A multicriteria image-based controller based on a mixed polytopic and norm-bounded representation of uncertainties

This paper presents a multicriteria image-based controller to position a 3-DOF camera with respect to a target. The proposed controller allows to stabilize the camera and determine the associated region of stability in spite of unknown value of the target points depth, bounds on admissible visual feature errors which guarantee visibility, and limits on the camera velocity and acceleration. The description of the closed-loop system is based on a mixed polytopic and norm-bounded representation of uncertainties combined with an original sector condition. This formulation allows to consider LMI-based optimization schemes for computing the feedback gain that leads to the maximization of the size of the region of stability associated to the closed-loop system. Simulations of the control method are presented in the case of a camera mounted on a pan-platform supported by a cart-like robot.