Towards an LMI approach to multicriteria visual servoing in robotics

This paper attempts to propose a general framework to the multicriteria analyisis and synthesis of visual servoing schemes in robotics. Two of the most prominent control strategies are unified under a common state-space representation, which is highly nonlinear and possibly uncertain. This model is then embedded into a Linear Differential Inclusion with linear fractional uncertainty, so that the problem can be tackled in a robust linear Control context. Many visual servoing requirements can be dealt with, e.g. convergence, avoidance of actuators saturations, image and 3D contraints. Existing work on the analysis and control of rational systems through quadratic Lyanpunov, functions is a seminal basis to the approach. As the symmetry and convexity properties of the consequent ellipsoidal invariant sets is penalizing in this robotics Context, some extensions are presented, which can be of independent interest. When possible, the criteria are dealt with through Linear Matrix Inequalities.