An LMI solution to visual-based localization as the dual of visual servoing

This paper proposes a new approach to the localization of a perspective camera with respect to a known target. The problem is stated as the dual - in the automatic control sense - of visual servoing: while visual servoing would move a camera from visual data so as to stabilize its relative pose with respect to a target, the aim of localization is to estimate/forecast this relative situation from the knowledge of visual data and of the camera command input. The proposed methodology entails a discrete-time rational state space model of interactions. This model is embedded in a structured norm-bounded linear recursive inclusion, so that the forecast of the relative situation at the next sampling time is computed by robust filtering techniques. The solution is obtained via an optimization problem under linear matrix inequalities constraints. Despite its difficulty of implementation, the proposed set-membership method seems quite promising, for it can handle parametric uncertainties as well as dynamic and measurement noises, and encloses the relative situations compatible with the visual data.