visual servoing. It will be proved that the visual control system is almost globally asymptotically stable in the sense that the only trajectories not converging to the desired equilibrium point are those belonging to a zero Lebesgue measure set in the feature space. Moreover, a sufficient condition guaranteeing that the feature trajectories remain in the camera FoV is derived and an algorithm to prevent feature loss caused by violation of the camera FoV constraint is proposed.