| Summary: | Learning-based control systems have shown impressive empirical performance on challenging problems in all aspects of robot control and, in particular, in walking robots such as bipeds and quadrupeds. Unfortunately, these methods have a major critical drawback: a reduced lack of guarantees for safety and stability. In recent years, new techniques have emerged to obtain these guarantees thanks to data-driven methods that allow learning certificates together with control strategies. These techniques allow the user to verify the safety of a trained controller while providing supervision during training so that safety and stability requirements can directly influence the training process. This survey presents a comprehensive and up-to-date study of the evolving field of stability certification of neural controllers taking into account such certificates as Lyapunov functions and barrier functions. Although specific attention is paid to legged robots, several promising strategies for learning certificates, not yet applied to walking machines, are also reviewed.
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