Control Barrier functions (CBFs) have attracted extensive attention for designing safe controllers for their deployment in real-world safety-critical systems. However, the perception of the surrounding environment is often subject to stochasticity and further distributional shift from the nominal one. In this paper, we present distributional robust CBF (DR-CBF) to achieve resilience under distributional shift while keeping the advantages of CBF, such as computational efficacy and forward invariance. To achieve this goal, we first propose a single-level convex reformulation to estimate the conditional value at risk (CVaR) of the safety constraints under distributional shift measured by a Wasserstein metric, which is by nature tri-level programming. Moreover, to construct a control barrier condition to enforce the forward invariance of the CVaR, the technique of differentiable convex programming is applied to enable differentiation through the optimization layer of CVaR estimation. We also provide an approximate variant of DR-CBF for higher-order systems. Simulation results are presented to validate the chance-constrained safety guarantee under the distributional shift in both first and second-order systems.

提出了一种分布鲁棒CBF（DR-CBF）方法，通过使用Wasserstein度量来测量分布偏移，实现了目标函数的三层规划，并应用不同iable凸规划技术来确保条件风险值的前不变性，为了验证分布偏移下的机遇约束安全保证在一阶和二阶系统中的有效性，提供了模拟结果。

使用条件风险价值和可微凸规划的Wasserstein分布鲁棒控制屏障函数