GRASP Special Seminar - Ram Vasudevan, University of California, Berkeley, "Towards a Universal Temporal Ordering of Discrete Events for Walking via Optimal Control"
In this talk, I begin by describing how the sequence of contact point enforcements or discrete events along with a Lagrangian that is intrinsic to a biped completely determines the mathematical model for a biped. Given this insight, in the first part of the talk I describe a nine subject straight line walking motion capture experiment and two methods to extract temporal orderings: function fitting and persistent homology. Surprisingly the result of either method is that all participants regardless of age, height, sex, or weight had an identical temporal ordering of such events. In the second part of the talk, I describe how to generalize the detection of constraint enforcement by recasting the problem as an optimal control problem of switched dynamical systems. Given this result, we construct a numerical solution to the optimal control problem for a constrained switched nonlinear dynamical system with a running and final cost which provably converges to a local optimum.