Hamilton–Jacobi (HJ) reachability-based filtering provides a powerful framework to co-optimize performance and safety (or liveness) for autonomous systems. Under this filtering scheme, a nominal controller is minimally modified to ensure system safety or liveness. However, the resulting controllers can exhibit abrupt switching and bang-bang behavior, which is not suitable for applications of autonomous systems in the real world. This work presents a novel, unifying framework to design safety and liveness filters through reachability analysis. We explicitly characterize the maximal set of control inputs that ensures safety (or liveness) at a given state. Different safety filters can then be constructed using different subsets of this maximal set along with a projection operator to modify the nominal controller. We use the proposed framework to design three safety filters, each balancing performance, computation time, and smoothness differently. We highlight their relative strengths and limitations by applying these filters to autonomous navigation and rocket landing scenarios and on a physical robot testbed. We also discuss practical aspects associated with implementing these filters on real-world autonomous systems. Our research advances the understanding and potential application of reachability-based controllers on real-world autonomous systems.

中文翻译：

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使用 Hamilton-Jacobi 可达性分析进行安全性和活性过滤


基于 Hamilton-Jacobi (HJ) 可达性的过滤提供了一个强大的框架来共同优化自治系统的性能和安全性（或活性）。在这种过滤方案下，对标称控制器进行最小程度的修改以确保系统安全或活跃。然而，由此产生的控制器可能会表现出突然的切换和爆炸行为，这不适合现实世界中自主系统的应用。这项工作提出了一种新颖的统一框架，通过可达性分析来设计安全性和活性过滤器。我们明确地描述了在给定状态下确保安全（或活性）的最大控制输入集。然后可以使用该最大集合的不同子集以及投影算子来构造不同的安全滤波器，以修改标称控制器。我们使用所提出的框架设计了三个安全滤波器，每个滤波器都以不同的方式平衡性能、计算时间和平滑度。我们通过将这些过滤器应用于自主导航和火箭着陆场景以及物理机器人测试台来强调它们的相对优势和局限性。我们还讨论了与在现实世界的自治系统上实现这些过滤器相关的实际问题。我们的研究促进了基于可达性的控制器在现实世界自主系统上的理解和潜在应用。