Human-like motion generation for robots often draws inspiration from biomechanical studies, which often categorize complex human motions into hierarchical taxonomies. While these taxonomies provide rich structural information about how movements relate to one another, this information is frequently overlooked in motion generation models, leading to a disconnect between the generated motions and their underlying hierarchical structure. This paper introduces the \ac{gphdm}, a novel approach that learns latent representations preserving both the hierarchical structure of motions and their temporal dynamics to ensure physical consistency. Our model achieves this by extending the dynamics prior of the Gaussian Process Dynamical Model (GPDM) to the hyperbolic manifold and integrating it with taxonomy-aware inductive biases. Building on this geometry- and taxonomy-aware frameworks, we propose three novel mechanisms for generating motions that are both taxonomically-structured and physically-consistent: two probabilistic recursive approaches and a method based on pullback-metric geodesics. Experiments on generating realistic motion sequences on the hand grasping taxonomy show that the proposed GPHDM faithfully encodes the underlying taxonomy and temporal dynamics, and it generates novel physically-consistent trajectories.

翻译：机器人拟人运动生成常借鉴生物力学研究，后者通常将复杂人体运动归类为层次化分类体系。尽管这些分类体系提供了关于运动间关联的丰富结构信息，但运动生成模型往往忽视这些信息，导致生成的运动与其底层层次结构脱节。本文提出高斯过程双曲动态模型（GPHDM），该方法通过学习同时保持运动层次结构及其时间动态性的潜在表示，以确保物理一致性。我们通过将高斯过程动态模型（GPDM）的动态先验扩展至双曲流形，并将其与分类感知归纳偏置相结合来实现这一目标。基于此几何与分类感知框架，我们提出三种生成兼具分类结构性与物理一致性的运动新机制：两种概率递归方法及基于拉回度量测地线的方法。在手部抓取分类体系上生成逼真运动序列的实验表明，所提出的GPHDM能准确编码底层分类体系与时间动态性，并生成新颖的物理一致轨迹。