Dynamic extension and sliding control in image-based visual servoing

This paper describes an image-based visual control approach to solve the problem of robust relative positioning between a 6-DOF robot camera and a target object. Assuming weak perspective camera model and local linear approximation of visible object´s surface, an image-based representation of a robot camera-object interaction model is derived, based on the matrix of 2D affine transformations. Dynamic extension of the visual model permits to estimate 3D parameters directly as functions of state variables. The image-based visual system is stabilized by sliding mode control, which ensures asymptotic stability, assuming exact model and state measurements. In the presence of bounded uncertainties, under appropriate choice of control gains, the sliding conditions hold, ensuring that the tracking error is also bounded. Simulation results validate the theoretical framework both in terms of system convergence and control robustness