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

2026-04-20

AI Summary

This work addresses the challenge of modeling high-dimensional hybrid dynamical systems, such as legged robots, by proposing a data-driven low-dimensional modeling framework. The approach employs an autoencoder to learn latent representations of periodic hybrid trajectories and constructs a Poincaré map in the latent space to capture gait dynamics. Leveraging Lyapunov analysis, the method estimates the region of attraction in this reduced space and maps the stability guarantees back to the full-order state space via the decoder. This is the first approach to seamlessly integrate latent-space modeling, Poincaré maps, and region-of-attraction analysis, ensuring that the low-dimensional model not only accurately represents system dynamics but also preserves and recovers the original system’s stability and safety properties. Validation on hopping and full-body humanoid robot simulations successfully reproduces the stable structures and attraction boundaries of the full-order models.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Deep Generative Models & Autoencoders
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Responsible Web: Machine-in-the-loop, human agency and autonomy

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.

Problem

• reduced-order models
• hybrid systems
• legged robots
• stability
• latent dynamics

Innovation

• latent dynamics
• Poincaré map
• region of attraction
• hybrid systems
• autoencoder