Abstract: 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 multicritic 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.