Séminaire (organisé par l’équipe de recherche ASER)

Anton Shiriaev

Professeur à l’Umea University, Suède

Motion Planning and Orbital Stabilization of Cycles for Underactuated Mechanical Systems

Mercredi 15 avril à 15h en RD134

Résumé :

Most people will agree that performing a pirouette is intrinsically challenging : for humans it takes both natural talent and years of training. Looking at it from the perspective of a control systems scientist does not necessarily make it any easier, but does allow us to be more specific about what the problem is. For one, the motion is periodic, and it is well known that stabilization of periodic motions provides many challenges over and above those found when stabilizing an equilibrium point. A second difficulty is that, standing on tip-toes, the dancer cannot directly maintain their upright position, that is, the system is underactuated : there are less independent control inputs than dynamical degrees of freedom.

This talk is about motion planning and orbital stabilization of periodic motions of underactuated mechanical systems. In particular, we will discuss a feedback control design based on construction of a transverse linearization. Roughly speaking, the transverse linearization is a periodic linear system of dimension one less than the nonlinear system such that stabilization of this system is in certain sense equivalent to exponential orbital stabilization of a desired periodic motion of the original nonlinear system. We consider a large class of mechanical systems that includes many popular research benchmark set-ups (the Furuta pendulum, the Acrobot, a pendulum on a cart, a spherical pendulum) and applications (bipeds, ocean-going vessels). Remarkably, for this class of nonlinear controlled systems the transverse linearization of any feasible orbit, which in general is related to defining moving Poincaré sections, can be introduced analytically. This fact opens a broad range of opportunities.


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FR SHIC 3272

Collegium UTC/CNRS