Time-delayed feedback at the edge of stability: Expert stick balancing

Start: 04/02/2018 - 4:15pm
End  : 04/02/2018 - 5:15pm

Applied Math Seminar

John Milton (Keck Science Department)


Stabilizing unstable states is a challenging task for control engineers and, at the same time, it is an exciting problem for computational neuroscientists. The mathematics involve investigating the properties of delay, or functional, differential equations. The benchmark paradigm is the stabilization of the upright position of an inverted pendulum. This talk reviews 14 years of student research at the Claremont Colleges aimed at determining the nature of the control mechanisms for human expert stick balancing. For seated expert stick balancers the time delay is 0.23s, the shortest stick that can be balanced for 240s is 0.32m and there is a sensory dead zone of 1-3 degrees for the estimation of the vertical displacement angle in the sagittal plane. These observations motivate a switching-type, pendulum-cart model for balance control which utilizes an internal model to compensate for the time delay by predicting the sensory consequences of the stick's movements. Numerical simulations using the semi-discretization method suggest that the feedback gains are tuned near the edge of stability. For these choices of the feedback gains the cost function which takes into account the position of the fingertip and the corrective forces is minimized. Surprisingly this model also explains why for the most expert, the stick always falls!

Emmy Noether Rm Millikan 1021 Pomona College

Claremont Graduate University | Claremont McKenna | Harvey Mudd | Pitzer | Pomona | Scripps
Proudly Serving Math Community at the Claremont Colleges Since 2007
Copyright © 2018 Claremont Center for the Mathematical Sciences