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. The proposed filters can easily handle dynamics uncertainties, disturbances, and bounded control inputs. 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：基于哈密顿-雅可比（HJ）可达性的滤波方法为自主系统在性能与安全性（或活性）的协同优化中提供了强大框架。在该滤波方案下，标称控制器被最小化调整以确保系统安全性或活性。然而，由此产生的控制器可能出现剧烈切换及bang-bang行为，不适用于真实世界自主系统的实际应用。本文提出一种新颖的统一框架，通过可达性分析设计安全滤波器与活性滤波器。我们明确表征了在给定状态下确保安全性（或活性）的最大控制输入集合。通过选取该最大集合的不同子集并结合投影算子对标称控制器进行修正，可构建不同类型的滤波器。利用所提框架，我们设计了三种安全滤波器，它们在性能、计算时间及平滑性方面各有侧重。这些滤波器可轻松处理动力学不确定性、干扰及有界控制输入。通过将滤波器应用于自主导航、火箭着陆场景及物理机器人试验平台，我们重点分析了其相对优势与局限性，并探讨了在真实自主系统中实现这些滤波器的实践考量。本研究深化了对基于可达性控制器在真实自主系统中应用的理解与潜力。