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.

翻译：线性参数变化动力系统（LPV-DS）是一种有效方法，通过统计建模和半定优化学习稳定的时间不变运动策略，以编码复杂运动实现机器人反应式控制。尽管具有优势，但LPV-DS学习方法在保持高模型精度的同时，面临计算效率提升的挑战。为此，我们提出方向感知混合模型（DAMM），这是一种新型统计模型，通过在n-球面$\mathbb{S}^n$上应用黎曼度量，高效融合非欧几里得方向数据与$\mathbb{R}^m$欧几里得状态。此外，我们开发了一种混合马尔可夫链蒙特卡洛技术，结合吉布斯采样与分裂/合并提案，支持并行计算以大幅加速推断。广泛实验表明，与标准估计方法相比，集成DAMM的LPV-DS在多种数据集上实现了更高的复现精度、更好的模型效率以及近乎实时/在线学习。最后，我们在真实机器人实验中证明了其增量学习多行为策略的适用性。