ハイブリッド系のためのハミルトン・ヤコビ到達可能性：安全性保証付き統一目標駆動制御
Hamilton-Jacobi Reachability for Hybrid Systems: Unified Goal-Driven Control with Safety Guarantees
連続・離散が混在するハイブリッド系にHJ到達可能性解析を拡張し、安全集合の計算と、安全性を保ちつつ目標到達も保証する制御則の設計手法を提案した。
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著者: Javier Borquez, Shuang Peng, Somil Bansal
分類: cs.RO, eess.SY
原文アブストラクト
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.