Safety has been a critical issue for the deployment of learning-based approaches in real-world applications. To address this issue, control barrier function (CBF) and its variants have attracted extensive attention for safety-critical control. However, due to the myopic one-step nature of CBF and the lack of principled methods to design the class-$\mathcal{K}$ functions, there are still fundamental limitations of current CBFs: optimality, stability, and feasibility. In this paper, we proposed a novel and unified approach to address these limitations with Adaptive Multi-step Control Barrier Function (AM-CBF), where we parameterize the class-$\mathcal{K}$ function by a neural network and train it together with the reinforcement learning policy. Moreover, to mitigate the myopic nature, we propose a novel \textit{multi-step training and single-step execution} paradigm to make CBF farsighted while the execution remains solving a single-step convex quadratic program. Our method is evaluated on the first and second-order systems in various scenarios, where our approach outperforms the conventional CBF both qualitatively and quantitatively.

翻译：安全问题一直是基于学习的方法在实际应用中部署的关键挑战。为解决这一问题，控制障碍函数（CBF）及其变体在安全关键控制领域受到了广泛关注。然而，由于CBF的短视单步特性以及缺乏设计$\mathcal{K}$类函数的原则性方法，当前CBF仍存在最优性、稳定性与可行性方面的根本性局限。本文提出了一种新颖统一的框架——自适应多步控制障碍函数（AM-CBF），通过将$\mathcal{K}$类函数参数化为神经网络，并将其与强化学习策略联合训练，从而克服上述局限。此外，为缓解CBF的短视性，我们提出了一种创新的\textit{多步训练与单步执行}范式：在保持单步凸二次规划求解效率的同时，赋予CBF前瞻性。我们在多种场景下针对一阶和二阶系统进行了评估，结果表明本方法在定性与定量层面均优于传统CBF。