  Energy-function-based safety certificates can provide provable safety
guarantees for the safe control tasks of complex robotic systems. However, all
recent studies about learning-based energy function synthesis only consider the
feasibility, which might cause over-conservativeness and result in less
efficient controllers. In this work, we proposed the magnitude regularization
technique to improve the efficiency of safe controllers by reducing the
conservativeness inside the energy function while keeping the promising
provable safety guarantees. Specifically, we quantify the conservativeness by
the magnitude of the energy function, and we reduce the conservativeness by
adding a magnitude regularization term to the synthesis loss. We propose the
SafeMR algorithm that uses reinforcement learning (RL) for the synthesis to
unify the learning processes of safe controllers and energy functions.
Experimental results show that the proposed method does reduce the
conservativeness of the energy functions and outperforms the baselines in terms
of the controller efficiency while guaranteeing safety.
