On the Optimality, Stability, and Feasibility of Control Barrier Functions: An Adaptive Learning-Based Approach
This addresses safety issues for deploying learning-based approaches in real-world applications, representing an incremental improvement by enhancing existing CBF methods.
The paper tackled the limitations of control barrier functions (CBFs) in safety-critical control, such as optimality, stability, and feasibility, by proposing an Adaptive Multi-step Control Barrier Function (AM-CBF) that parameterizes class-K functions with neural networks and uses a multi-step training approach, resulting in outperformance over conventional CBFs in evaluations on first and second-order systems.
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.