Rational systems and Matrix Inequalities to the multicriteria analysis of visual servos

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.