Fitting parameters of linear dynamical systems to regularize forcing terms in Dynamical Movement Primitives

Abstract

Due to their flexibility and ease of use, Dynamical Movement Primitives (DMPs) are widely used in robotics applications and research. DMPs combine linear dynamical systems to achieve robustness to perturbations and adaptation to moving targets with non-linear function approximators to fit a wide range of demonstrated trajectories. We propose a novel DMP formulation with a generalized logistic function as a delayed goal system. This formulation inherently has low initial jerk, and generates the bell-shaped velocity profiles that are typical of human movement. As the novel formulation is more expressive, it is able to fit a wide range of human demonstrations well, also without a non-linear forcing term. We exploit this increased expressiveness by automating the fitting of the dynamical system parameters through optimization. Our experimental evaluation demonstrates that this optimization regularizes the forcing term, and improves the interpolation accuracy of parametric DMPs.