Gioele Buriani, Jingyue Liu, Maximilian Stölzle, Cosimo Della Santina, Jiatao Ding, Symbolic learning of interpretable reduced-order models for jumping quadruped robots, IFAC Journal of Systems and Control, Volume 35, 2026, 100360, DOI: 10.1016/j.ifacsc.2025.100360.
Abstract: 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. We 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. We focus our 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.
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