## 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

*Speaker:*

Anton Shiriaev

Dept. of Applied Physics and Electronics, Umea University, SWEDEN

& Dept. of Engineering Cybernetics, NTNU Trondheim, NORWAY

http://www.control.tfe.umu.se/Anton/Anton.htm

*Title*:

*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.

*Contact:*

Alessandro De Luca

deluca@dis.uniroma1.it<mailto:deluca@dis.uniroma1.it>

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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

email: deluca@dis.uniroma1.it<mailto:deluca@dis.uniroma1.it>

url: http://www.dis.uniroma1.it/labrob/people/deluca/deluca.html