Modeling Kinematic and Dynamic Structures with Hypergraph-Based Formalism

This paper introduces a hypergraph-based formalism for modeling kinematic and dynamic structures in robotics, addressing limitations of the existing formats such as Unified Robot Description Format (URDF), MuJoCo-XML, and Simulation Description Format (SDF). Our method represents mechanical constraints and connections as hyperedges, enabling the native description of multi-joint closures, tendon-driven actuation, and multi-physics coupling. We present a tensor-based representation derived via star-expansion, implemented in the Hypergraph Model Cognition Framework (HyMeKo) language. Comparative experiments show a substantial reduction in model verbosity compared to URDF while retaining expressiveness for large-language model integration. The approach is demonstrated on simple robotic arms and a quarter vehicle model, with derived state-space equations. This work suggests that hypergraph-based models can provide a modular, compact, and semantically rich alternative for the next-generation simulation and design workflows. The introduced formalism reaches 50% reduction compared to URDF descriptions and 20% reduction compared to MuJoCo-XML descriptions.