Robotic taxonomies serve as high-level hierarchical abstractions that classify how humans move and interact with their environment. They have proven useful to analyse grasps, manipulation skills, and whole-body support poses. Despite substantial efforts devoted to design their hierarchy and underlying categories, their use in application fields remains limited. This may be attributed to the lack of computational models that fill the gap between the discrete hierarchical structure of the taxonomy and the high-dimensional heterogeneous data associated to its categories. To overcome this problem, we propose to model taxonomy data via hyperbolic embeddings that capture the associated hierarchical structure. We achieve this by formulating a novel Gaussian process hyperbolic latent variable model that incorporates the taxonomy structure through graph-based priors on the latent space and distance-preserving back constraints. We validate our model on three different robotics taxonomies to learn hyperbolic embeddings that faithfully preserve the original graph structure. We show that our model properly encodes unseen poses from existing or new taxonomy categories, can be used to generate trajectories between the embeddings, and outperforms its Euclidean counterparts.

翻译：机器人学分类体系作为高层级的层次化抽象，用于对人类运动及与环境交互的方式进行归类。这类体系已被证明在分析抓取动作、操作技能和全身支撑姿态方面具有实用价值。尽管人们在设计其层级结构和底层分类方面付出了大量努力，但它们在应用领域的使用仍然有限。这可能归因于缺乏能够弥合分类学离散层次结构与其相关类别高维异质数据之间差距的计算模型。为解决这一问题，我们提出通过双曲嵌入对分类数据进行建模，以捕捉其内在的层次结构。我们通过构建一种新型高斯过程双曲隐变量模型来实现这一目标，该模型通过基于图的隐空间先验和保持距离的逆向约束来整合分类结构。我们在三种不同的机器人学分类体系上验证了该模型，学习了能够忠实保持原始图结构的双曲嵌入。结果表明，我们的模型能够正确编码来自现有或新分类类别的未见数据点，可用于生成嵌入之间的轨迹，且性能优于其欧氏空间对应模型。