A smooth compositional framework for learned control barrier functions with provable safety guarantees

This paper develops a rigorous compositional framework for provably safe controllers in unknown environments. We address two key challenges: the lack of out-of-distribution safety guarantees for learned function approximators, and a previously unidentified failure mode in smooth composition. We first introduce a safe-by-design paradigm for learning local Control Barrier Functions, where a structured neural network with a quadratic penalty term provides provable conservative estimates in unexplored regions. Having established local safety, we then formally identify, analyse, and compensate for a weight interference term that emerges from the smooth fusion of local functions. We derive an analytical bound on this term and construct a robust, state-dependent safety margin that provably guarantees forward invariance of the safe set. The framework is validated in simulation, achieving zero collision rates in the evaluated scenarios and generating significantly smoother, more efficient control actions than non-smooth baselines.