# Discrete-Time Hybrid Automata Learning: Legged Locomotion Meets Skateboarding

arXiv: https://arxiv.org/abs/2503.01842 · HTML: https://mlsanity.com/paper/2503.01842/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Mar 2025.

## Built on by (most cited first, 7 of 7)

- [Ego-Vision World Model for Humanoid Contact Planning](https://mlsanity.com/paper/2510.11682/) (2025)
- [CHyLL: Learning Continuous Neural Representations of Hybrid Systems](https://mlsanity.com/paper/2512.10117/) (2025)
- [Embedding Hybrid Systems into Continuous Latent Vector Fields](https://mlsanity.com/paper/2606.10596/) (2026)
- [Quadrupedal Robot Skateboard Mounting via Reverse Curriculum Learning](https://mlsanity.com/paper/2505.06561/) (2025)
- [SAC-MoE: Reinforcement Learning with Mixture-of-Experts for Control of Hybrid Dynamical Systems with Uncertainty](https://mlsanity.com/paper/2511.12361/) (2025)
- [Learning Continuous Neural Representation of Stochastic Hybrid Systems](https://mlsanity.com/paper/2609.38893/) (2026)
- [Sim-to-Real RL for ASVs using SysID](https://mlsanity.com/paper/2610.12202/) (2026)

## Abstract (arXiv)

Hybrid dynamical systems, which include continuous flow and discrete mode switching, can model robotics tasks like legged robot locomotion. Model-based methods usually depend on predefined gaits, while model-free approaches lack explicit mode-switching knowledge. Current methods identify discrete modes via segmentation before regressing continuous flow, but learning high-dimensional complex rigid body dynamics without trajectory labels or segmentation is a challenging open problem. This paper introduces Discrete-time Hybrid Automata Learning (DHAL), a framework to identify and execute mode-switching without trajectory segmentation or event function learning. Besides, we embedded it in reinforcement learning pipeline and incorporates a beta policy distribution and a multi-critic architecture to model contact-guided motions, exemplified by a challenging quadrupedal robot skateboard task. We validate our method through sufficient real-world tests, demonstrating robust performance and mode identification consistent with human intuition in hybrid dynamical systems.