Seminario di Robotica - Martedì 15 Dicembre 2009, ore 14:00, aula B1

*Seminario di Robotica*

*Date and location:*
Martedì 15 Dicembre 2009, ore 14:00, aula B1

Anton Shiriaev
Dept. of Applied Physics and Electronics, Umea University, SWEDEN
& Dept. of Engineering Cybernetics, NTNU Trondheim, NORWAY

*On Motion Planning, Motion Representation and its Orbital Stabilization
for Mechanical Systems*

*Abstract: *

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<>



Alessandro De Luca

Dipartimento di Informatica e Sistemistica "A. Ruberti"
Universita' di Roma "La Sapienza"
Via Ariosto 25
00185 Roma, Italy
tel: +39 06 77274052
fax: +39 06 77274033