Supervisors: Benoit Clement ( homepage ), Jordan Ninin ( homepage ).
A robot moves in an environment which is, in most case, uncertain and may disturb the robot's mission (sea current, wind, etc). The control law of the robot must take these disturbances into account, and guarantee that the robot is not sensitive to them. Control theory provides criteria to quantify the sensitivity of the robot with respect to external disturbances. Therefore, the synthesis of a control law can be formulated as an optimization problem: find the control law which minimizes the sensitivity of the robot to disturbances, i.e. which minimizes the synthesis criterion. In order to formulate the synthesis criterion, a model of the robot must be available. However, the characteristics of the robot might not be precisely known (weight, size, friction coefficients,...), and as a consequence the model suffers from uncertainty. The control law must be robust to both external disturbances and model uncertainty. The robust synthesis problem is formulated as a worst-case minimization problem. That is, the control law that minimizes the maximum over the uncertainty is searched. We propose to solve this problem with global optimization based on interval analysis. A global optimization approach allows to compute an upper and a lower bound on the minimum of the synthesis criterion, contrary to existing synthesis methods based on local optimization which provide only an upper bound on the minimum. The enclosure of the minimum provided by global optimization enables to know which performance can be expected from the control law.