Quasi-min-max model predictive control for image-based visual servoing

This 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 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 system subject to robot physical limitations and visibility constraints. The control signal is calculated on-line by carrying out the convex optimization that solved by semi-definite programming involving Linear Matrix Inequalities (LMIs) in MPC. The proposed IBVS controller avoids the inverse of 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. Thanks to the ability of handling constraints, the image features are always kept in the image plane even when both the initial and the desired features are close to the boundary of 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.