Generalizing Safety Beyond Collision-Avoidance via Latent-Space Reachability Analysis

#1 Readers familiar with the continuous-time HJ reachability formulation [48] will note that a common assumption is Lipschitz-continuous dynamics:This ensures the existence and uniqueness of the state trajectory when the dynamics are an ordinary differential equation [44].In discrete-time, assuming Lipschitz-continuous dynamics ensures convergence of traditional numerical methods for the nondiscounted optimal control problem [17].In this work, we only assume the dynamics are bounded, C R, ||f (s, a)|| C, as explained in Section III