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. Moreover, we embed it in a reinforcement learning pipeline and incorporate 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.

We use different LED lights to indicate transitions between dynamic modes in the automata. Similar to segmentation techniques in computer vision, the learned hybrid modes can help us analyze motion patterns more systematically, improve interpretability in decision-making, and refine control strategies for enhanced adaptability.

We appreciate the valuable discussions, hardware guidance and constructive feedback from Yulun Zhuang and Yi Cheng. We also extend our gratitude to Linqi Ye for the initial brainstorming and insightful suggestions, which were inspired by the invaluable time I spent at SHU.