Euclideanizing Flows: Diffeomorphic Reduction for Learning Stable Dynamical Systems
Proceedings of the 2nd Conference on Learning for Dynamics and Control, PMLR 120:630-639, 2020.
Execution of complex tasks in robotics requires motions that have complex geometric structure. We present an approach which allows robots to learn such motions from a few human demonstrations. The motions are encoded as rollouts of a dynamical system on a Riemannian manifold. Additional structure is imposed which guarantees smooth convergent motions to a goal location. The aforementioned structure involves viewing motions on an observed Riemannian manifold as deformations of straight lines on a latent Euclidean space. The observed and latent spaces are related through a diffeomorphism. Thus, this paper presents an approach for learning flexible diffeomorphisms, resulting in a stable dynamical system. The efficacy of this approach is demonstrated through validation on an established benchmark as well demonstrations collected on a real-world robotic system.