Learning H-Infinity Locomotion Control

Stable locomotion in precipitous environments is an essential task for quadruped robots, requiring the ability to resist various external disturbances. Recent neural policies enhance robustness against disturbances by learning to resist external forces sampled from a fixed distribution in the simulated environment. However, the force generation process doesn't consider the robot's current state, making it difficult to identify the most effective direction and magnitude that can push the robot to the most unstable but recoverable state. Thus, challenging cases in the buffer are insufficient to optimize robustness. In this paper, we propose to model the robust locomotion learning process as an adversarial interaction between the locomotion policy and a learnable disturbance that is conditioned on the robot state to generate appropriate external forces. To make the joint optimization stable, our novel $H_{\infty}$ constraint mandates the bound of the ratio between the cost and the intensity of the external forces. We verify the robustness of our approach in both simulated environments and real-world deployment, on quadrupedal locomotion tasks and a more challenging task where the quadruped performs locomotion merely on hind legs. Training and deployment code will be made public.