Hamilton-Jacobi Reachability for Hybrid Systems: Unified Goal-Driven Control with Safety Guarantees

2026-09-15

AI Summary

本文通过扩展Hamilton-Jacobi可达性分析到混合动力系统，提出了一种确保安全性和性能的方法，并结合了最小限制安全过滤器和后向可达-避免管技术。

Abstract

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.

Problem

• Hybrid Systems
• Safety Guarantees
• Hamilton-Jacobi Reachability
• Continuous Dynamics
• Discrete Mode Transitions

Innovation

• Hybrid Dynamical Systems
• Hamilton-Jacobi Reachability
• Safety Guarantees
• Goal-Driven Control
• Safe Sets