AIC Seminar Series

Learning to control high-dimensional, non-linear dynamical systems is hard, in part because of the Curse of Dimensionality. The volume of the state space increases exponentially with the number of state variables used to describe the system. Learning a controller over this space often requires an exponential amount of training data, limiting us to relatively low-dimensional systems.

Many robotic systems, however, do not inhabit the entire volume of the state space. In fact, any system with a periodic gait lives on a 1-dimensional manifold embedded in the full state space of the system. In this talk, we introduce Shaped Manifold Control, which simultaneously estimates the manifold over which the system operates and learns an effective controller over this manifold. SMC sidesteps the curse of dimensionality because is learns over a 1-dimensional manifold, regardless of the dimensionality of the full state space. We have successfully applied SMC to a number of simulated high-dimensional continuous dynamical systems, including swimming and walking robots, and will also discuss our plans for using it for the control of a robotic hand prosthesis using direct cortical control.