Symbolic learning of interpretable reduced-order models for jumping quadruped robots
Gioele Buriani (Student TU Delft)
Jingyue Liu (TU Delft - Learning & Autonomous Control)
Maximilian Stölzle (Massachusetts Institute of Technology, TU Delft - Learning & Autonomous Control)
Cosimo Della Santina (Deutsches Zentrum für Luft- und Raumfahrt (DLR), TU Delft - Learning & Autonomous Control)
J. Ding (Università degli Studi di Trento)
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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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