Nonlinear controllability and stability analysis of adaptive image-based systems

In this paper, a novel adaptive visual feedback scheme is presented to solve the problem of controlling the relative pose between a robot camera and a rigid object of interest. After deriving the image-based state space representation of the camera-object visual interaction model in terms of global coordinates (2D points) fully defined in the image plane, it is shown that the system is completely controllable. By exploiting nonlinear controllability properties, global uniform asymptotic stability of the image reference set-point is proved using Lyapunov's direct method. Moreover, global uniform boundedness of the whole state vector is ensured by using an adaptive nonlinear control scheme, in case of unknown depth of the object. Experimental results with a 6-DOF robot manipulator endowed with a camera on its wrist validate the framework.