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HALO learns reduced-order models of periodic hybrid dynamics by combining autoencoders with learned latent Poincar茅 maps. This allows for Lyapunov analysis and region-of-attraction estimation in the latent space, which can then be lifted back to the full-order state space. Experiments on simulated robots show that HALO's low-dimensional models retain stability information and predict full-order region-of-attraction boundaries.
Guaranteeing stability for complex robot locomotion just got easier: HALO learns low-dimensional models that accurately predict stability regions in the full state space.
Reduced-order models are powerful for analyzing and controlling high-dimensional dynamical systems. Yet constructing these models for complex hybrid systems such as legged robots remains challenging. Classical approaches rely on hand-designed template models (e.g., LIP, SLIP), which, though insightful, only approximate the underlying dynamics. In contrast, data-driven methods can extract more accurate low-dimensional representations, but it remains unclear when stability and safety properties observed in the latent space meaningfully transfer back to the full-order system. To bridge this gap, we introduce HALO (Hybrid Auto-encoded Locomotion), a framework for learning latent reduced-order models of periodic hybrid dynamics directly from trajectory data. HALO employs an autoencoder to identify a low-dimensional latent state together with a learned latent Poincar\'e map that captures step-to-step locomotion dynamics. This enables Lyapunov analysis and the construction of an associated region of attraction in the latent space, both of which can be lifted back to the full-order state space through the decoder. Experiments on a simulated hopping robot and full-body humanoid locomotion demonstrate that HALO yields low-dimensional models that retain meaningful stability structure and predict full-order region-of-attraction boundaries.
