Legged robots navigating cluttered environments must be jointly agile for efficient task execution and safe to avoid collisions with obstacles or humans. Existing studies either develop conservative controllers (< 1.0 m/s) to ensure safety, or focus on agility without considering potentially fatal collisions. This paper introduces Agile But Safe (ABS), a learning-based control framework that enables agile and collision-free locomotion for quadrupedal robots. ABS involves an agile policy to execute agile motor skills amidst obstacles and a recovery policy to prevent failures, collaboratively achieving high-speed and collision-free navigation. The policy switch in ABS is governed by a learned control-theoretic reach-avoid value network, which also guides the recovery policy as an objective function, thereby safeguarding the robot in a closed loop. The training process involves the learning of the agile policy, the reach-avoid value network, the recovery policy, and an exteroception representation network, all in simulation. These trained modules can be directly deployed in the real world with onboard sensing and computation, leading to high-speed and collision-free navigation in confined indoor and outdoor spaces with both static and dynamic obstacles.

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