Taxonomy-Aware Dynamic Motion Generation on Hyperbolic Manifolds
Luis Augenstein, Noémie Jaquier, Tamim Asfour, Leonel Rozo
AI summary
Problem
Current motion generation models frequently overlook the rich hierarchical structure of biomechanical taxonomies, creating a disconnect between generated movements and their underlying classifications. Furthermore, existing hyperbolic latent models lack temporal dynamics, often producing physically impractical trajectories.
Approach
The authors extend the Gaussian Process Dynamical Model to hyperbolic manifolds, integrating taxonomy-aware inductive biases to learn latent representations that preserve both hierarchical structure and temporal dynamics. They introduce three novel generation mechanisms to ensure physically consistent trajectory synthesis.
Key results
- Extends the GPDM dynamics prior to hyperbolic manifolds for taxonomy-aware learning
- Introduces two probabilistic recursive methods and a pullback-metric geodesics approach for motion generation
- Successfully encodes hierarchical taxonomy structure and temporal dynamics in hand grasping data
- Generates novel, physically consistent motion trajectories that align with biomechanical classifications
Why it matters
Enables robots to synthesize realistic, human-like motions that respect biomechanical hierarchies, reducing training data needs and improving physical feasibility for humanoid robotics.
Abstract
Human-like motion generation for robots often draws inspiration from biomechanical studies, which 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 Gaussian Process Hyper- bolic Dynamical Model (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.