Control barrier functions (CBFs) provide a theoretical foundation for safety-critical control in robotic systems. However, most existing methods rely on explicit analytical expressions of unsafe state regions, which are often impractical for irregular and dynamic unsafe regions. This paper introduces SafeLink, a novel CBF construction method based on cost-sensitive incremental random vector functional-link (RVFL) neural networks. By designing a valid cost function, SafeLink assigns different sensitivities to safe and unsafe state points, thereby eliminating false negatives in classification of unsafe state points. Under the constructed CBF, theoretical guarantees are established regarding system safety and the Lipschitz continuity of the control inputs. Furthermore, incremental update theorems are provided, enabling precise real-time adaptation to changes in unsafe regions. An analytical expression for the gradient of SafeLink is also derived to facilitate control input computation. The proposed method is validated on the endpoint position control task of a nonlinear two-link manipulator. Experimental results demonstrate that the method effectively learns the unsafe regions and rapidly adapts as these regions change, achieving computational speeds significantly faster than baseline methods while ensuring the system safely reaches its target position.

翻译：控制屏障函数（CBFs）为机器人系统的安全关键控制提供了理论基础。然而，现有方法大多依赖于危险状态区域的显式解析表达式，这对于不规则且动态变化的危险区域通常不切实际。本文提出SafeLink，一种基于成本敏感增量随机向量函数链接（RVFL）神经网络的新型CBF构建方法。通过设计有效的成本函数，SafeLink对安全状态点和危险状态点赋予不同的敏感度，从而消除危险状态点分类中的漏报现象。在所构建的CBF框架下，本文从理论上保证了系统安全性及控制输入的Lipschitz连续性。此外，研究还提供了增量更新定理，使系统能够精确实时地适应危险区域的变化。同时推导了SafeLink梯度的解析表达式，以简化控制输入的计算。所提方法在非线性双连杆机械臂的末端位置控制任务上得到验证。实验结果表明，该方法能有效学习危险区域，并在区域变化时快速适应，其计算速度显著优于基线方法，同时确保系统安全抵达目标位置。