Abstract
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.
Abstract (translated)
控制障碍函数通过指定执行安全约束的控制控制器来提供安全证书。然而，其响应取决于 classK 函数，用于限制系统路径上障碍函数的变化率。本文介绍了 Rate Tunable Control Barrier Function(RT-CBF)的概念，以便在线调整基于 CBF 的控制控制器的响应。与现有的 CBF 方法，该方法使用一个固定(预先定义)的 classK 函数以确保安全，我们参数化并适应 classK 函数参数在线。此外，我们讨论了多个障碍约束所面临的挑战，即确保它们承认一个共同的控制输入，使其在整个时间范围内同时满足它们。在实践中，RT-CBF 允许设计参数动态特性，以(1) 实现更好的响应性能，性能以累积的成本为定义标准，或(2) 实现更保守的响应。我们提出了一个模型预测框架，计算未来状态的敏感性与参数之间的关系，并使用Sequential Quadratic Programming 推导在线 law 更新参数以改善性能。当预测不可用时，我们也提供点充分条件，应将其施加给任何用户提供的参数动态特性，以确保多个 CBF 约束继续承认共同的控制输入。最后，我们介绍了 RT-CBF 用于分散的不合作多Agent系统，其中基于实时满足约束条件的易用性计算的信任因子用于更新参数以实现更保守的响应。
URL
https://arxiv.org/abs/2303.12966
