Representing movement primitives as implicit dynamical systems learned from multiple demonstrations

This work deals with the problem of parameter estimation of dynamical systems intended to model demonstrated motion profiles for a system of interest. The regression problem is formulated as a constrained nonlinear least squares problem. We present an approach that extends the concept of dynamical movement primitives to account for multiple demonstrations of a motion. We maintain an implicit dynamical system that resembles the demonstrated trajectories in a locally optimal way. This is achieved by solving a quadratic program (that encodes our notion of resemblance) at each sampling time step. Our method guarantees predictable state evolution even in regions of the state space not covered by the demonstrations.