BEGIN:VCALENDAR
PRODID:-//eluceo/ical//2.0/EN
VERSION:2.0
CALSCALE:GREGORIAN
BEGIN:VEVENT
UID:www.tcs.tifr.res.in/event/1101
DTSTAMP:20230914T125950Z
SUMMARY:Optimal Control Problems with Symmetry Breaking Cost Functions
DESCRIPTION:Speaker: Rohit Gupta (University of Michigan)\n\nAbstract: \nSy
 mmetry reduction is a well studied subject in geometric mechanics\, where 
 symmetries are usually described as an invariance under an action of a Lie
  group. Symmetry breaking is also common in several physical contexts\, fr
 om classical mechanics to particle physics and in certain cases\, it is st
 ill possible to carry out symmetry reduction. The simplest example is the 
 heavy top dynamics (the motion of a rigid body with a fixed point in a gra
 vitational field)\, where due to the presence of gravity\, we get a Lagran
 gian that is SO(2)-invariant but not SO(3)-invariant\, contrary to what ha
 ppens for the free rigid body. Based on the ideas of symmetry reduction st
 udied in geometric mechanics\, symmetry reduction of optimal control probl
 ems (OCPs) for left-invariant control systems on Lie groups has been studi
 ed extensively over the past couple of decades and by exploiting these sym
 metries\, the system can be reduced to a lower-dimensional one or decouple
 d into subsystems. In this talk\, I will discuss symmetry reduction of OCP
 s for left-invariant control affine systems on Lie groups with partially b
 roken symmetries\, more specifically\, cost functions that break some but 
 not all of the symmetries. I will illustrate the theory with the motion pl
 anning problem of a controlled unicycle (a popular model used in robotics)
  in the presence of an obstacle\, where the symmetry breaking appears natu
 rally in the form of a barrier function.\n\nBio: Rohit Gupta received the 
 M.S.E. degree in Mechanical Engineering and the Ph.D. degree in Aerospace 
 Engineering from the University of Michigan in 2012 and 2016\, respectivel
 y. From January 2016 to August 2017\, he was a postdoctoral research assoc
 iate at the Institute for Mathematics and its Applications (IMA) at the Un
 iversity of Minnesota. From August 2017 to August 2018\, he was a postdoct
 oral research associate in the department of Mathematics at Michigan State
  University. From September 2018 to August 2019\, he was a postdoctoral re
 search fellow in the department of mechanical engineering at the Universit
 y of Michigan. From September 2019 to August 2020\, he was a postdoctoral 
 research fellow in the department of electrical engineering and computer s
 cience at the University of Michigan. His research interests include geome
 tric mechanics\, geometric control\, optimal control and optimization.\n
URL:https://www.tcs.tifr.res.in/web/events/1101
DTSTART;TZID=Asia/Kolkata:20201124T140000
DTEND;TZID=Asia/Kolkata:20201124T150000
END:VEVENT
END:VCALENDAR