08 January 2026
Legged robots are now pervasive systems, deployed in applications ranging from planetary exploration to search-and-rescue operations. Yet, their dynamics remain remarkably difficult to model especially when seeking a description expressive enough to capture essential behaviours and lightweight enough for real-time use. Reduced-order models are central to motion planning and control of quadruped robots, yet existing templates are often hand-crafted for a specific locomotion modality. This motivates the need for automatic methods that extract task-specific, interpretable low-dimensional dynamics directly from data.
In this study, EMERGE partners from the Delft University of Technology propose a methodology that combines a linear autoencoder with symbolic regression to derive such models. The linear autoencoder provides a consistent latent embedding for configurations, velocities, accelerations, and inputs, enabling the sparse identification of nonlinear dynamics (SINDy) to operate in a compact, physics-aligned space. A multi-phase, hybrid-aware training scheme ensures coherent latent coordinates across contact transitions. They focus the validation on quadruped jumping—a representative, challenging, yet contained scenario in which a principled template model is especially valuable. The resulting symbolic dynamics outperform the state-of-the-art handcrafted actuated spring-loaded inverted pendulum (aSLIP) baseline in simulation and hardware across multiple robots and jumping modalities.
Read the paper in the link below.
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