Learning Contracting Vector Fields For Stable Imitation Learning
This work addresses the challenge of stable imitation learning for robotics or motion planning, though it appears incremental as it builds on kernel methods and optimization techniques.
The paper tackles the problem of learning stable dynamical systems from sampled trajectories by proposing a non-parametric framework that constructs smooth vector fields with controlled contraction and curvature properties, demonstrating it on human handwriting imitation tasks with complex motions.
We propose a new non-parametric framework for learning incrementally stable dynamical systems x' = f(x) from a set of sampled trajectories. We construct a rich family of smooth vector fields induced by certain classes of matrix-valued kernels, whose equilibria are placed exactly at a desired set of locations and whose local contraction and curvature properties at various points can be explicitly controlled using convex optimization. With curl-free kernels, our framework may also be viewed as a mechanism to learn potential fields and gradient flows. We develop large-scale techniques using randomized kernel approximations in this context. We demonstrate our approach, called contracting vector fields (CVF), on imitation learning tasks involving complex point-to-point human handwriting motions.