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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
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