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:可调速控障函数:在线适应的方法与算法
控制障碍函数通过指定强制安全约束的控制器提供安全证书。 然而,它们的响应取决于用于限制沿系统轨迹的障碍函数的变化速率的classK函数。 本文介绍了可调速控障函数(RT-CBF)的概念,允许在线调整基于CBF的控制器的响应。 与现有的使用固定的(预定义的)classK函数来确保安全的CBF方法不同,本文在线参数化和调整classK函数参数。 此外,我们讨论了与多个障碍约束相关的挑战,即确保它们同步地为所有时间接受满足它们的公共控制输入。 在实践中,RT-CBF使得可以设计参数动态来获得更好的反应,其中性能用时间范围内累积的成本来定义,或者获得更少保守的响应。 我们提出了一个模型预测框架,用于计算未来状态与参数之间的敏感性,并使用序列二次规划推导在线定律,以在改善性能方向上更新参数。 当无法进行预测时,我们还提供逐点充分条件,以强制施加在任何用户给定参数动态上,使多个CBF约束继续同时接受公共控制输入。 最后,我们引入了用于分散式非合作多智能体系统的RT-CBF,其中基于瞬时约束满足的难度计算信任因子,用于在线更新参数以获得更少保守的响应。