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PRODID:-//University of Illinois//Web Services Calendar//EN
VERSION:2.0
CALSCALE:GREGORIAN
BEGIN:VEVENT
DTSTAMP:20120214T115939Z
DTSTART;TZID=America/Chicago:20071026T150000
DTEND;TZID=America/Chicago:20071026T150000
SUMMARY:CAESAR Seminar and Decision\, Control\, and Optimization Seminar:
  A. Shiriaev: "Can We Make a Robot Ballerina Perform a Pirouette?: Orbit
 al Stabilization of Periodic Motions of Underactuated Mechanical Systems
 "
CREATED:20071012T100000Z
DESCRIPTION:ABSTRACT:Most people will agree that performing a pirouette i
 s intrinsically challenging: for humans it takes both natural talent and
  years of training. Looking at it from the perspective of a control syst
 ems scientist does not necessarily make it any easier\, but does allow u
 s 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 tiptoes\, t
 he dancer cannot directly maintain their upright position\; that is\, th
 e system is underactuated: there are less independent control inputs tha
 n dynamical degrees of freedom.This talk is about orbital stabilization 
 of periodic motions of underactuated mechanical systems. In particular\,
  we will discuss a feedback control design based on construction of a "t
 ransverse linearization." Roughly speaking\, the transverse linearizatio
 n is a periodic linear system of dimension one less than the nonlinear s
 ystem such that stabilization of this system is in a certain sense equiv
 alent to exponential orbital stabilization of a desired periodic motion 
 of the original nonlinear system. We consider a large class of mechanica
 l systems that includes many popular research benchmark set-ups (the Fur
 uta 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 Poi
 ncar???????? sections\, can be introduced analytically. This fact opens 
 a broad range of opportunities.The approach can be considered as an alte
 rnative to the standard Poincar?? first-return map\, the most frequently
  used tool for analysis of existence and stability of periodic trajector
 ies. Calculation of the Poincar?? map of a nonlinear system typically re
 quires numerical solution of the system dynamics for a large number of i
 nitial conditions\, which is computationally expensive and motivates inv
 estigation of alternative strategies.The most prominent remaining challe
 nges that restrict wider application of this technique are numerical. In
  the end\, one must find a stabilizing controller for a periodic linear 
 system. For example\, the theory behind the LQR approach for periodic sy
 stems is well-established\, but requires finding the stabilizing solutio
 n of a matrix Riccati differential equation with periodic coefficients. 
 In certain cases this is achievable (we will show experimental results o
 n several set-ups including the Furuta pendulum)\; however\, there is a 
 strong need for more reliable numerical methods.
LAST-MODIFIED:20071012T100000Z
LOCATION:141 Coordinated Science Laboratory
CATEGORIES:Seminar
ORGANIZER:japplequ@illinois.edu
URL:http://illinois.edu/calendar/detail/442?key=200001012000010174598
UID:74598@illinois.edu
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