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 due to the curse of dimensionality, impacting model and 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 Proposals, 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、时不变的运动策略，为机器人反应式控制编码复杂运动。尽管具有优势，LPV-DS学习方法因维数诅咒面临挑战，影响模型和计算效率。为此，我们提出定向感知混合模型（DAMM），这是一种新颖的统计模型，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/合并提议，支持并行计算以大幅加速推断。广泛的实证测试表明，与标准估计方法相比，集成DAMM的LPV-DS在各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，我们在实际机器人实验中展示了其适用于增量学习多行为策略的能力。