发表机构
Universidad de Santiago de Chile; University of Southern California; Stanford University（智利圣地亚哥大学; 南加州大学; 斯坦福大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文扩展Hamilton-Jacobi可达性分析至混合系统，提出安全集刻画、最小限制安全滤波器及混合后向可达-避碰管，实现安全与目标驱动控制，并经四足机器人仿真与实验验证。
AI 中文摘要
混合动力系统为机器人系统提供了强大的建模框架，特别是在接触丰富的环境中。然而，由于连续动力学与离散模式转换之间的复杂耦合，确保此类系统的安全性和性能仍然具有挑战性。在这项工作中，我们将经典的Hamilton-Jacobi (HJ) 可达性分析（一种用于连续时间非线性系统的形式化验证方法）扩展到混合动力系统。我们的框架通过定义在离散和连续状态上的广义值函数来刻画混合系统的安全集，同时考虑控制约束和模型不确定性。我们还提供了一种数值算法来计算该值函数。基于这些安全集，我们提出了两种不同的机制来整合性能目标。首先，我们引入了一种混合最小限制安全滤波器，该滤波器仅在必要时对名义控制器的离散和连续组件进行干预，以避免不安全状态，从而尽可能保持名义行为。其次，我们制定并计算了混合后向可达-避碰管，使得能够同时强制执行安全性和目标到达行为，这是先前在混合HJ可达性中未涉及的扩展。这使得能够综合保证安全性和任务完成的连续和离散控制策略。我们通过仿真研究和四足机器人上的真实世界实验验证了我们的框架，展示了其在混合模式规划和安全关键应用中的有效性。
英文摘要
Hybrid dynamical systems provide a powerful modeling framework for robotic systems, particularly in contact-rich environments. However, ensuring safety and performance in such systems remains challenging due to the intricate coupling between continuous dynamics and discrete mode transitions. In this work, we extend classical Hamilton-Jacobi (HJ) reachability analysis, a formal verification method for continuous-time nonlinear systems, to hybrid dynamical systems. Our framework characterizes safe sets for hybrid systems through a generalized value function defined over both discrete and continuous states while accounting for control constraints and model uncertainty. We additionally provide a numerical algorithm to compute this value function. Building on these safe sets, we propose two different mechanisms to integrate performance objectives. First, we introduce a hybrid least-restrictive safety filter that intervenes on both the discrete and continuous components of a nominal controller only when necessary to avoid unsafe states, thereby preserving nominal behavior whenever possible. Second, we formulate and compute hybrid backward reach-avoid tubes, enabling the simultaneous enforcement of safety and goal-reaching behavior, an extension not previously addressed within hybrid HJ reachability. This enables the synthesis of continuous and discrete control policies that guarantee both safety and task completion. We validate our framework through simulation studies and real-world experiments on a quadrupedal robot, demonstrating its effectiveness in hybrid mode planning and safety-critical applications.
Journal refBorquez J, Peng S, Bansal S. Hamilton-Jacobi reachability for hybrid systems: Unified goal-driven control with safety guarantees. The International Journal of Robotics Research. 2026;0(0)
