# Ram Vasudevan, October 2012

- 10:30 - Richard Murray, 109 Steele Lab
- 11:00 - Seminar, 114 Steele Lab
- 12:00 - Lunch with Richard, John Doyle + other faculty
- 1:30 - John Doyle, xxx ANB
- 2:00 - Mathieu Desbrun, xxx ANB
- 2:30 - Joel Burdick, 308 Thomas
- 3:15 - Necmiye, 130 Steele
- 4:00 - Open
- 4:45 - Scott Livingston
- 5:30 - Depart

Identification of Hybrid Dynamical Models of Human Motion via Switched System Optimal Control

Ram Vasudevan UC Berkeley

Abstract: Given the loss of freedom and the slow recovery time common to injuries arising due to falls amongst the elderly, the development of techniques capable of pinpointing instabilities in gait is critical. Devising an algorithm capable of detecting such deficiencies in gait requires employing models rich enough to encapsulate the discontinuities in human motion that naturally arise due to interaction with the environment. Hybrid systems, which describe the evolution of their state both continuously via a controlled differential equation and discretely according to a control graph or a discrete input, are a class of models capable of representing such motion. Many concepts from classical dynamical systems, such as stability, have natural analogs in hybrid systems, but the application of such notions demands first performing identification.

This talk begins by illustrating how a sequence of contact point enforcements along with a Lagrangian intrinsic to the human completely determines a hybrid system description for periodic human motion. The detection of contact point enforcement is then transformed into an optimal control problem for constrained switched systems. To resolve this problem, two numerically tractable algorithms are constructed. The first approach employs a variation that alters the discrete switching input by adding a single mode at each iteration of the algorithm. The second approach relaxes the discrete switching input and performs optimization over a relaxed discrete switching input space. The utility of both approaches is illustrated by considering several examples.

Bio: Ram Vasudevan received his Ph.D. Candidate in Electrical Engineering and Computer Sciences at the University of California Berkeley in 2012. His research interests include hybrid systems, biologically inspired robotics, and computer vision. He is a Regent's and Chancellor's Scholar and a co-recipient of the Innovations in Networking Award presented by the Corporation for Education Network Initiatives in California. He received his B.S in Electrical Engineering and Computer Sciences and M.S. both from the University of California Berkeley in 2006 and 2009, respectively.