In this paper, we address the problem of the total visual features loss during visual servoing. We present a new method allowing to reconstruct these features even if the image is completely unavailable. The proposed method has been developed for a 6 degree-of-freedom (DOF) calibrated camera and a static landmark of interest which can be characterized by point features. It relies on a predictor/corrector pair coupled with a depth estimation algorithm. Numerous simulation results are provided and show the relevance of the proposed approach.

This chapter outlines a generic method to the analysis of eye-in-hand position-based or image-based visual servos. This analysis is said to be "multicriteria" as both the convergence and the fulfillment of important constraints can be assessed, including the target visibility, the avoidance of actuators' saturations, and the exclusion of 3D areas. The field of nonlinear "rational" systems is first shown to constitute a sound and versatile framework to the problem. The fundamentals of a solution based on Lyapunov theory are overviewed next, together with the noteworthy difficulties raised by robotics. Constructive results are finally presented, on the basis of biquadratic or piecewise-biquadratic Lyapunov functions, leading to feasibility/optimization programs subject to linear matrix inequalities (LMIs). A case study illustrates the approach.

This paper outlines a generic method to the analysis of eye-in-hand position-based or image-based visual servos. Aside from convergence, the fulfillment of additional important criteria can be assessed, e.g. the target visibility, the avoidance of actuators' saturations, and the guarantee of 3D constraints. The field of nonlinear "rational" systems is first shown to constitute a sound and versatile framework to the problem. The fundamentals of a solution based on Lyapunov theory are overviewed next, together with the noteworthy difficulties raised by robotics. Constructive results are finally sketched out, in terms of a feasibility/optimization program subject to matrix inequalities. A case study illustrates the approach.

This paper is about robust filtering/prediction of nonlinear discrete-time systems with rational dependence on the state or uncertainty vectors. The problem is dealt with in a set-membership context, in that the system initial condition, the uncertainties, as well as the noises affecting the dynamics and the measurements are unknown but bounded. A new recursive approach to the prediction of confidence ellipsoids enclosing the state vector at each sampling time is proposed, based on the reformulation of the system model as a Recursive Algebraic Representation. The solution is expressed as a convex optimization problem under Linear Matrix Inequality (LMI) constraints. The method is assessed on some examples.