  Robotic tasks often require motions with complex geometric structures. We
present an approach to learn such motions from a limited number of human
demonstrations by exploiting the regularity properties of human motions e.g.
stability, smoothness, and boundedness. The complex motions are encoded as
rollouts of a stable dynamical system, which, under a change of coordinates
defined by a diffeomorphism, is equivalent to a simple, hand-specified
dynamical system. As an immediate result of using diffeomorphisms, the
stability property of the hand-specified dynamical system directly carry over
to the learned dynamical system. Inspired by recent works in density
estimation, we propose to represent the diffeomorphism as a composition of
simple parameterized diffeomorphisms. Additional structure is imposed to
provide guarantees on the smoothness of the generated motions. The efficacy of
this approach is demonstrated through validation on an established benchmark as
well demonstrations collected on a real-world robotic system.
