On the stability of visual servoing using a 3D-camera

Besides conventional 2D image information, a special laser-based camera delivers depth information related to each image dot, i.e. a full 3D image. Such camera systems suggest themselves for increasing autonomy of robots and vehicles. If instead of distances/angles between camera and objects some image coordinates of features are used as control output variables the resulting control scheme is referred to as Image-Based Visual Servoing (IBVS). After a short introduction into the principles of IBVS, a general parametric control scheme (based on the image-jacobian-matrix) is given and its stability properties are discussed, both, for a general camera configuration and for the particular case of the 3D-camera. It turns out that in this particular case stability can be proved by investigating the semi-definiteness of the derivative V of some Lyapunov function V which is the main result of this paper.