Euclideanizing Flows: Diffeomorphic Reduction for Learning Stable Dynamical Systems

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.