Learning Robust and Correct Controllers Guided by Feasibility-Aware Signal Temporal Logic via BarrierNet

Abstract

Control Barrier Functions (CBFs) have emerged as a powerful tool for enforcing safety in optimization-based controllers, and their integration with Signal Temporal Logic (STL) has enabled the specification-driven synthesis of complex robotic behaviors. However, existing CBF-STL approaches typically rely on fixed hyperparameters and myopic, per-time step optimization, which can lead to overly conservative behavior, infeasibility near tight input limits, and difficulty satisfying long-horizon STL tasks. To address these limitations, we propose a feasibility-aware learning framework that embeds trainable, time-varying High Order Control Barrier Functions (HOCBFs) into a differentiable Quadratic Program (dQP). Our approach provides a systematic procedure for constructing time-varying HOCBF constraints for a broad fragment of STL and introduces a unified robustness measure that jointly captures STL satisfaction, QP feasibility, and control-bound compliance. Three neural networks-InitNet, RefNet, and an extended BarrierNet-collaborate to generate reference inputs and adapt constraint-related hyperparameters automatically over time and across initial conditions, reducing conservativeness while maximizing robustness. The resulting controller achieves STL satisfaction with strictly feasible dQPs and requires no manual tuning. Simulation results demonstrate that the proposed framework maintains high STL robustness under tight input bounds and significantly outperforms fixed-parameter and non-adaptive baselines in complex environments.