Quasi‐Min‐Max Model Predictive Control for Image‐Based Visual Servoing with Tensor Product Model Transformation

Abstract

AbstractThis paper presents a novel image‐based visual servoing (IBVS) controller based on quasi‐min‐max model predictive control (MPC). By transforming the image Jacobian matrix (i.e. interaction matrix) into a convex combination of linear time‐invariant vertices form with the tensor‐product (TP) model transformation method, the visual servoing system is represented as a polytopic linear parameter‐varying (LPV) system. A robust controller is designed for the robotic visual servoing system subject to input and output constraints such as robot physical limitations and visibility constraints. The control signal is calculated online by carrying out the convex optimization involving linear matrix inequalities (LMIs) in model predictive control. The proposed visual servoing method avoids the inverse of the image Jacobian matrix and hence can solve the intractable problems for the classical IBVS controller, such as large displacements between the initial and the desired position of the camera. The ability of handling constraints can keep the image features in the boundary of the desired field of view (FOV). To verify the effectiveness of the proposed algorithm, the simulation results on a 6 degrees‐of‐freedom (DOF) robot manipulator with eye‐in‐hand configuration are presented and discussed.