Hamilton-Jacobi (HJ) reachability analysis is a powerful tool for analyzing the safety of autonomous systems. However, the provided safety assurances are often predicated on the assumption that once deployed, the system or its environment does not evolve. Online, however, an autonomous system might experience changes in system dynamics, control authority, external disturbances, and/or the surrounding environment, requiring updated safety assurances. Rather than restarting the safety analysis from scratch, which can be time-consuming and often intractable to perform online, we propose to compute \textit{parameter-conditioned} reachable sets. Assuming expected system and environment changes can be parameterized, we treat these parameters as virtual states in the system and leverage recent advances in high-dimensional reachability analysis to solve the corresponding reachability problem offline. This results in a family of reachable sets that is parameterized by the environment and system factors. Online, as these factors change, the system can simply query the corresponding safety function from this family to ensure system safety, enabling a real-time update of the safety assurances. Through various simulation studies, we demonstrate the capability of our approach in maintaining system safety despite the system and environment evolution.

翻译：汉密尔顿-雅可比（HJ）可达性分析是分析自主系统安全性的一种强大工具。然而，所提供的安全性保证通常基于一个假设，即系统或环境在部署后不会发生变化。但在在线运行中，自主系统可能经历动力学特性、控制权限、外部扰动和/或周围环境的变化，从而需要更新安全性保证。为避免从头重启安全性分析（此类分析耗时且通常难以在线执行），我们提出计算**参数条件化**可达集。假设预期的系统与环境变化可参数化，我们将这些参数视为虚拟状态引入系统，并借助高维可达性分析的最新进展，离线求解对应的可达性问题。由此生成一组由环境与系统因素参数化的可达集。在线运行时，当这些因素发生变化时，系统可直接从该族中查询对应的安全函数以确保系统安全，实现安全性保证的实时更新。通过多项仿真研究，我们验证了该方法在系统与环境演化过程中维持系统安全的能力。