Retraction Maps, Feedback Linearization and Nonholonomic Integrators
This talk will introduce the utility of retraction maps on Riemannian manifolds to two applications in applied mechanics and control.
Overview
In this talk I shall introduce the utility of retraction maps on Riemannian manifolds to two applications in applied mechanics and control. The first is feedback linearization (FL.) I shall address "discrete" FL, and the fact that a continuous-time controlled dynamical system (CDS) being feedback linearizable does not assure the same property for its discrete counterpart. It is here that I shall use the tool of retraction maps, after a preliminary introduction to the topic. The second half of my talk will present another application of retractions - intrinsic nonholonomic integrators. CDSs with nonholonomic constraints are found in many applications, in particular robotics, and the well-known rolling coin problem. Constructing faithful integrators for such systems that evolve on non-flat spaces is a challenge, and once again retractions provide a tool to proceed on our journey and obtain useful results.
Presenters
Ravi Banavar, Professor, Systems and Control Engineering, IIT Bombay
Brief Biography
Ravi N. Banavar is currently a Professor in Systems and Control Engineering at IIT Bombay. He received his B.Tech. in Mechanical Engineering from IIT Madras (1986), his Masters (Mechanical, 1988) and Ph.D. (Aerospace, 1992) degrees from Clemson University and the University of Texas at Austin, respectively. He had a brief teaching stint at UCLA during 1991–92, soon after which he joined the Systems and Control Engineering group at IIT Bombay in early 1993. From 2009 onwards, during his tenure as the Convener of the group, the faculty strength grew from 5 to 9 members, with a broad spectrum of academic strengths in nonlinear control, switched systems, optimization, geometric mechanics, formation and cooperative control, robotics and adaptive control. He has spent a few sabbatical breaks at UCLA, Los Angeles, IISc, Bangalore, IIT Gandhinagar, and LSS, Supelec, France. He was an Associate Editor of the Elsevier journal, Systems and Control Letters from 2013 to 2025, is currently on the Editorial Advisory Board of the Taylor and Francis publication, The International Journal of Control, and a Technical Associate Editor of the IEEE Control Systems Society magazine. His current research interests lie in: Optimal control on Lie Groups, geometric mechanics, nonlinear systems, discretization of dynamical systems on manifolds, consensus and coordination problems on Lie groups with applications to mechanical and aerospace systems, geometric observer design on Lie groups with applications in robotics and inertial navigation.
Related People
Hosts
Shinkyu Park
- Assistant Professor, Electrical and Computer Engineering