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Robots often need to follow safety rules, especially in complex environments. Until recently, controllers used fixed-parameter Control Barrier Functions (CBFs), making them overly cautious or unable to find a solution when movement limits were tight. A new approach merges these CBFs with Signal Temporal Logic (STL) in a learning system that adapts in real time. Three neural networksβ€”InitNet, RefNet, and BarrierNetβ€”work together to generate reference commands and automatically adjust constraints, creating time‑varying higher‑order barriers. The result is a differentiable quadratic program (dQP) that stays feasible and ensures the robot follows STL specifications without breaking speed or force limits. Simulations show the controller keeps high STL robustness even with tight input bounds, far outperforming traditional methods. In practice, robots can tackle longer, more complex tasks without manual tuning, making their actions smoother and safer.

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Higher‑Order Control Barrier Functions (HOCBFs) extend traditional CBFs by incorporating higher‑order derivatives of safety constraints, allowing the handling of more complex dynamics such as acceleration or jerk. In this work, HOCBFs are parameterized by time‑varying functions, enabling the modeling of constraints that adapt to dynamic scenarios. The differentiable Quadratic Program (dQP) formulation embeds HOCBFs as linear constraints but with gradients computable with respect to neural network parameters. This makes end‑to‑end training possible via back‑propagation, simultaneously optimizing STL robustness, QP feasibility, and control‑limit compliance. The unified robustness metric combines three components: (i) the STL satisfaction margin, (ii) the QP feasibility margin (how far the problem is from infeasibility), and (iii) input limit violations. The three neural networks have distinct roles: InitNet generates initial HOCBF parameters, RefNet produces a desired control reference, and BarrierNet adjusts constraint parameters in real time. Training occurs on a simulated scenario dataset, with a loss composed of terms penalizing STL violation, QP infeasibility, and excessive control usage. Results show that, compared to fixed‑parameter methods, the new framework reduces conservatism by 35% and improves STL satisfaction by 20% under tight control limits.

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Date Published:
Original Article arxiv.org
Fact-check verified on 24/04/2026 Primary Study / Original Source
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Creative Commons License CC BY-NC-SA 4.0

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