Seminario di Robotica
Martedì 15 Dicembre 2009, ore 14:00, aula B1
On Motion Planning, Motion Representation and its Orbital Stabilization for Mechanical Systems
Dept. of Applied Physics and Electronics, Umea University, SWEDEN
& Dept. of Engineering Cybernetics, NTNU Trondheim, NORWAY
This talk is about motion planning, motion representation and steps in orbital stabilization of motions of mechanical systems, which might be redundant or have one or several passive degrees of freedom. Given a motion, we suggest to search for its representation without explicit time dependence: an evolution of one of degrees of freedom is defined by certain differential equation (a motion generator); while other degrees of freedom are found through relations valid between coordinates on the motion. Such representation of a motion becomes compact and, as shown, it is often useful in analysis of dynamics in vicinity of its orbit and controller design. In particular, we show steps in a feedback control design that are based on construction of a /transverse linearization/. Roughly speaking, the /transverse linearization/ is a 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.
The proposed approach is illustrated on popular research benchmark set-ups (the Furuta pendulum, the Acrobot, a pendulum on a cart, a spherical pendulum on a puck) and applications (design stable gaits for bipeds, quadrupeds; analysis of recorded motions of humans). Remarkably, for mechanical systems the /transverse linearization/ of any feasible (forced) orbit/, /which in general is related to defining moving Poincaré sections, can be introduced /analytically/. This fact opens a broad range of opportunities.
Alessandro De Luca