|
U of M College of
Engineering Control Seminar Series Sponsored by Eaton, Ford, General Motors, Toyota and Whirlpool |
Learnable Nonlinear Dynamic Systems for Control
Professor Stefan
Schaal
Department of
Computer Science
and the Neuroscience
Program
University of
Southern California
Abstract:
Nonlinear dynamic systems have
been an appealing modeling approach for biological and robotic movement
generation for a long time. As a drawback of the dynamic systems approach to
motor control, however, it has been rather problematic to find general design
principles for nonlinear differential equations, such that desired motor
behaviors can be embedded in them without the need for lengthy manual parameter
tuning, problems due to unknown stability properties, and potentially complex
behaviors of the underlying equations. In this talk, we introduce a novel
modeling framework for nonlinear dynamic systems that incoporates techniques
from statistical learning to shape the attractor landscapes of a certain class
of nonlinear differential equations. The core idea of this approach is to
transform the state variables of a well understood attractor system with the
help of a learnable nonlinear function into a new set of equations which can
have almost arbitrary smooth attractors. Both limit cycle and point attractor
systems can be generated without any need of manual parameter tuning.
Multi-dimensional attractors are possible with complex phase relationships
between the individual degrees-of-freedom, as needed to generate phase-locked and synchronized movement
in multi degree-of-freedom movement systems. Due to the dynamic systems
formulation, useful invariance properties can be enforced in the differential
equations in the sense of structural equivalence. We demonstrate how this approach can be used in generating
movement in various different tasks, including arm movements, imitation
learning of movements, reinforcement learning of movements, and locomotion with
a simple biped robot that learns resonance tuning of its walking pattern.
Videos of humanoid robot implementations illustrate the results of our
research.
3:30 – 4:30 p.m.