Control Barrier Functions offer safety certificates by dictating controllers that enforce safety constraints. However, their response depends on the classK function that is used to restrict the rate of change of the barrier function along the system trajectories. This paper introduces the notion of Rate Tunable Control Barrier Function (RT-CBF), which allows for online tuning of the response of CBF-based controllers. In contrast to the existing CBF approaches that use a fixed (predefined) classK function to ensure safety, we parameterize and adapt the classK function parameters online. Furthermore, we discuss the challenges associated with multiple barrier constraints, namely ensuring that they admit a common control input that satisfies them simultaneously for all time. In practice, RT-CBF enables designing parameter dynamics for (1) a better-performing response, where performance is defined in terms of the cost accumulated over a time horizon, or (2) a less conservative response. We propose a model-predictive framework that computes the sensitivity of the future states with respect to the parameters and uses Sequential Quadratic Programming for deriving an online law to update the parameters in the direction of improving the performance. When prediction is not possible, we also provide point-wise sufficient conditions to be imposed on any user-given parameter dynamics so that multiple CBF constraints continue to admit common control input with time. Finally, we introduce RT-CBFs for decentralized uncooperative multi-agent systems, where a trust factor, computed based on the instantaneous ease of constraint satisfaction, is used to update parameters online for a less conservative response.

翻译：控制屏障函数通过指定强制执行安全约束的控制器来提供安全证书。然而，其响应取决于用于限制屏障函数沿系统轨迹变化速率的K类函数。本文提出了速率可调控制屏障函数的概念，允许在线调谐基于CBF的控制器响应。与现有采用固定预设K类函数确保安全的CBF方法不同，我们对K类函数参数进行参数化并在线自适应调整。此外，我们讨论了多屏障约束带来的挑战，即确保这些约束始终存在一个能同时满足所有约束的共同控制输入。实践中，RT-CBF能够设计参数动力学以实现：（1）更优性能响应（基于时间跨度累积成本定义性能）；（2）降低保守性响应。我们提出了一种模型预测框架，通过计算未来状态对参数的敏感性，并采用序列二次规划推导出在线更新参数以提升性能的方向性法则。当无法进行预测时，我们还提供了需施加于任意用户给定参数动力学的逐点充分条件，使得多个CBF约束能随时间推移持续存在共同的控制输入。最后，我们将RT-CBF引入去中心化非协作多智能体系统，其中基于约束满足瞬时难易度计算的信任因子被用于在线更新参数，以获得保守性更低的响应。