Learning task-space synergies using Riemannian geometry

In the context of robotic control, synergies can form elementary units of behavior. By specifying task-dependent coordination behaviors at a low control level, one can achieve task-specific disturbance rejection. In this work we present an approach to learn the parameters of such low-level controllers by demonstration. We identify a synergy by extracting covariance information from demonstration data. The extracted synergy is used to derive a time-invariant state feedback controller through optimal control. To cope with the non-Euclidean nature of robot poses, we utilize Riemannian geometry, where both estimation of the covariance and the associated controller take into account the geometry of the pose manifold. We demonstrate the efficacy of the approach experimentally in a bimanual manipulation task.