Robustness analysis of uncalibrated eye‐in‐hand visual servo system in the presence of parametric uncertainty

Abstract

Purpose The purpose of this paper is to present the methodology to the robust stability analysis of a vision‐based control loop in an uncalibrated environment. The type of uncertainties considered is the parametric uncertainties. The approach adopted in this paper utilizes quadratic Lyapunov function to determine the composite Jacobian matrix and ensures the robust stability using linear matrix inequality (LMI) optimization. The effectiveness of the proposed approach can be witnessed by applying it to two‐link robotic manipulator with the camera mounted on the end‐effector. Design/methodology/approach The objective of this research is the analysis of uncertain nonlinear system by representing it in differential‐algebraic form. By invoking the suitable system representation and Lyapunov analysis, the stability conditions are described in terms of linear matrix inequalities. Findings The proposed method is proved robust in the presence of parametric uncertainties. Originality/value Through a differential‐algebraic equation, LMI conditions are devised that ensure the stability of the uncertain system while providing an estimate of the domain of attraction based upon quadratic Lyapunov function.