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The Linear Parameter Varying Dynamical System (LPV-DS) is an effectiveapproach that learns stable, time-invariant motion policies using statisticalmodeling and semi-definite optimization to encode complex motions for reactiverobot control. Despite its strengths, the LPV-DS learning approach faceschallenges due to the curse of dimensionality, impacting model andcomputational efficiency. To address this, we introduce theDirectionality-Aware Mixture Model (DAMM), a novel statistical model thatapplies the Riemannian metric on the n-sphere $\mathbb{S}^n$ to efficientlyblend non-Euclidean directional data with $\mathbb{R}^m$ Euclidean states.Additionally, we develop a hybrid Markov chain Monte Carlo technique thatcombines Gibbs Sampling with Split/Merge Proposals, allowing for parallelcomputation to drastically speed up inference. Our extensive empirical testsdemonstrate that LPV-DS integrated with DAMM achieves higher reproductionaccuracy, better model efficiency, and near real-time/online learning comparedto standard estimation methods on various datasets. Lastly, we demonstrate itssuitability for incrementally learning multi-behavior policies in real-worldrobot experiments.

Directionality-Aware Mixture Model Parallel Sampling for Efficient Linear Parameter Varying Dynamical System Learning