Robust Decoupling Control of an Image-Based Visual System

Abstract

In this paper, nonlinear control theory is applied to solve the problem of controlling the position of a robot camera with respect to an object. An image-based state space representation of a robot camera-object interaction model is derived, assuming affine shape transformations in the image space and local linear approximation of visible object's surface. The image-based visual system is stabilized by a robust decoupling control law, which ensure asymptotic stability except at image singularities, assuming exact model and state measurements. In the presence of multiplicative uncertainties in the decoupling matrix and additive uncertainties in the object motion and in the state measurements, the closed-loop system behavior is characterised by an attractor. Simulation results validate the theoretical framework both in terms of system convergence and control robustness.