HALO: Hybrid Auto-encoded Locomotion with Learned Latent Dynamics, Poincaré Maps, and Regions of Attraction

Blake Werner, Sergio Esteban, Massimiliano de Sa, Max H. Cohen, Aaron Ames
Proceedings of The 8th Annual Learning for Dynamics and Control Conference, PMLR 331:440-459, 2026.

Abstract

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 Poincaré 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v331-werner26a, title = {HALO: Hybrid Auto-encoded Locomotion with Learned Latent Dynamics, Poincaré Maps, and Regions of Attraction}, author = {Werner, Blake and Esteban, Sergio and Sa, Massimiliano de and Cohen, Max H. and Ames, Aaron}, booktitle = {Proceedings of The 8th Annual Learning for Dynamics and Control Conference}, pages = {440--459}, year = {2026}, editor = {Sukhatme, Gaurav and Lindemann, Lars and Tu, Stephen and Wierman, Adam and Atanasov, Nikolay}, volume = {331}, series = {Proceedings of Machine Learning Research}, month = {17--19 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v331/main/assets/werner26a/werner26a.pdf}, url = {https://proceedings.mlr.press/v331/werner26a.html}, abstract = {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 Poincaré 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.} }
Endnote
%0 Conference Paper %T HALO: Hybrid Auto-encoded Locomotion with Learned Latent Dynamics, Poincaré Maps, and Regions of Attraction %A Blake Werner %A Sergio Esteban %A Massimiliano de Sa %A Max H. Cohen %A Aaron Ames %B Proceedings of The 8th Annual Learning for Dynamics and Control Conference %C Proceedings of Machine Learning Research %D 2026 %E Gaurav Sukhatme %E Lars Lindemann %E Stephen Tu %E Adam Wierman %E Nikolay Atanasov %F pmlr-v331-werner26a %I PMLR %P 440--459 %U https://proceedings.mlr.press/v331/werner26a.html %V 331 %X 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 Poincaré 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.
APA
Werner, B., Esteban, S., Sa, M.d., Cohen, M.H. & Ames, A.. (2026). HALO: Hybrid Auto-encoded Locomotion with Learned Latent Dynamics, Poincaré Maps, and Regions of Attraction. Proceedings of The 8th Annual Learning for Dynamics and Control Conference, in Proceedings of Machine Learning Research 331:440-459 Available from https://proceedings.mlr.press/v331/werner26a.html.

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