Control of underactuated manipulators using nonlinear H∞ techniques

In this paper, two nonlinear H_∞ control techniques are used to control a underactuated manipulator. The dynamic coupling between the links is used to control all manipulator\´s free joints. The first technique consists in representing the nonlinear system in a quasi-linear parameter varying form and in solving a set of linear matrix inequalities (LMI) generated from the gridding of the state space range. To the second technique, an explicit solution of the H_∞ control of robot manipulators is found using an appropriate state transformation and the game theory. Experimental results obtained from the underactuated manipulator (UArm II) using the two methodologies are presented.