  Linear Parameter Varying Dynamical Systems (LPV-DS) encode trajectories into
an autonomous first-order DS that enables reactive responses to perturbations,
while ensuring globally asymptotic stability at the target. However, the
current LPV-DS framework is established on Euclidean data only and has not been
applicable to broader robotic applications requiring pose control. In this
paper we present an extension to the current LPV-DS framework, named
Quaternion-DS, which efficiently learns a DS-based motion policy for
orientation. Leveraging techniques from differential geometry and Riemannian
statistics, our approach properly handles the non-Euclidean orientation data in
quaternion space, enabling the integration with positional control, namely
SE(3) LPV-DS, so that the synergistic behaviour within the full SE(3) pose is
preserved. Through simulation and real robot experiments, we validate our
method, demonstrating its ability to efficiently and accurately reproduce the
original SE(3) trajectory while exhibiting strong robustness to perturbations
in task space.
