  The Linear Parameter Varying Dynamical System (LPV-DS) is an effective
approach that learns stable, time-invariant motion policies using statistical
modeling and semi-definite optimization to encode complex motions for reactive
robot control. Despite its strengths, the LPV-DS learning approach faces
challenges in achieving a high model accuracy without compromising the
computational efficiency. To address this, we introduce the
Directionality-Aware Mixture Model (DAMM), a novel statistical model that
applies the Riemannian metric on the n-sphere $\mathbb{S}^n$ to efficiently
blend non-Euclidean directional data with $\mathbb{R}^m$ Euclidean states.
Additionally, we develop a hybrid Markov chain Monte Carlo technique that
combines Gibbs Sampling with Split/Merge Proposal, allowing for parallel
computation to drastically speed up inference. Our extensive empirical tests
demonstrate that LPV-DS integrated with DAMM achieves higher reproduction
accuracy, better model efficiency, and near real-time/online learning compared
to standard estimation methods on various datasets. Lastly, we demonstrate its
suitability for incrementally learning multi-behavior policies in real-world
robot experiments.
