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

TL;DR

This paper introduces a novel directionality-aware mixture model and a parallel sampling method to improve the efficiency and accuracy of learning linear parameter varying dynamical systems for robot control.

Contribution

It presents the DAMM statistical model and a hybrid MCMC sampling technique, enabling faster and more accurate LPV-DS learning with real-time capabilities.

Findings

Higher reproduction accuracy in motion modeling.

Improved computational efficiency and near real-time learning.

Successful application to real-world robot experiments.

Abstract

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.