Taxonomy-aware Dynamic Motion Generation on Hyperbolic Manifolds

2025-09-25

AI Summary

Existing robot motion generation models often neglect the hierarchical structure inherent in biomechanical movement classification, resulting in generated motions that are misaligned with human motor hierarchies and physically inconsistent. To address this, we propose the Gaussian Process Hyperbolic Dynamics Model (GPHDM), the first framework to extend Gaussian process dynamics to hyperbolic manifolds. GPHDM explicitly encodes both hierarchical movement structure and temporal dynamics in a latent hyperbolic space. It incorporates three key innovations: (i) a classification-aware inductive bias to enforce semantic hierarchy; (ii) geodesic optimization under the pullback metric to preserve hierarchical relationships; and (iii) a recursive probabilistic mechanism for coherent temporal evolution. Evaluated on hand-grasping tasks, GPHDM generates novel, natural, and biomechanically plausible motion sequences. Quantitatively, it achieves significantly higher hierarchical fidelity and dynamic consistency compared to Euclidean baseline methods.

Technology Category

• Machine Learning: Learning with Manifolds
• Intelligent Robots: Motion and Path Planning
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

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 generates novel physically-consistent trajectories.

Problem

• Overlooks hierarchical motion taxonomies in robot motion generation models
• Disconnects generated motions from their underlying hierarchical structure
• Ensures physical consistency while preserving taxonomic relationships

Innovation

• Extends Gaussian Process Dynamical Model to hyperbolic manifolds
• Integrates taxonomy-aware inductive biases for hierarchical structure
• Proposes probabilistic recursive and geodesic-based motion generation