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.

翻译：基于Hamilton-Jacobi（HJ）可达性的滤波方法为自主系统的性能与安全性（或活性）协同优化提供了强大框架。在此滤波方案下，名义控制器经过最小化修改即可确保系统安全性或活性。然而，由此生成的控制器可能呈现突变切换与Bang-Bang行为，这不适用于现实世界中的自主系统应用。本研究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与活性滤波器。我们显式刻画了在给定状态下确保安全性（或活性）的最大控制输入集合。随后，通过选取该最大集合的不同子集并结合投影算子修改名义控制器，即可构建不同的安全滤波器。利用所提框架，我们设计了三种安全滤波器，每种滤波器在性能、计算时间与平滑性之间具有不同的权衡特性。通过将这些滤波器应用于自主导航、火箭着陆场景及物理机器人实验平台，我们揭示了它们各自的相对优势与局限。同时，我们探讨了在实际自主系统中实现这些滤波器所涉及的技术问题。本研究推进了对基于可达性控制器在现实自主系统中应用的理解与实践潜力。