Orientation Probabilistic Movement Primitives on Riemannian Manifolds
This work addresses a domain-specific problem for robotics by enabling ProMPs to handle quaternion-based rotational trajectories, which is an incremental improvement over existing methods.
The paper tackles the problem of encoding and retrieving full-pose robot trajectories, including rotations described by quaternions, by proposing a Riemannian formulation of Probabilistic Movement Primitives (ProMPs) that enables learning complex motion patterns, as demonstrated in toy examples and real learning-from-demonstration experiments.
Learning complex robot motions necessarily demands to have models that are able to encode and retrieve full-pose trajectories when tasks are defined in operational spaces. Probabilistic movement primitives (ProMPs) stand out as a principled approach that models trajectory distributions learned from demonstrations. ProMPs allow for trajectory modulation and blending to achieve better generalization to novel situations. However, when ProMPs are employed in operational space, their original formulation does not directly apply to full-pose movements including rotational trajectories described by quaternions. This paper proposes a Riemannian formulation of ProMPs that enables encoding and retrieving of quaternion trajectories. Our method builds on Riemannian manifold theory, and exploits multilinear geodesic regression for estimating the ProMPs parameters. This novel approach makes ProMPs a suitable model for learning complex full-pose robot motion patterns. Riemannian ProMPs are tested on toy examples to illustrate their workflow, and on real learning-from-demonstration experiments.