BRINGING ROBOTICS TAXONOMIES TO CONTINUOUS DOMAINS VIA GPLVM ON HYPERBOLIC MANIFOLDS

Abstract

Robotic taxonomies have appeared 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 the efforts devoted to design their hierarchy and underlying categories, their use in application fields remains scarce. 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. To do so, we formulate a Gaussian process hyperbolic latent variable model and enforce the taxonomy structure through graph-based priors on the latent space and distance-preserving back constraints. We test our model on the whole-body support pose taxonomy to learn hyperbolic embeddings that comply with the original graph structure. We show that our model properly encodes unseen poses from existing or new taxonomy categories, it can be used to generate trajectories between the embeddings, and it outperforms its Euclidean counterparts.

1. INTRODUCTION

Roboticists are often inspired by biological insights to create robotic systems that exhibit human-or animal-like capabilities (Siciliano & Khatib, 2016) . In particular, it is first necessary to understand how humans move and interact with their environment to then generate biologically-inspired motions and behaviors of robotics hands, arms or humanoids. In this endeavor, researchers proposed to structure and categorize human hand postures and body poses into hierarchical classifications known as taxonomies. Their structure depends on the variables considered to categorize human motions and their interactions with the environment, as well as on associated qualitative measures. Different taxonomies have been proposed in the area of human and robot grasping (Cutkosky, 1989; Feix et al., 2016; Abbasi et al., 2016; Stival et al., 2019) . Feix et al. ( 2016) introduced a taxonomy of hand grasps whose structure was mainly defined by the hand pose and the type of contact with the object. Later, Stival et al. ( 2019) claimed that the taxonomy designed in (Feix et al., 2016) heavily depended on subjective qualitative measures, and proposed a quantitative tree-like taxonomy of hand grasps based on muscular and kinematic patterns. A similar data-driven approach was used to design a grasp taxonomy based on sensed contact forces in (Abbasi et al., 2016) . Robotic manipulation also gave rise to various taxonomies. Bullock et al. ( 2013) introduced a hand-centric manipulation taxonomy that classifies manipulation skills according to the type of contact with the objects and the object motion imparted by the hand. A different strategy was developed in (Paulius et al., 2019) , where a manipulation taxonomy was designed based on a categorization of contacts and motion trajectories. Humanoid robotics also made significant efforts to analyze human motions, thus proposing taxonomies as high-level abstractions of human motion configurations. Borràs et al. (2017) analyzed the contacts of the human limbs with the environment and designed a taxonomy of whole-body support poses. In addition to being used for analysis purposes in robotics or biomechanics, some of the aforementioned taxonomies were leveraged for modeling grasp actions (Romero et al., 2010; Lin & Sun, 2015) , for planning contact-aware whole-body pose sequences (Mandery et al., 2016) , and for learning manipulation skills embeddings (Paulius et al., 2020) . However, despite most taxonomies carry 1

